WO2021111625A1 - 弾塑性解析方法及び弾塑性解析プログラム - Google Patents
弾塑性解析方法及び弾塑性解析プログラム Download PDFInfo
- Publication number
- WO2021111625A1 WO2021111625A1 PCT/JP2019/047888 JP2019047888W WO2021111625A1 WO 2021111625 A1 WO2021111625 A1 WO 2021111625A1 JP 2019047888 W JP2019047888 W JP 2019047888W WO 2021111625 A1 WO2021111625 A1 WO 2021111625A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- plastic
- tensor
- elasto
- strain
- deformation gradient
- Prior art date
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Definitions
- the present invention relates to an elasto-plastic analysis method and an elasto-plastic analysis program.
- elasto-plastic analysis is particularly important for evaluating the strength of a structure using a structural material, the amount of deformation during processing of the material, and the like.
- the conditions for plasticization of a structural material are defined by introducing a scalar value function called a yield function, and the increase in plastic strain is defined as a scalar called a plastic potential.
- a flow rule based on a value function is defined by introducing a scalar value function called a yield function, and the increase in plastic strain.
- the flow rule when the yield function is used as the plastic potential is called the related flow rule
- the flow rule when using a plastic potential different from the yield function is called the unrelated flow rule.
- the governing equation of the initial value boundary value problem of elasto-plastic analysis consists of the law of conservation of momentum, the law of conservation of angular momentum, the displacement-strain relational equation, the stress-strain relational equation, and the equation related to plastic strain.
- the flow rule is used as an equation for plastic strain. Since it is difficult to analytically solve the initial value boundary value problem of elasto-plastic analysis, the partial differential equations are replaced with simultaneous linear equations by dividing the structure into minute regions and interpolating the functions for each region. Evaluation is performed using the finite element method for calculation.
- Patent Document 1 discloses a stress-strain relationship simulation method that simulates the strain of a material during machining by using a plastic constitutive equation that combines a flow rule and various models.
- the analysis results and experimental results may not match in the load history in which the direction of the load changes suddenly on the way.
- the analysis result does not match the experimental result
- the elasto-plastic body A is elastic in the direction orthogonal to the first simple shear received in the state where the plastic deformation generated by the simple shear remains.
- FIG. 1B shows the elasto-plastic deformation behavior (shear strain ⁇ ) of the elasto-plastic body A subjected to the first simple shear (a to e) of FIG. 1A in a material having an elasto-plastic constitutive law that hardens according to the plastic strain.
- An example of a typical stress-strain curve showing the relationship with shear stress ⁇ ) is shown.
- the points a to e in FIG. 1B correspond to the states a to e in FIG. 1A.
- the bow singer effect is that when a material having an elasto-plastic constitutive law that hardens according to plastic strain is yielded by applying a load in a certain forward direction and then yielding by applying a load in the reverse direction, the material is yielded in the opposite direction.
- This is a phenomenon in which the absolute value
- FIG. 1C A typical stress-strain curve (i) of the elastic deformation behavior (relationship between the direct strain ⁇ and the direct stress ⁇ ) of the elastic plastic body A in the state g) is shown in FIG. 1C. All stress-strain curves shown in FIG. 1C are characteristic behaviors in elasto-plastic deformation described in FIG. 1B, such as elastic deformation, plasticization, hardening according to plastic strain, elastic unloading, Bauschinger effect, etc. Is shown.
- the stress-strain relationship in the vertical direction when the load is applied in the vertical direction from the beginning and yielding is completely the same. That is, the stress-strain curve of the elasto-plastic body A that receives tension and compression via the load history shown in FIG. 1A ((i) in FIG. 1C) is similar to that of the elasto-plastic body B that receives the load history shown in FIG. 1D.
- the analysis method is modified by various methods so that the analysis result matches the experimental result by improving the flow rule, the yield function, and the introduction and improvement of the plastic potential.
- the analysis method modified based on the prior art so as to sufficiently reproduce the Bauschinger effect the elasto-plastic deformation behavior that does not generate the shear strain in the same direction as the plastic shear strain generated in the past load history is that.
- the phenomenon that it does not change regardless of the presence or absence of plastic shear strain invariance of elasto-plastic deformation behavior with respect to the plastic deformation history in a specific direction
- the Bauschinger effect cannot be sufficiently reproduced by the analysis method modified so as to satisfy the invariance of the plastic deformation behavior.
- the related flow rule used for elasto-plastic analysis is expressed by Eq. (1).
- d ⁇ p ij is a plastic strain increment tensor
- ⁇ ij is a stress tensor
- f f ( ⁇ ij )
- ⁇ is a constant.
- Equation 1 for each elasto-plastic body, there is a material constitutive law that connects the plastic strain increment tensor and the stress tensor, and the scalar potential function of the stress tensor for expressing the material constitutive law is It is implicitly assumed to exist.
- equation (1) means that the plastic strain increment is independent of the displacement increment.
- equation (1) means that the expression formula of the plastic strain increment, which has no relation to the displacement increment, properly expresses the actual phenomenon.
- the present invention has been made in view of the above circumstances, and does not require the existence of a material constitutive law that connects the plastic strain increment tensor and the stress tensor in the elasto-plastic analysis, and the stress for expressing the material constitutive law.
- We introduce an equation for plastic strain that does not require the existence of a tensor scalar potential function.
- Providing is an exemplary task.
- the elasto-plastic analysis method and the elasto-plastic analysis program as exemplary aspects of the present invention have the following configurations.
- One aspect of the present invention is an elasto-plastic analysis method for an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, for an elasto-plastic body in a dynamic or static equilibrium state.
- the plastic strain corresponding to the load increment based on the step of determining the strain index and the value obtained by subtracting the elastic limit strain index determined based on the material properties of the elasto-plastic body from the trial elastic strain index.
- Another aspect of the present invention is an elasto-plastic analysis method of an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, and is an elasto-plastic body in a dynamic or static equilibrium state.
- the plastic deformation gradient tensor is not changed, and the load increment is applied to the total deformation gradient tensor in the pseudo-equilibrium state after loading, and the inverse tensor of the plastic deformation gradient tensor is applied to the trial elastic deformation gradient tensor.
- the step the step of determining the trial elastic deformation gradient index based on the trial elastic deformation gradient tensor, the trial elastic deformation gradient index, and the elastic limit deformation gradient index determined based on the material properties of the elasto-plastic body. Based on the ratio of, the step of determining the plastic deformation gradient increment index corresponding to the load increment, the step of determining the plastic deformation gradient incremental tensor based on the plastic deformation gradient increment index, and the determined plastic deformation gradient.
- This is an elasto-plastic analysis method including a step of determining a plastic strain incremental tensor using an incremental tensor.
- Another aspect of the present invention is an elastic plastic analysis method for an elastic plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, and is an elastic plastic body in a dynamic or static equilibrium state.
- the step to obtain the logarithmic trial elastic deformation gradient tensor obtained by subtracting the logarithmic deformation gradient tensor from the logarithmic total deformation gradient tensor in the pseudo-equilibrium state after loading the load increment without changing the plastic deformation gradient tensor, and the logarithmic trial.
- the logarithm of the elastic limit deformation gradient index determined based on the material properties of the elasto-plastic body is taken. Based on the value obtained by subtracting the log-elasticity limit deformation gradient index obtained, the step of determining the log-plastic deformation gradient increment index corresponding to the load increment and the log-plastic deformation based on the log-plastic deformation gradient increment index. It is an elastic plastic analysis method including a step of determining a gradient incremental tensor and a step of determining a logarithmic strain incremental tensor using the determined logoplastic deformation gradient incremental tensor.
- Another aspect of the present invention is an elasto-plastic analysis program of an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, which is in a dynamic or static equilibrium state in a computer.
- the procedure for obtaining the trial elastic strain tensor obtained by subtracting the plastic strain tensor from the total strain tensor in the pseudo-equilibrium state after loading the load increment without changing the plastic strain tensor to the elasto-plastic body, and the trial elastic strain tensor.
- the load increment is based on the procedure for determining the trial elastic strain index based on the trial elastic strain index and the value obtained by subtracting the elastic limit strain index determined based on the material properties of the elasto-plastic body from the trial elastic strain index. It is an elasto-plastic analysis program for executing a procedure including a procedure for determining as a corresponding plastic strain increment index and a procedure for determining a plastic strain increment tensor based on the plastic strain increment index.
- Another aspect of the present invention is an elasto-plastic analysis program of an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, which is in a dynamic or static equilibrium state in a computer.
- the plastic deformation gradient tensor is not changed on the elasto-plastic body, and the load increment is applied to the total deformation gradient tensor in the pseudo-equilibrium state after loading.
- the procedure for determining the plastic deformation gradient increment index corresponding to the load increment based on the ratio to the gradient index, the procedure for determining the plastic deformation gradient increment tensor based on the plastic deformation gradient increment index, and the determined procedure It is an elasto-plastic analysis program for executing a procedure including a procedure for determining a plastic strain incremental tensor using a plastic deformation gradient incremental tensor.
- Another aspect of the present invention is an elasto-plastic analysis program of an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, which is in a dynamic or static equilibrium state in a computer.
- the procedure for obtaining the logarithmic trial elastic deformation gradient tensor obtained by subtracting the logarithmic deformation gradient tensor from the logarithmic deformation gradient tensor in the pseudo-equilibrium state after loading the load increment without changing the plastic deformation gradient tensor on the elasto-plastic body.
- An elasto-plastic analysis program for executing a procedure including a procedure for determining a log-plastic deformation gradient incremental tensor and a procedure for determining a log-plastic strain incremental tensor using the determined log-plastic deformation gradient incremental tensor. ..
- the Bauschinger effect and the invariance of the elasto-plastic deformation behavior with respect to the plastic deformation history in a specific direction can be reproduced at the same time.
- the schematic diagram which shows the load history which applies tension and compression to an elasto-plastic body in a direction orthogonal to a shearing direction after simple shearing.
- a stress-strain curve showing an example of elasto-plastic deformation behavior of an elasto-plastic body subject to simple shear in FIG. 1A.
- the schematic diagram which shows the load history which gives the stress-strain curve of FIG. 1C (iii) to an elasto-plastic body.
- the spindle of the trial elastic strain and the trial elastic principal strain according to the second embodiment The figure which shows the surface ( ⁇ ) which the shear component of the trial elastic strain in Embodiment 2 becomes the maximum, and the shear component becomes the maximum.
- FIG. The figure which shows the surface ( ⁇ ) which maximizes the shear component of the trial elastic strain in Embodiment 2.
- the figure which applied the shear load of step (2) to the test piece of an Example The figure which unloads the shear load of step (2) to the test piece of an Example until the elastic component of a shear strain becomes zero.
- the figure which applied the compressive load of step (4) to the test body of an Example. The figure which shows the numerical calculation value from step (1) to step (3) of an Example.
- the governing equation of the initial value boundary value problem of elasto-plastic analysis consists of the law of conservation of momentum, the law of conservation of angular momentum, the displacement-strain relational equation, the stress-strain relational equation, and the equation related to plastic strain.
- the flow rule is used as an equation for plastic strain.
- the elasto-plastic body undergoes plastic deformation when the strain exceeds the elastic limit of the elasto-plastic body.
- the strain at this elastic limit is called “elastic limit strain”.
- the strain that exceeds the elastic limit strain is referred to as “plastic strain”.
- an "index" uniquely defined for the amount of tensor is introduced.
- the "index” in the present embodiment represents a scalar value or a vector value obtained by subjecting a tensor to an appropriate mathematical process.
- the inventors of the present invention agree with the experimental results by introducing an equation regarding plastic strain using an elastic limit strain index uniquely defined for elastic limit strain instead of the conventional flow rule. It was discovered that the results of elastic plasticity analysis can be obtained. Specifically, it is as follows.
- the initial value boundary value problem of elasto-plastic analysis in the case of minute deformation in which the strain is sufficiently small and the deformation of the elasto-plastic body can be regarded as sufficiently small is solved by an appropriate numerical analysis method such as the finite element method.
- the method of obtaining the numerical analysis result by calculating with will be described.
- a load increment is applied to an elasto-plastic body in a dynamic or static equilibrium state (step S10 in FIG. 2), and the total strain tensor in a pseudo-equilibrium state after the load increment is applied without changing the plastic strain tensor. To get.
- the trial elastic strain tensor is a minute elastic strain tensor given on a trial basis for iterative calculation.
- the trial elastic strain index ⁇ ei which is uniquely defined based on the trial elastic strain tensor ⁇ e , is determined (step S14).
- the trial elastic strain index ⁇ ei is a scalar or vector.
- ⁇ cri be the elastic limit strain index uniquely defined based on the elastic limit strain, which is the material property of each elasto-plastic material (step S16).
- the elastic limit strain index ⁇ cri is a scalar or vector.
- the elastic limit strain index ⁇ cri may be a constant or a function of some physical quantity.
- the plastic strain increment index d ⁇ pi is determined based on the value obtained by subtracting the elastic limit strain index ⁇ cri from the trial elastic strain index ⁇ ei. For example, the value obtained by subtracting the elastic limit strain index ⁇ cri from the trial elastic strain index ⁇ ei is defined as the plastic strain increment index d ⁇ pi (step S18).
- Equation (3) Is.
- the inequality sign in the conditional equations of equations (3A) and (3B) is evaluated based on the scalar value obtained by applying appropriate mathematical processing to the vector when the index is a vector value.
- the component d ⁇ p ij of the plastic strain increment tensor is determined (step S20).
- d? P ij represents a plastic strain increment in the case of setting the coordinate system x 1 -x 2 -x 3, the x j-axis direction of i-th surface (surface orthogonal to the x i axis).
- the component of the tensor can be determined using the index by the method shown in the second embodiment. Then, the equilibrium error in the entire elasto-plastic body is calculated (step S22).
- step S24 it is determined whether or not the result of the balance error calculation for the load increment given in step S10 satisfies the end condition.
- the termination condition is, for example, when the balance error in the entire elasto-plastic body reaches within a predetermined error range. If the end condition is satisfied in step S24 (S24: Y), the process proceeds to step S26. If the end condition is not satisfied in step S24 (S24: N), the process returns to step S12, a new trial elastic strain tensor is given, and the subsequent steps are repeated. In step S26, it is determined whether or not the predetermined load increment has been completed (all the load increments have been given).
- step S26 If the predetermined load increment has not been completed in step S26 (S26: N), the process returns to step S10, a new load increment is given, and the subsequent steps are repeated.
- step S26 S26: Y
- the numerical analysis is completed.
- the second embodiment which is a specific example of the general elasto-plastic analysis method in the case of minute deformation described in the first embodiment, will be described with reference to the drawings.
- the elastic limit shear strain ⁇ cr which is an example of the elastic limit strain index ⁇ cri described in the first embodiment, is considered.
- the elastic limit shear strain ⁇ cr is a numerical value obtained by a material test of an elasto-plastic body.
- the elastic limit shear strain ⁇ cr is set as a positive constant.
- the elasto-plastic body in the static equilibrium state is loaded with a load increment, and the total strain tensor ⁇ total in the pseudo-equilibrium state after the load increment is obtained without changing the plastic strain tensor ⁇ p .
- the difference between the total strain tensor ⁇ total and the plastic strain tensor ⁇ p is calculated and used as the trial elastic strain tensor ⁇ e . That is, the trial elastic strain tensor ⁇ e is defined by Eq. (2).
- the components of this trial elastic strain tensor are represented by the main axis coordinate system shown in FIG. 3 and the coordinate system set on the surface where the shear component is maximized.
- Figure 3 represents the main axis of the trial elastic strain tensor at x 1, x 2, x 3 .
- the corresponding trial elastic principal strains are ⁇ 1 , ⁇ 2 , and ⁇ 3 , and ⁇ 1 ⁇ ⁇ 2 ⁇ ⁇ 3 .
- the components of the trial elastic strain on the surface ( ⁇ ), which is one of the surfaces where the shear component is maximized are ⁇ ( ⁇ ) S , ⁇ ( ⁇ ) S ⁇ , and ⁇ ( ⁇ ) N. It is expressed as.
- Coordinate system x '1 -x 2 -x' 3 in FIG. 4 can be obtained by the spindle coordinate system x 1 -x 2 -x 3 is [pi / 4 rotates counterclockwise about the x 2 axis. As long as the main direction of the trial elastic strain and the plane where the shear component is maximized are defined as shown in Fig.
- the components of the plastic strain increment are expressed as d ⁇ p ( ⁇ ) S , d ⁇ p ( ⁇ ) S ⁇ , and d ⁇ p ( ⁇ ) N for each axis, respectively.
- the equations that define the plastic strain increments d ⁇ p ( ⁇ ) S and d ⁇ p ( ⁇ ) S ⁇ on the plane ( ⁇ ) with respect to the load increment are the following equations (4A) and (4B) using the elastic limit shear strain ⁇ cr. ).
- the vector consisting of this component is defined as d ⁇ p ⁇ [d ⁇ p 11 , d ⁇ p 22 , d ⁇ p 33 , d ⁇ p 12 , d ⁇ p 23 , d ⁇ p 31 ] T.
- the superscript T for a vector or matrix represents transpose.
- the components of the plastic strain increment tensor in these planes and the components of the plastic strain increment tensor in the principal axis coordinate system are tensors. Not relevant through the coordinate transformation law of quantities. Therefore, for (Case 2) and (Case 3), the singular value decomposition of the matrix that associates the components in ⁇ , ⁇ , and ⁇ of the plastic strain increment tensor with the components in the spindle coordinate system is introduced, and the spindle of the plastic strain increment tensor is introduced. Identify the components in the coordinate system.
- (Case 2) the following vectors are constructed using the components of the plastic strain increment tensor on the plane ⁇ and the plane ⁇ .
- the vector d ⁇ p consisting of the components in the spindle coordinate system of the plastic strain increment tensor and d ⁇ p ( ⁇ ) are related as follows using the matrix M ( ⁇ ) of 4 rows and 6 columns. here, Is.
- the singular value decomposition of M ( ⁇ ) is expressed as follows using a matrix U of 4 rows and 4 columns, a matrix W of 4 rows and 6 columns, and a matrix V ( ⁇ ) T of 6 rows and 6 columns. here, Is.
- Equations (5), (15) and (22) represent the components of the non-zero plastic strain increment tensor in the spindle coordinate system in (Case 1), (Case 2) and (Case 3), respectively.
- the components of the plastic strain incremental tensor in the spindle coordinate system can be obtained according to the value of the plastic strain incremental tensor.
- the initial value boundary value problem of elasto-plastic analysis is calculated by an appropriate numerical analysis method such as the finite element method, and the numerical analysis result is obtained.
- the elastic limit shear strain ⁇ cr which is a positive constant, is used as an example of the elastic limit strain index ⁇ cri.
- the example of the elastic limit strain index ⁇ cri is not limited to this.
- ⁇ c is a positive constant
- ⁇ is a non-zero constant
- ⁇ ( ⁇ ) N is a strain component in the direction orthogonal to the plane ( ⁇ ) whose direction is uniquely determined by the value of ⁇ .
- an upper limit value of the equivalent strain may be set and used as the elastic limit strain index ⁇ cri.
- the surface ⁇ is unique depending on the value of ⁇ from the surface which is one of the surfaces where the shear component is maximized.
- the surface is slightly tilted in the direction determined by, and the trial elastic strain index at this time is ⁇ ( ⁇ ) S - ⁇ ( ⁇ ) N.
- Trial elastic deformation gradient tensor method A load increment was applied to an elasto-plastic body in a dynamic or static equilibrium state (step S30 in FIG. 7), and the load increment was applied without changing the plastic deformation gradient tensor. Obtain the total deformation gradient tensor in the later pseudo-equilibrium state.
- (F p) -1 ⁇ _F total represents the mathematical process to appropriately act in opposite tensor (F p) total deformation -1 gradient tensor F total plastic strain deformation gradient tensor F p.
- the trial elastic deformation gradient index Fei is a scalar or a vector.
- the elastic limit deformation gradient index F cri is a scalar or vector.
- the elastic limit deformation gradient index F cri may be a constant or a function of some physical quantity.
- the plastic deformation gradient increment index dF pi is determined based on the value obtained by dividing the trial elastic deformation gradient index Fei by the elastic limit deformation gradient index F cri. For example, the value obtained by dividing the trial elastic deformation gradient index Fei by the elastic limit deformation gradient index F cri is set as the plastic deformation gradient increment index dF pi (step S38).
- dF p ij is the case of setting the coordinate system x 1 -x 2 -x 3, represents the plastic deformation gradient increment to x j-axis direction of i-th surface (surface orthogonal to the x i axis).
- the component of the tensor can be determined using the index by the method shown in the second embodiment.
- step S42 Apply the appropriate definition of strain to the determined plastic deformation gradient incremental tensor, for example the definition of a Green finite strain tensor or the definition of an Almansi finite strain tensor, to obtain a plastic strain incremental tensor.
- step S42 the definition of a Green finite strain tensor or the definition of an Almansi finite strain tensor.
- step S44 the equilibrium error in the entire elasto-plastic body is calculated (step S44).
- step S46 it is determined whether or not the result of the balance error calculation for the load increment given in step S30 satisfies the end condition.
- the termination condition is, for example, when the balance error in the entire elasto-plastic body reaches within a predetermined error range. If the end condition is satisfied in step S46 (S46: Y), the process proceeds to step S48.
- step S46 If the end condition is not satisfied in step S46 (S46: N), the process returns to step S32, a new trial elastic deformation gradient tensor is given, and the subsequent steps are repeated.
- step S48 it is determined whether or not the predetermined load increment has been completed (all the load increments have been given). If the predetermined load increment has not been completed in step S48 (S48: N), the process returns to step S30, a new load increment is given, and the subsequent steps are repeated. When the predetermined load increment is completed in step S48 (S48: Y), the numerical analysis is completed.
- the logarithmic trial elastic deformation gradient index LnF ei is a scalar or vector.
- LnF cri be the logarithmic elastic limit deformation gradient index obtained by taking the logarithm of the elastic limit deformation gradient index F cri , which is uniquely defined based on the elastic limit deformation gradient which is the material property of each elasto-plastic material (step S56). ..
- the log-elastic limit deformation gradient index LnF cri is a scalar or vector.
- the log-elastic limit deformation gradient index LnF cri may be a constant or a function of some physical quantity.
- the value obtained by subtracting the logarithmic elastic limit deformation gradient index LnF cri from the logarithmic trial elastic deformation gradient index LnF ei is defined as the logarithmic plastic deformation gradient increment index dLnF pi (step S58).
- LnF ei -LnF cri dLnF pi ... Equation (26) Is.
- dLnF pi LnF ei -LnF cri (LnF ei > LnF cri )... Equation (26A)
- dLnF pi 0 (LnF ei ⁇ LnF cri )... Equation (26B)
- the inequality sign in the conditional equations of equations (26A) and (26B) is evaluated based on the scalar value obtained by applying appropriate mathematical processing to the vector when the index is a vector value.
- dLnF p ij represents the logarithmic plastic deformation gradient increment in the x j axis direction of the i-plane (the plane orthogonal to the x i- axis) when the coordinate system x 1 -x 2- x 3 is set.
- the component of the tensor can be determined using the index by the method shown in the second embodiment.
- step S62 the definition of a Green finite strain tensor or the definition of an Almansi finite strain tensor, and log-plastic strain increment.
- the tensor is determined (step S62).
- step S64 the equilibrium error in the entire elasto-plastic body is calculated (step S64).
- step S66 it is determined whether or not the result of the balance error calculation for the load increment given in step S50 satisfies the end condition.
- the termination condition is, for example, when the balance error in the entire elasto-plastic body reaches within a predetermined error range. If the end condition is satisfied in step S66 (S66: Y), the process proceeds to step S68.
- step S66 If the end condition is not satisfied in step S66 (S66: N), the process returns to step S52, a new logarithmic trial elastic deformation gradient tensor is given, and the subsequent steps are repeated.
- step S68 it is determined whether or not the predetermined load increment has been completed (all the load increments have been given). If the predetermined load increment has not been completed in step S68 (S68: N), the process returns to step S50, a new load increment is given, and the subsequent steps are repeated. When the predetermined load increment is completed in step S68 (S68: Y), the numerical analysis is completed.
- the existence of the material constitutive law that connects the plastic strain increment tensor and the stress tensor is not required, and the existence of the scalar potential function of the stress tensor for expressing the material constitutive law is not required. That is, the flow rule based on the scalar potential function of the stress tensor, which has been indispensable for obtaining the plastic strain increment by the conventional elasto-plastic analysis method, is unnecessary. Further, in each of the above embodiments, it is not necessary to set a law for moving or deforming the yield function, which has been indispensable for analyzing the elasto-plastic deformation behavior after yielding by the conventional elasto-plastic analysis method. Is. Regardless of the stress-strain relationship after yielding and the load history, it is not necessary to change the setting of the elastic limit shear strain index during the analysis, and it does not change in the entire deformation history.
- an elasto-plastic analysis method and an elasto-plastic analysis program capable of simultaneously reproducing the Bauschinger effect and the invariance of the elasto-plastic deformation behavior with respect to the plastic-deformation history in a specific direction. ..
- the physical characteristic constants of the elasto-plastic body 10 used in the numerical calculation are shown in Table 1 below.
- the physical characteristic constants in Table 1 are set assuming steel materials.
- the summation rule is used for subscripts with lowercase letters in the English alphabet.
- step (1) as shown in the outline arrow in FIG. 9B, a x 2 direction of the external shear load S1 in addition to the upper surface of the elastic-plastic body 10, is deformed beyond the elastic limit.
- the maximum displacement amount ⁇ u 2 on the upper surface is 0.375 mm.
- FIGS. 9B to 9D the shape of the elasto-plastic body 10 before deformation is shown by a thin line and the shape of the elasto-plastic body 10 after deformation is shown by a thick line for easy understanding.
- step (2) as shown in the outline arrow in FIG. 9C, the -x 2 direction of the external shear load S2 added to the upper surface, is deformed beyond the elastic limit.
- step (3) the external shear load S2 is unloaded. As shown in FIG. 9D, the unloading is performed until the elastic shear strain is completely eliminated and only the plastic shear strain remains.
- step (4) The maximum displacement amplitude ⁇ u 3 of the upper surface of the elasto-plastic body 10 is 0.3 mm at the time of tension and compression.
- the load direction of the load in step (4) is a direction perpendicular to the load direction of the load in steps (1) and (2).
- FIGS. 11 and 12 The results of the numerical calculations from the above steps (1) to (4) are shown in FIGS. 11 and 12.
- the calculated value of step (1) is indicated by a white square
- the calculated value of step (2) is indicated by a white circle
- the calculated value of step (3) is indicated by a black triangle.
- the vertical axis x 2 direction of the shear load of 11 shows the displacement of the x 2 direction.
- Load in Y1 is 1.0 ⁇ 10 6 (N).
- step (2) when gradually added shearing force -x 2 direction, and reaches the elastic limit at point Y2.
- Load of Y2 is -0.8 ⁇ 10 6 (N). In other words, the Bauschinger effect can be reproduced.
- the calculation results during tension and compression in step (4) are shown by white squares. Further, the calculated value when a tensile (compressive) load is applied without applying a shear load, that is, when only a tensile (compressive) load is applied without going through the steps (1) to (3) described above. It is indicated by a white circle.
- the vertical axis of FIG. 12 x 3 direction tensile (compressive) loading, the horizontal axis represents the amount of displacement x 3 direction.
- a step (4) load 2.0 ⁇ 10 the elastic limit Y3 6 when tensile (N), the load of the elastic limit Y4 during compression 1.6 ⁇ 10 6 (N ).
- the Bauschinger effect can be reproduced.
- the load-displacement history due to the tensile (compressive) load in step (4) that is, the load-displacement history due to the tensile (compressive) load after the plastic deformation due to the shear load occurs is the tension (compression) without applying the shear load. ) It was the same as the load-displacement history when a load was applied.
- the elasto-plastic analysis method illustrated in the above embodiments and examples can be configured as an elasto-plastic analysis program and can be used for elasto-plastic analysis of structural materials such as metals. Further, the present invention can be configured as a storage medium that stores the elasto-plastic analysis program, or an elasto-plastic analysis device (system) that performs calculations according to the built-in elasto-plastic analysis program.
- the present invention includes the following gist.
- the elasto-plastic analysis method is an elasto-plastic analysis method for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves the boundary value problem.
- the trial elastic strain index is determined based on the step of obtaining the trial elastic strain tensor obtained by subtracting the plastic strain tensor from the total strain tensor in the pseudo-equilibrium state after loading without changing the load increment, and the trial elastic strain tensor.
- the plastic strain increment index corresponding to the load increment is determined based on the value obtained by subtracting the elastic limit strain index determined based on the material properties of the elasto-plastic body from the trial elastic strain index.
- a value obtained by subtracting the elastic limit strain index from the trial elastic strain index is determined as the plastic strain increment index corresponding to the load increment, and when the trial elastic strain index is equal to or less than the elastic limit strain index. , The purpose is to set the plastic strain increment index to zero.
- the elasto-plastic analysis method is an elasto-plastic analysis method of an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, and is a plastic deformation gradient tensor for an elasto-plastic body in a dynamic or static equilibrium state.
- the step of obtaining the trial elastic deformation gradient tensor by applying the inverse tensor of the plastic deformation gradient tensor to the total deformation gradient tensor in the pseudo-equilibrium state after loading without changing the load increment and the trial.
- the step of determining the plastic deformation gradient increment index corresponding to the load increment, the step of determining the plastic deformation gradient increment tensor based on the plastic deformation gradient increment index, and the determined plastic deformation gradient increment tensor using the determined plastic deformation gradient increment tensor Includes steps to determine the plastic strain increment tensor.
- the ratio of the trial elastic deformation gradient index to the elastic limit deformation gradient index is set as the plastic deformation gradient increment index corresponding to the load increment, and when the ratio is 1 or less, the plastic deformation gradient increment index is set to zero.
- the purpose is to do.
- the elasto-plastic analysis method is an elasto-plastic analysis method for an elasto-plastic body performed by using a numerical analysis method for numerically solving a boundary value problem, and is a plastic deformation gradient tensor for an elasto-plastic body in a dynamic or static equilibrium state.
- a plastic deformation gradient tensor for an elasto-plastic body in a dynamic or static equilibrium state.
- the logarithmic elasticity obtained by taking the step of determining the logarithmic trial elastic deformation gradient index based on the logarithmic trial elastic deformation gradient index and the logarithm of the elastic limit deformation gradient index determined based on the material properties of the elasto-plastic body from the logarithmic trial elastic deformation gradient index.
- the step of determining the log-plastic deformation gradient increment index corresponding to the load increment based on the value obtained by subtracting the limit deformation gradient index, and the log-plastic deformation gradient increment tensor based on the log-plastic deformation gradient increment index are determined.
- the step of determining the log-plastic strain incremental tensor using the determined log-plastic deformation gradient incremental tensor are determined.
- the elasto-plastic analysis program is an elasto-plastic analysis program for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves boundary value problems.
- the procedure for obtaining the trial elastic strain tensor obtained by subtracting the plastic strain tensor from the total strain tensor in the pseudo-equilibrium state after loading without changing the strain tensor, and the trial elastic strain based on the trial elastic strain tensor.
- the plastic strain increment corresponding to the load increment based on the procedure for determining the index and the value obtained by subtracting the elastic limit strain index determined based on the material properties of the elasto-plastic body from the trial elastic strain index.
- the elasto-plastic analysis program is an elasto-plastic analysis program for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves boundary value problems.
- the procedure for obtaining the trial elastic deformation gradient tensor by applying the inverse tensor of the plastic deformation gradient tensor to the total deformation gradient tensor in the pseudo-equilibrium state after loading without changing the deformation gradient tensor.
- the ratio of the procedure for determining the trial elastic deformation gradient index based on the trial elastic deformation gradient tensor, the trial elastic deformation gradient index, and the elastic limit deformation gradient index determined based on the material properties of the elasto-plastic body.
- the procedure for determining the plastic deformation gradient increment index corresponding to the load increment the procedure for determining the plastic deformation gradient increment tensor based on the plastic deformation gradient increment index, and the determined plastic deformation gradient increment tensor. It is an elasto-plastic analysis program for executing a procedure including, and a procedure for determining a plastic strain increment tensor using.
- the elasto-plastic analysis program is an elasto-plastic analysis program for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves boundary value problems.
- the procedure for obtaining the logarithmic trial elastic deformation gradient tensor obtained by subtracting the logarithmic plastic deformation gradient tensor from the logarithmic total deformation gradient tensor in the pseudo-equilibrium state after loading without changing the deformation gradient tensor, and the logarithmic trial elastic deformation.
- the elasto-plastic analysis system is an elasto-plastic analysis system for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves the boundary value problem.
- the load is based on a value obtained by subtracting the trial elastic strain index determining unit for determining the elastic strain index and the elastic limit strain index determined based on the material properties of the elasto-plastic body from the trial elastic strain index.
- An elasto-plastic analysis system including a plastic strain increment index determination unit that determines a plastic strain increment index corresponding to an increment and a plastic strain increment tensor determination unit that determines a plastic strain increment tensor based on the plastic strain increment index. ..
- the elasto-plastic analysis system is an elasto-plastic analysis system for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves boundary value problems, and is a plastic deformation gradient tensor for elasto-plastic bodies in a dynamic or static equilibrium state.
- the trial elastic deformation gradient tensor is obtained by applying the inverse tensor of the plastic deformation gradient tensor to the total deformation gradient tensor in the pseudo-equilibrium state after loading without changing the load increment.
- the trial elastic deformation gradient index determining unit determines the trial elastic deformation gradient index based on the trial elastic deformation gradient tensor, the trial elastic deformation gradient index, and the material properties of the elasto-plastic body.
- a plastic deformation gradient increment index determining unit that determines a plastic deformation gradient increment index corresponding to the load increment based on the ratio to the elastic limit deformation gradient index, and a plastic deformation gradient increment tensor based on the plastic deformation gradient increment index.
- It is an elasto-plastic analysis system including a plastic deformation gradient incremental tensor determination unit for determining a plastic strain gradient increment tensor and a plastic strain incremental tensor determination unit for determining a plastic strain incremental tensor using the determined plastic deformation gradient incremental tensor.
- the elasto-plastic analysis system is an elasto-plastic analysis system for elasto-plastic bodies performed using a numerical analysis method that numerically solves the boundary value problem, and is a plastic deformation gradient tensor for elasto-plastic bodies in a dynamic or static equilibrium state.
- Logistical Plastic Deformation Gradient Increment Index Determined Based on the Value Obtained by Subtracting the Elastic Limit Deformation Gradient Index Obtained by Taking the Log of the Elastic Limit Deformation Gradient Index.
- An elasto-plastic analysis system that includes a log-plastic strain increment tensor determination unit to determine.
- the storage medium is an elasto-plastic analysis program for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves the boundary value problem.
- the procedure for obtaining the trial elastic strain tensor obtained by subtracting the plastic strain tensor from the total strain tensor in the pseudo-equilibrium state after loading without changing the load increment, and the trial elastic strain index based on the trial elastic strain tensor.
- As a plastic strain increment index corresponding to the load increment based on a value obtained by subtracting the procedure for determining and the elastic limit strain index determined based on the material properties of the elasto-plastic body from the trial elastic strain index.
- It is a computer-readable storage medium that stores an elasto-plastic analysis program for executing a procedure including a procedure for determining a procedure and a procedure for determining a plastic strain increment tensor based on the plastic strain increment index.
- the storage medium is an elasto-plastic analysis program for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves the boundary value problem.
- the procedure for obtaining the trial elastic deformation gradient tensor by applying the inverse tensor of the plastic deformation gradient tensor to the total deformation gradient tensor in the pseudo-equilibrium state after loading without changing the tensor, and the procedure described above. Based on the procedure for determining the trial elastic deformation gradient index based on the trial elastic deformation gradient tensor, and the ratio of the trial elastic deformation gradient index to the elastic limit deformation gradient index determined based on the material properties of the elasto-plastic body.
- the procedure for determining the plastic deformation gradient increment index corresponding to the load increment, the procedure for determining the plastic deformation gradient incremental tensor based on the plastic deformation gradient increment index, and the determined plastic deformation gradient incremental tensor are used. It is a computer-readable storage medium that stores a procedure for determining a plastic strain increment tensor and an elasto-plastic analysis program for performing a procedure including.
- the storage medium is an elasto-plastic analysis program for elasto-plastic bodies that is performed using a numerical analysis method that numerically solves the boundary value problem.
- the procedure for obtaining the logarithmic trial elastic deformation gradient tensor obtained by subtracting the logarithmic plastic deformation gradient tensor from the logarithmic deformation gradient tensor in the pseudo-equilibrium state after loading without changing the tensor, and the logarithmic trial elastic deformation gradient tensor.
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
Description
以下、本発明の実施形態1に係る弾塑性体の解析方法について図2を参照して説明する。弾塑性解析の初期値境界値問題の支配方程式は、運動量保存則、角運動量保存則、変位-ひずみ関係式、応力-ひずみ関係式、塑性ひずみに関する方程式、からなる。従来技術においては、塑性ひずみに関する方程式として流れ則が用いられている。
εe=εtotal-εp …式(2)
である。試行弾性ひずみテンソルとは、繰り返し計算のために試行的に与える微小な弾性ひずみテンソルである。次に、試行弾性ひずみテンソルεeに基づいて一意に定義される試行弾性ひずみ指標εeiを決定する(ステップS14)。試行弾性ひずみ指標εeiはスカラー又はベクトルである。
εei-εcri=dεpi …式(3)
である。ただし、εei≦εcriである場合は、dεpi=0とする。即ち、
dεpi=εei-εcri (εei>εcri) …式(3A)
dεpi=0 (εei≦εcri) …式(3B)
とする。式(3A)および式(3B)の条件式の中の不等号は、指標がベクトル値である場合はベクトルに適切な数学的処理を施して得られるスカラー値に基づいて評価される。
実施形態1で説明した、微小変形の場合における一般的な弾塑性解析方法についての具体的な一例である実施形態2について、図面を参照して説明する。静的状態における弾塑性体の微小変形を考える。実施形態2では、実施形態1で説明した弾性限界ひずみ指標εcriの一例である弾性限界せん断ひずみεcrを考慮する。なお、弾性限界せん断ひずみεcrは、弾塑性体の材料試験により得られる数値である。実施形態2では、弾性限界せん断ひずみεcrを正の定数とする。
(ケース1)
(ケース2)
(ケース2)
(ケース3)
次に実施形態3として、弾塑性体の形状の変形が無視できない有限変形の場合について図面を参照して説明する。この場合の数値解析方法は、次の2つの方法をとることができる。
動的あるいは静的平衡状態にある弾塑性体に、荷重増分を負荷し(図7のステップS30)、塑性変形勾配テンソルは変えずに、荷重増分を負荷した後の擬似的平衡状態における全変形勾配テンソルを得る。この全変形勾配テンソルFtotalに、塑性変形勾配テンソルFpの逆テンソル(Fp)-1を適切に作用させたものを、試行弾性変形勾配テンソルFeとする(ステップS32)。即ち、
Fe=(Fp)-1〇Ftotal …式(23)
である。ここで(Fp)-1〇Ftotalは、塑性ひずみ変形勾配テンソルFpの逆テンソル(Fp)-1を全変形勾配テンソルFtotalに適切に作用させる数学的処理を表す。次に、試行弾性変形勾配テンソルFeに基づいて一意に定義される試行弾性変形勾配指標Feiを決定する(ステップS34)。試行弾性変形勾配指標Feiはスカラー又はベクトルである。
Fei/Fcri=dFpi …式(24)
である。ただし、Fei≦Fcriである場合は、dFpi=0とする。即ち、
dFpi=Fei/Fcri (Fei>Fcri) …式(24A)
dFpi=0 (Fei≦Fcri) …式(24B)
とする。式(24A)および式(24B)の条件式の中の不等号は、指標がベクトル値である場合はベクトルに適切な数学的処理を施して得られるスカラー値に基づいて評価される。
動的あるいは静的平衡状態にある弾塑性体に、荷重増分を負荷し(図8のステップS50)、塑性変形勾配テンソルは変えずに、荷重増分を負荷した後の擬似的平衡状態における全変形勾配テンソルを得る。この全変形勾配テンソルFtotalの対数を取って得られる対数全変形勾配テンソルLnFtotalと、塑性変形勾配テンソルFpの対数を取って得られる対数塑性変形勾配テンソルLnFpとの差に基づいて、対数試行弾性変形勾配テンソルLnFeを決定する。例えば、対数全変形勾配テンソルLnFtotalと対数塑性変形勾配テンソルLnFpとの差を対数試行弾性変形勾配テンソルLnFeとする(ステップS52)。即ち、
LnFe=LnFtotal-LnFp …式(25)
である。対数試行弾性変形勾配テンソルLnFeに基づいて一意に定義される対数試行弾性変形勾配指標LnFeiを決定する(ステップS54)。対数試行弾性変形勾配指標LnFeiはスカラー又はベクトルである。
LnFei-LnFcri=dLnFpi …式(26)
である。ただし、LnFei≦LnFcriである場合は、dLnFpi=0とする。即ち、
dLnFpi=LnFei-LnFcri (LnFei>LnFcri) …式(26A)
dLnFpi=0 (LnFei≦LnFcri) …式(26B)
とする。式(26A)および式(26B)の条件式の中の不等号は、指標がベクトル値である場合はベクトルに適切な数学的処理を施して得られるスカラー値に基づいて評価される。
弾塑性解析方法は、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析方法であって、動的又は静的平衡状態にある弾塑性体に塑性ひずみテンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全ひずみテンソルから前記塑性ひずみテンソルを差し引いて得られる試行弾性ひずみテンソルを求めるステップと、前記試行弾性ひずみテンソルに基づいて試行弾性ひずみ指標を決定するステップと、前記弾塑性体の材料特性に基づいて決定される弾性限界ひずみ指標を、前記試行弾性ひずみ指標から差し引いて得られる値に基づいて、前記荷重増分に対応する塑性ひずみ増分指標を決定するステップと、前記塑性ひずみ増分指標に基づいて塑性ひずみ増分テンソルを決定するステップと、を含む。これにより、バウシンガー効果と、特定の方向の塑性変形履歴に対する弾塑性変形挙動の不変性と、を同時に再現することができる。
前記試行弾性ひずみ指標から前記弾性限界ひずみ指標を差し引いて得られる値を、前記荷重増分に対応する前記塑性ひずみ増分指標として決定し、前記試行弾性ひずみ指標が前記弾性限界ひずみ指標以下である場合は、前記塑性ひずみ増分指標をゼロとすることを趣旨とする。
弾塑性解析方法は、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析方法であって、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全変形勾配テンソルに、前記塑性変形勾配テンソルの逆テンソルを作用させる数学的処理をほどこして試行弾性変形勾配テンソルを求めるステップと、前記試行弾性変形勾配テンソルに基づいて試行弾性変形勾配指標を決定するステップと、前記試行弾性変形勾配指標と、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標との比に基づいて、前記荷重増分に対応する塑性変形勾配増分指標を決定するステップと、前記塑性変形勾配増分指標に基づいて塑性変形勾配増分テンソルを決定するステップと、決定された前記塑性変形勾配増分テンソルを用いて塑性ひずみ増分テンソルを決定するステップと、を含む。
前記試行弾性変形勾配指標と前記弾性限界変形勾配指標との比を前記荷重増分に対応する前記塑性変形勾配増分指標とし、前記比が1以下である場合は、前記塑性変形勾配増分指標をゼロとすることを趣旨とする。
弾塑性解析方法は、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析方法であって、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における対数全変形勾配テンソルから対数塑性変形勾配テンソルを差し引いて得られる対数試行弾性変形勾配テンソルを求めるステップと、前記対数試行弾性変形勾配テンソルに基づいて対数試行弾性変形勾配指標を決定するステップと、前記対数試行弾性変形勾配指標から、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標の対数を取って得られる対数弾性限界変形勾配指標を差し引いて得られる値に基づいて、前記荷重増分に対応する対数塑性変形勾配増分指標を決定するステップと、前記対数塑性変形勾配増分指標に基づいて対数塑性変形勾配増分テンソルを決定するステップと、決定された前記対数塑性変形勾配増分テンソルを用いて対数塑性ひずみ増分テンソルを決定するステップと、を含む。
前記対数試行弾性変形勾配指標から前記対数弾性限界変形勾配指標を差し引いて得られる値を前記荷重増分に対応する前記対数塑性変形勾配増分指標とし、前記対数試行弾性変形勾配指標が前記対数弾性限界変形勾配指標以下である場合は、前記対数塑性変形勾配増分指標をゼロとすることを趣旨とする。
弾塑性解析プログラムは、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、コンピュータに、動的又は静的平衡状態にある弾塑性体に塑性ひずみテンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全ひずみテンソルから前記塑性ひずみテンソルを差し引いて得られる試行弾性ひずみテンソルを求める手順と、前記試行弾性ひずみテンソルに基づいて試行弾性ひずみ指標を決定する手順と、前記弾塑性体の材料特性に基づいて決定される弾性限界ひずみ指標を、前記試行弾性ひずみ指標から差し引いて得られる値に基づいて、前記荷重増分に対応する塑性ひずみ増分指標として決定する手順と、前記塑性ひずみ増分指標に基づいて塑性ひずみ増分テンソルを決定する手順と、を含む手順を実行させるための弾塑性解析プログラムである。
弾塑性解析プログラムは、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、コンピュータに、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全変形勾配テンソルに、前記塑性変形勾配テンソルの逆テンソルを作用させる数学的処理をほどこして試行弾性変形勾配テンソルを求める手順と、前記試行弾性変形勾配テンソルに基づいて試行弾性変形勾配指標を決定する手順と、前記試行弾性変形勾配指標と、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標との比に基づいて、前記荷重増分に対応する塑性変形勾配増分指標を決定する手順と、前記塑性変形勾配増分指標に基づいて塑性変形勾配増分テンソルを決定する手順と、決定された前記塑性変形勾配増分テンソルを用いて塑性ひずみ増分テンソルを決定する手順と、を含む手順を実行させるための弾塑性解析プログラムである。
弾塑性解析プログラムは、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、コンピュータに、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における対数全変形勾配テンソルから対数塑性変形勾配テンソルを差し引いて得られる対数試行弾性変形勾配テンソルを求める手順と、前記対数試行弾性変形勾配テンソルに基づいて対数試行弾性変形勾配指標を決定する手順と、前記対数試行弾性変形勾配指標から、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標の対数を取って得られる対数弾性限界変形勾配指標を差し引いて得られる値に基づいて、前記荷重増分に対応する対数塑性変形勾配増分指標を決定する手順と、前記対数塑性変形勾配増分指標に基づいて対数塑性変形勾配増分テンソルを決定する手順と、決定された前記対数塑性変形勾配増分テンソルを用いて対数塑性ひずみ増分テンソルを決定する手順と、を含む手順を実行させるための弾塑性解析プログラムである。
弾塑性解析システムは、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析システムであって、動的又は静的平衡状態にある弾塑性体に塑性ひずみテンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全ひずみテンソルから前記塑性ひずみテンソルを差し引いて得られる試行弾性ひずみテンソルを求める試行弾性ひずみテンソル取得部と、前記試行弾性ひずみテンソルに基づいて試行弾性ひずみ指標を決定する試行弾性ひずみ指標決定部と、前記弾塑性体の材料特性に基づいて決定される弾性限界ひずみ指標を、前記試行弾性ひずみ指標から差し引いて得られる値に基づいて、前記荷重増分に対応する塑性ひずみ増分指標を決定する塑性ひずみ増分指標決定部と、前記塑性ひずみ増分指標に基づいて塑性ひずみ増分テンソルを決定する塑性ひずみ増分テンソル決定部と、を含む弾塑性解析システムである。
弾塑性解析システムは、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析システムであって、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全変形勾配テンソルに、前記塑性変形勾配テンソルの逆テンソルを作用させる数学的処理をほどこして試行弾性変形勾配テンソルを求める試行弾性変形勾配テンソル取得部と、前記試行弾性変形勾配テンソルに基づいて試行弾性変形勾配指標を決定する試行弾性変形勾配指標決定部と、前記試行弾性変形勾配指標と、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標との比に基づいて、前記荷重増分に対応する塑性変形勾配増分指標を決定する塑性変形勾配増分指標決定部と、前記塑性変形勾配増分指標に基づいて塑性変形勾配増分テンソルを決定する塑性変形勾配増分テンソル決定部と、決定された前記塑性変形勾配増分テンソルを用いて塑性ひずみ増分テンソルを決定する塑性ひずみ増分テンソル決定部と、を含む弾塑性解析システムである。
弾塑性解析システムは、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析システムであって、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における対数全変形勾配テンソルから対数塑性変形勾配テンソルを差し引いて得られる対数試行弾性変形勾配テンソルを求める対数試行弾性変形勾配テンソル取得部と、前記対数試行弾性変形勾配テンソルに基づいて対数試行弾性変形勾配指標を決定する対数試行弾性変形勾配指標決定部と、前記対数試行弾性変形勾配指標から、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標の対数を取って得られる対数弾性限界変形勾配指標を差し引いて得られる値に基づいて、前記荷重増分に対応する対数塑性変形勾配増分指標を決定する対数塑性変形勾配増分指標決定部と、前記対数塑性変形勾配増分指標に基づいて対数塑性変形勾配増分テンソルを決定する対数塑性変形勾配増分テンソル決定部と、決定された前記対数塑性変形勾配増分テンソルを用いて対数塑性ひずみ増分テンソルを決定する対数塑性ひずみ増分テンソル決定部と、を含む弾塑性解析システムである。
記憶媒体は、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、コンピュータに、動的又は静的平衡状態にある弾塑性体に塑性ひずみテンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全ひずみテンソルから前記塑性ひずみテンソルを差し引いて得られる試行弾性ひずみテンソルを求める手順と、前記試行弾性ひずみテンソルに基づいて試行弾性ひずみ指標を決定する手順と、前記弾塑性体の材料特性に基づいて決定される弾性限界ひずみ指標を、前記試行弾性ひずみ指標から差し引いて得られる値に基づいて、前記荷重増分に対応する塑性ひずみ増分指標として決定する手順と、前記塑性ひずみ増分指標に基づいて塑性ひずみ増分テンソルを決定する手順と、を含む手順を実行させるための弾塑性解析プログラムを記憶させた、コンピュータ読み取り可能な記憶媒体である。
記憶媒体は、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、コンピュータに、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全変形勾配テンソルに、前記塑性変形勾配テンソルの逆テンソルを作用させる数学的処理をほどこして試行弾性変形勾配テンソルを求める手順と、前記試行弾性変形勾配テンソルに基づいて試行弾性変形勾配指標を決定する手順と、前記試行弾性変形勾配指標と、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標との比に基づいて、前記荷重増分に対応する塑性変形勾配増分指標を決定する手順と、前記塑性変形勾配増分指標に基づいて塑性変形勾配増分テンソルを決定する手順と、決定された前記塑性変形勾配増分テンソルを用いて塑性ひずみ増分テンソルを決定する手順と、を含む手順を実行させるための弾塑性解析プログラムを記憶させた、コンピュータ読み取り可能な記憶媒体である。
記憶媒体は、境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、コンピュータに、動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における対数全変形勾配テンソルから対数塑性変形勾配テンソルを差し引いて得られる対数試行弾性変形勾配テンソルを求める手順と、前記対数試行弾性変形勾配テンソルに基づいて対数試行弾性変形勾配指標を決定する手順と、前記対数試行弾性変形勾配指標から、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標の対数を取って得られる対数弾性限界変形勾配指標を差し引いて得られる値に基づいて、前記荷重増分に対応する対数塑性変形勾配増分指標を決定する手順と、前記対数塑性変形勾配増分指標に基づいて対数塑性変形勾配増分テンソルを決定する手順と、決定された前記対数塑性変形勾配増分テンソルを用いて対数塑性ひずみ増分テンソルを決定する手順と、を含む手順を実行させるための弾塑性解析プログラムを記憶させた、コンピュータ読み取り可能な記憶媒体である。
S1,S2:外部せん断荷重
E:引張荷重
C:圧縮荷重
Claims (9)
- 境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析方法であって、
動的又は静的平衡状態にある弾塑性体に塑性ひずみテンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全ひずみテンソルから前記塑性ひずみテンソルを差し引いて得られる試行弾性ひずみテンソルを求めるステップと、
前記試行弾性ひずみテンソルに基づいて試行弾性ひずみ指標を決定するステップと、
前記弾塑性体の材料特性に基づいて決定される弾性限界ひずみ指標を、前記試行弾性ひずみ指標から差し引いて得られる値に基づいて、前記荷重増分に対応する塑性ひずみ増分指標を決定するステップと、
前記塑性ひずみ増分指標に基づいて塑性ひずみ増分テンソルを決定するステップと、
を含む弾塑性解析方法。 - 前記試行弾性ひずみ指標から前記弾性限界ひずみ指標を差し引いて得られる値を、前記荷重増分に対応する前記塑性ひずみ増分指標として決定し、前記試行弾性ひずみ指標が前記弾性限界ひずみ指標以下である場合は、前記塑性ひずみ増分指標をゼロとする、請求項1に記載の弾塑性解析方法。
- 境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析方法であって、
動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全変形勾配テンソルに、前記塑性変形勾配テンソルの逆テンソルを作用させる数学的処理をほどこして試行弾性変形勾配テンソルを求めるステップと、
前記試行弾性変形勾配テンソルに基づいて試行弾性変形勾配指標を決定するステップと、
前記試行弾性変形勾配指標と、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標との比に基づいて、前記荷重増分に対応する塑性変形勾配増分指標を決定するステップと、
前記塑性変形勾配増分指標に基づいて塑性変形勾配増分テンソルを決定するステップと、
決定された前記塑性変形勾配増分テンソルを用いて塑性ひずみ増分テンソルを決定するステップと、
を含む弾塑性解析方法。 - 前記試行弾性変形勾配指標と前記弾性限界変形勾配指標との比を前記荷重増分に対応する前記塑性変形勾配増分指標とし、前記比が1以下である場合は、前記塑性変形勾配増分指標をゼロとする、請求項3に記載の弾塑性解析方法。
- 境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析方法であって、
動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における対数全変形勾配テンソルから対数塑性変形勾配テンソルを差し引いて得られる対数試行弾性変形勾配テンソルを求めるステップと、
前記対数試行弾性変形勾配テンソルに基づいて対数試行弾性変形勾配指標を決定するステップと、
前記対数試行弾性変形勾配指標から、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標の対数を取って得られる対数弾性限界変形勾配指標を差し引いて得られる値に基づいて、前記荷重増分に対応する対数塑性変形勾配増分指標を決定するステップと、
前記対数塑性変形勾配増分指標に基づいて対数塑性変形勾配増分テンソルを決定するステップと、
決定された前記対数塑性変形勾配増分テンソルを用いて対数塑性ひずみ増分テンソルを決定するステップと、
を含む弾塑性解析方法。 - 前記対数試行弾性変形勾配指標から前記対数弾性限界変形勾配指標を差し引いて得られる値を前記荷重増分に対応する前記対数塑性変形勾配増分指標とし、前記対数試行弾性変形勾配指標が前記対数弾性限界変形勾配指標以下である場合は、前記対数塑性変形勾配増分指標をゼロとする、請求項5に記載の弾塑性解析方法。
- 境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、
コンピュータに、
動的又は静的平衡状態にある弾塑性体に塑性ひずみテンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全ひずみテンソルから前記塑性ひずみテンソルを差し引いて得られる試行弾性ひずみテンソルを求める手順と、
前記試行弾性ひずみテンソルに基づいて試行弾性ひずみ指標を決定する手順と、
前記弾塑性体の材料特性に基づいて決定される弾性限界ひずみ指標を、前記試行弾性ひずみ指標から差し引いて得られる値に基づいて、前記荷重増分に対応する塑性ひずみ増分指標として決定する手順と、
前記塑性ひずみ増分指標に基づいて塑性ひずみ増分テンソルを決定する手順と、
を含む手順を実行させるための弾塑性解析プログラム。 - 境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、
コンピュータに、
動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における全変形勾配テンソルに、前記塑性変形勾配テンソルの逆テンソルを作用させる数学的処理をほどこして試行弾性変形勾配テンソルを求める手順と、
前記試行弾性変形勾配テンソルに基づいて試行弾性変形勾配指標を決定する手順と、
前記試行弾性変形勾配指標と、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標との比に基づいて、前記荷重増分に対応する塑性変形勾配増分指標を決定する手順と、
前記塑性変形勾配増分指標に基づいて塑性変形勾配増分テンソルを決定する手順と、
決定された前記塑性変形勾配増分テンソルを用いて塑性ひずみ増分テンソルを決定する手順と、
を含む手順を実行させるための弾塑性解析プログラム。 - 境界値問題を数値的に解く数値解析手法を用いて行う弾塑性体の弾塑性解析プログラムであって、
コンピュータに、
動的又は静的平衡状態にある弾塑性体に塑性変形勾配テンソルは変えずに荷重増分を負荷後の擬似的平衡状態における対数全変形勾配テンソルから対数塑性変形勾配テンソルを差し引いて得られる対数試行弾性変形勾配テンソルを求める手順と、
前記対数試行弾性変形勾配テンソルに基づいて対数試行弾性変形勾配指標を決定する手順と、
前記対数試行弾性変形勾配指標から、前記弾塑性体の材料特性に基づいて決定される弾性限界変形勾配指標の対数を取って得られる対数弾性限界変形勾配指標を差し引いて得られる値に基づいて、前記荷重増分に対応する対数塑性変形勾配増分指標を決定する手順と、
前記対数塑性変形勾配増分指標に基づいて対数塑性変形勾配増分テンソルを決定する手順と、
決定された前記対数塑性変形勾配増分テンソルを用いて対数塑性ひずみ増分テンソルを決定する手順と、
を含む手順を実行させるための弾塑性解析プログラム。
Priority Applications (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2021562425A JP7292755B2 (ja) | 2019-12-06 | 2019-12-06 | 弾塑性解析方法及び弾塑性解析プログラム |
PCT/JP2019/047888 WO2021111625A1 (ja) | 2019-12-06 | 2019-12-06 | 弾塑性解析方法及び弾塑性解析プログラム |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
PCT/JP2019/047888 WO2021111625A1 (ja) | 2019-12-06 | 2019-12-06 | 弾塑性解析方法及び弾塑性解析プログラム |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2021111625A1 true WO2021111625A1 (ja) | 2021-06-10 |
Family
ID=76221151
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/JP2019/047888 WO2021111625A1 (ja) | 2019-12-06 | 2019-12-06 | 弾塑性解析方法及び弾塑性解析プログラム |
Country Status (2)
Country | Link |
---|---|
JP (1) | JP7292755B2 (ja) |
WO (1) | WO2021111625A1 (ja) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN114912314A (zh) * | 2022-04-21 | 2022-08-16 | 中国科学院武汉岩土力学研究所 | 岩土介质弹塑性本构关系隐式自适应应力积分计算方法 |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2001201408A (ja) * | 2000-01-18 | 2001-07-27 | Toyota Motor Corp | 応力振動を抑制する動的陽解法有限要素法 |
JP2008142774A (ja) * | 2006-11-14 | 2008-06-26 | Jfe Steel Kk | 応力−ひずみ関係シミュレート方法、応力−ひずみ関係シミュレーションシステム、応力−ひずみ関係シミュレーションプログラム、及び当該プログラムを記録した記録媒体 |
US20150213164A1 (en) * | 2014-01-27 | 2015-07-30 | GM Global Technology Operations LLC | Product design reliability with consideration of material property changes during service |
-
2019
- 2019-12-06 WO PCT/JP2019/047888 patent/WO2021111625A1/ja active Application Filing
- 2019-12-06 JP JP2021562425A patent/JP7292755B2/ja active Active
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2001201408A (ja) * | 2000-01-18 | 2001-07-27 | Toyota Motor Corp | 応力振動を抑制する動的陽解法有限要素法 |
JP2008142774A (ja) * | 2006-11-14 | 2008-06-26 | Jfe Steel Kk | 応力−ひずみ関係シミュレート方法、応力−ひずみ関係シミュレーションシステム、応力−ひずみ関係シミュレーションプログラム、及び当該プログラムを記録した記録媒体 |
US20150213164A1 (en) * | 2014-01-27 | 2015-07-30 | GM Global Technology Operations LLC | Product design reliability with consideration of material property changes during service |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN114912314A (zh) * | 2022-04-21 | 2022-08-16 | 中国科学院武汉岩土力学研究所 | 岩土介质弹塑性本构关系隐式自适应应力积分计算方法 |
CN114912314B (zh) * | 2022-04-21 | 2024-04-02 | 中国科学院武汉岩土力学研究所 | 岩土介质弹塑性本构关系隐式自适应应力积分计算方法 |
Also Published As
Publication number | Publication date |
---|---|
JP7292755B2 (ja) | 2023-06-19 |
JPWO2021111625A1 (ja) | 2021-06-10 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Hora et al. | Modified maximum force criterion, a model for the theoretical prediction of forming limit curves | |
WO2014141794A1 (ja) | 応力-ひずみ関係シミュレート方法、スプリングバック量予測方法およびスプリングバック解析装置 | |
Burchitz | Improvement of springback prediction in sheet metal forming | |
Wang et al. | Anticlastic curvature in draw-bend springback | |
JP3809374B2 (ja) | 応力−ひずみ関係シミュレート方法および除荷過程における降伏点を求める方法 | |
Mapar et al. | A differential-exponential hardening law for non-Schmid crystal plasticity finite element modeling of ferrite single crystals | |
Labibzadeh et al. | A new method for CDP input parameter identification of the ABAQUS software guaranteeing uniqueness and precision | |
Mattiasson et al. | An evaluation of some recent yield criteria for industrial simulations of sheet forming processes | |
Peters | Yield functions taking into account anisotropic hardening effects for an improved virtual representation of deep drawing processes | |
Kosel et al. | Elasto-plastic springback of beams subjected to repeated bending/unbending histories | |
Voyiadjis et al. | Effects of stress invariants and reverse loading on ductile fracture initiation | |
WO2021111625A1 (ja) | 弾塑性解析方法及び弾塑性解析プログラム | |
Rashetnia et al. | Finite strain fracture analysis using the extended finite element method with new set of enrichment functions | |
US6205366B1 (en) | Method of applying the radial return method to the anisotropic hardening rule of plasticity to sheet metal forming processes | |
Spinu et al. | Modelling of rough contact between linear viscoelastic materials | |
Safikhani et al. | The strain gradient approach for determination of forming limit stress and strain diagrams | |
Meinders et al. | A sensitivity analysis on the springback behavior of the unconstrained bending problem | |
Nguyen et al. | Finite element method study to predict spring-back in roll-bending of pre-coated material and select bending parameters | |
Kocbay et al. | Stress resultant plasticity for plate bending in the context of roll forming of sheet metal | |
US5437190A (en) | Method for determining the effects of stress | |
Hassan et al. | Analysis of nonuniform beams on elastic foundations using recursive differentiation method | |
Kolesnikov et al. | Bending of inflated curved hyperelastic tubes | |
Wang et al. | Explicit dynamic analysis of sheet metal forming processes using linear prismatic and hexahedral solid-shell elements | |
Hora et al. | Damage dependent stress limit model for failure prediction in bulk forming processes | |
de Sousa et al. | Unconstrained springback behavior of Al–Mg–Si sheets for different sitting times |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
121 | Ep: the epo has been informed by wipo that ep was designated in this application |
Ref document number: 19954834 Country of ref document: EP Kind code of ref document: A1 |
|
ENP | Entry into the national phase |
Ref document number: 2021562425 Country of ref document: JP Kind code of ref document: A |
|
NENP | Non-entry into the national phase |
Ref country code: DE |
|
32PN | Ep: public notification in the ep bulletin as address of the adressee cannot be established |
Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205 DATED 09/09/2022) |
|
122 | Ep: pct application non-entry in european phase |
Ref document number: 19954834 Country of ref document: EP Kind code of ref document: A1 |