CN107506595B - material damage prediction method based on critical state dynamic movement - Google Patents
material damage prediction method based on critical state dynamic movement Download PDFInfo
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Abstract
The invention provides a material damage prediction method based on critical state dynamic movement, which comprises the following steps: step 1, determining a critical state point or line of the current material damage based on theoretical research, numerical analysis and field judgment, determining a damage area and a non-damage area, and establishing a geometric description equation through measurement research; step 2, analyzing the specific gravity distribution characteristics of the research object and establishing a specific gravity equation; step 3, analyzing the boundary condition stress characteristics of the damaged area and the non-damaged area, and establishing a boundary condition stress equation; step 4, dividing the research object into different regions of a rule for research, analyzing continuous and discontinuous physical mechanical quantity, and establishing a corresponding physical mechanical quantity solving method; step 5, selecting a stress expression equation and calculating each constant coefficient; and 6, carrying out prediction and forecast of material damage according to the critical state dynamic movement rule by combining the material peak intensity criterion, the constitutive equation and the field monitoring condition.
Description
Technical Field
The invention belongs to the technical field of force and deformation related calculation methods such as mechanics, civil engineering, geological engineering and the like, and particularly relates to a material damage prediction method based on critical state dynamic movement.
Background
Natural disasters, damage to human architectural structures and the like cause property and life loss in different degrees, so that the implementation of prediction and forecast on the basis of force and deformation is very necessary for the occurrence of damage such as natural disasters and the like. The existing stress and deformation solving is often established on a finite element and other numerical calculation methods, the finite element method adopts a point-area calculation mode for a two-dimensional structure and a point-substituted calculation mode for a three-dimensional structure, and therefore calculation results are often different for units with different sizes; when numerical calculation is performed, a linear method is generally used to solve a nonlinear problem, i.e., an initial stress method, and different convergence criteria are used, so that the calculation results are different.
Disclosure of Invention
The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a material damage prediction method based on a critical state dynamic motion, which can predict and predict material damage based on a force boundary condition, a force balance condition, a critical state damage point stress condition, and the like.
In order to achieve the purpose, the invention adopts the following scheme:
The invention provides a material damage prediction method based on critical state dynamic movement, which is characterized by comprising the following steps of: step 1, determining a critical state point or line (respectively aiming at two dimensions or three dimensions) of the current material damage based on theoretical research, numerical analysis and field judgment, determining a damaged area and a non-damaged area, simultaneously measuring the macroscopic geometric characteristics of a research object (comprising the damaged area and the non-damaged area), and establishing a geometric description equation corresponding to the macroscopic geometric characteristics; step 2, analyzing the specific gravity distribution characteristics of the research object, and establishing a specific gravity equation of the research object in the research area; step 3, analyzing the boundary condition stress characteristics of a damaged area and a non-damaged area of the research object, and establishing a boundary condition stress equation corresponding to the boundary condition stress characteristics; step 4, dividing the research object into regular different regions according to the characteristics of the research object, researching (for example, aiming at two-dimensional triangle, quadrangle and the like, and aiming at three-dimensional tetrahedron, hexahedron and the like), particularly, separating a damaged region from a non-damaged region, analyzing continuous and discontinuous physical mechanical quantities (for example, aiming at a push-type landslide damaged rear region mainly based on compression-shear damage, the shear stress and the driving gliding stress are discontinuous and the like, but the pressure stress and the back pressure stress of a vertical sliding surface are continuous), and establishing a discontinuous physical mechanical quantity solving method (for example, aiming at a landslide, the shear stress can be solved according to the patent: a calculation method for gradually damaging a potential sliding surface, and the patent no: 201510658880.6); in the physical mechanical quantity continuous area, corresponding stress and the like must be continuous; step 5, selecting a stress expression equation, wherein the stress expression equation meets the force, stress and/or bending moment balance equations corresponding to a damaged area and a non-damaged area of a research object (see a stress solution based on a force boundary and a balance condition, and the patent number is 201611034900.3); at a critical state point or line (respectively aiming at two-dimension or three-dimension), meeting the corresponding peak intensity criterion of the material, and calculating each constant coefficient; step 6, combining the material peak intensity criteria (such as molar coulomb criteria, Griffth criteria and the like), the subsequent damage path of the research object can be determined, namely the potential damage surface is determined; on the basis of detailed analysis of stress characteristics, the deformation characteristics of a research object are researched by combining the constitutive equation, comparison analysis is carried out on the calculated deformation and the field monitoring by combining the field monitoring, the behavior characteristics of the research object are determined, and prediction and forecast of material damage are implemented according to the dynamic movement rule of a critical state. According to the method, the stress of the research object is assumed to meet the boundary and balance conditions, and the failure point meets the strength criterion, so that prediction and prediction are implemented aiming at the failure process of the research object, and the stress, deformation and failure distribution characteristics of the research object in any geometric shape can be predicted. The method can be used for forecasting dynamic and static loading and unloading damage processes of various building structures such as dams, bridges, side slopes, roadbed, houses, tunnels, inclusions, roadways, culverts and the like.
The material damage prediction method based on the critical state dynamic movement provided by the invention can also have the following characteristics: in step 1, under the condition that a research object is in a two-dimensional geometric configuration, a critical state point of current material damage is determined based on two-dimensional theoretical research, numerical analysis and field judgment, a damaged area and a non-damaged area are determined, simultaneously, the macroscopic geometric characteristics of the research object are measured, and a geometric description equation corresponding to the macroscopic geometric characteristics is established.
The material damage prediction method based on the critical state dynamic movement provided by the invention can also have the following characteristics: in step 2in the case of a two-dimensional geometric configuration of the investigation object, the specific gravity of the investigation region includes the specific gravity γ in the X-axis directionw,xAnd specific gravity Y in the Y-axis directionw,y(ii) a In the case of a three-dimensional geometric configuration of the object under investigation, the specific gravity of the investigation region includes the specific gravity γ in the direction of the X-axisw,xSpecific gravity Y in the Y-axis directionw,yAnd specific gravity in Z-axis directionw,z。
the material damage prediction method based on the critical state dynamic movement provided by the invention can also have the following characteristics: in step 3, if the damage area is broken, according to the boundary condition of the breakage; otherwise, the damaged area and the non-damaged area all conform to the boundary condition characteristics.
The material damage prediction method based on the critical state dynamic movement provided by the invention can also have the following characteristics: in step 4, the shear stress and the driving glide stress are discontinuous in the transition type landslide failure rear region mainly including the compression shear failure, but the compression stress and the counter pressure stress of the vertical sliding surface are continuous.
action and Effect of the invention
1. The stress expression equation of the dynamic movement prediction method meets the force, stress and (or) bending moment equilibrium equations corresponding to a damaged area and a non-damaged area of a research object; at a critical state point or line, meeting the corresponding peak intensity criterion of the material;
2. the prediction method comprises the following steps: the stress and strain theoretical solutions of the discontinuous problems of the stress and the like in a damage area are mainly solved, and the prediction and the forecast of the material damage are implemented according to the dynamic movement of a critical state;
3. The forecasting method of the invention implements forecasting on dynamic and static damage processes of various building structures such as dams, bridges, side slopes, road beds, houses, tunnels, inclusions, roadways, culverts and the like, and has a promoting effect on related research and application.
Drawings
fig. 1 is a schematic diagram illustrating a critical state motion dynamic prediction of material failure according to an embodiment of the present invention.
Detailed Description
The following describes in detail a specific embodiment of the present invention based on a critical state dynamic motion material damage prediction method with reference to the drawings.
The embodiment takes two-dimensional landslide as an example, and discloses a material damage prediction method based on critical state dynamic movement, which specifically comprises the following steps:
Step 1, determining a critical state point (such as a point D in figure 1) of the current material damage based on two-dimensional theoretical research (see a Chinese invention patent: a stress solution based on a force boundary and a balance condition, a patent number: 201611034900.3), numerical analysis (such as a current finite element method, a discrete element method and the like) and field judgment, determining a damaged area (such as an ABDE area in figure 1) and a non-damaged area (such as a BCD area in figure 1), simultaneously measuring the macroscopic geometric characteristics of a research object (including the damaged area and the non-damaged area), and establishing a geometric description equation (such as AB, BC and EA in figure 1) corresponding to the macroscopic geometric characteristics (such as AB, BC and EA in figure 1 are linear equations (such as: y is K for a straight line BC)BCx+bBC，KBC,bBCSlope and intercept, respectively), DE is the curve equation);
Step 2, the research object is in a two-dimensional geometric configuration, and the specific gravity of the research area comprises the specific gravity gamma in the X-axis directionw,xand specific gravity Y in the Y-axis directionw,yThe following equation (note: other expressions are also possible):
γw,x＝γ0,x+a4,1x+a4,2y+a4,3x2+a4,4xy+a4,5y2+a4,6x3+a4,7x2y+a4,8xy2+…(1)
γw,y＝γ0,y+a5,1x+a5,2y+a5,3x2+a5,4xy+a5,5y2+a5,6x3+a5,7x2y+a5,8xy2+…(2)
Step 3. according to claim 3, the characteristics of the damaged and non-damaged areas of the study are analyzed, if the damaged area is broken, according to the boundary conditions of the breakage; otherwise, the damaged area and the non-damaged area all conform to boundary condition characteristics, such as: and satisfying the principles of Saint Wen south and establishing a boundary condition stress equation corresponding to the boundary condition stress characteristics.
If the failure zone (e.g. ABDE in FIG. 1) breaks, then: the AB boundary condition stress can be expressed as:
σxx|AB＝0,σyy|AB＝0,τxy|AB＝0 (3)
if the damaged area (e.g., ABDE in FIG. 1) is intact:
The AB boundary condition stress may be:
σxx|AB＝0,σyy|AB＝0,τxy|AB＝0 (4)
or
Or
the AE boundary condition stress may be:
σxx|AE＝0,σyy|AE＝0,τxy|AE＝0 (7)
or
Or
But not the destruction region (e.g., BCD in fig. 1), then:
The BC boundary condition stress may be:
Wherein:
σN BC＝l2σxx BC+m2σyy BC+2lmτxy BC (11)
In the formula: l, m is the cosine of the BC out-of-plane normal direction, σxx BC,σyy BC,τxy BCboundary stress of BC side, σxx,σyy,τxy: positive and shear stresses in the direction of X, Y, respectively; eta: unit length along the straight line BC, i.e.
And 4, discussing the characteristics of the ABCDE, dividing the ABCDE into two research objects of the ABCDE and the BCD, wherein the ABDE is a damaged area along the sliding surface, the BCD is a non-damaged area, and in the damaged area, the shearing stress and the anti-sliding friction resistance stress along the DE sliding surface are discontinuous, certainly, the displacement is also discontinuous, and other physical mechanical quantities are continuous.
On the basis of analyzing continuous and discontinuous physical mechanical quantities (for example, for a push-type landslide failure rear area mainly based on compression-shear failure, the shear stress and the driving gliding stress of the push-type landslide failure rear area are discontinuous, but the compression stress and the counter pressure stress of a vertical sliding surface are continuous), the discontinuous friction-resistance shear stress is calculated according to the Chinese invention patent- - ((the patent application number is 201610860012.0, the invention patent application name is a novel slope progressive failure whole-process calculation method or the patent application number is 2014100250810, the invention patent application name is a sliding surface boundary method for slope stability calculation).
step 5, selecting a stress expression equation which meets the balance equations of force, stress and/or bending moment corresponding to the damaged area and the non-damaged area of the research object (see a stress solution based on a force boundary and a balance condition, and the patent number is 201611034900.3); at a critical state point or line (respectively aiming at two-dimension or three-dimension), meeting the corresponding peak intensity criterion of the material, and calculating each constant coefficient; the method comprises the following steps:
aiming at an ABDE research object, according to the coordinate XOY in figure 1, selecting a stress power of 3 expression:
σxx＝a1,0+a1,1x+a1,2y+a1,3x2+a1,4xy+a1,5y2+a1,6x3+a1,7x2y+a1,8xy2+a1,9y3 (13)
σyy＝a2,0+a2,1x+a2,2y+a2,3x2+a2,4xy+a2,5y2+a2,6x3+a2,7x2y+a2,8xy2+a2,9y3 (14)
τxy＝a3,0+a3,1x+a3,2y+a3,3x2+a3,4xy+a3,5y2+a3,6x3+a3,7x2y+a3,8xy2+a3,9y3 (15)
The stresses must satisfy the equilibrium equation where the specific gravity is constant (i.e., gamma)w,x＝0，γw,yγ) to eliminate the 15 constant coefficients. The remaining 15 constants were undetermined.
With equation (3), 9 constant coefficients can be eliminated, leaving 6 constant coefficients.
by usingAnd the stress of the research object ABDE meets the current peak stress criterion (such as molar coulomb criterion and Griffth criterion) in the X-axis direction and the Y-axis direction, the stress and strain solution of the research object ABDE can be obtained, and of course, the moment of the research object ABDE also needs to be balanced.
Aiming at a study object BCD, selecting a stress power of 3 expression according to the X ' O ' Y ' coordinate in figure 1:
σxx'＝b1,0+b1,1x'+b1,2y'+b1,3x'2+b1,4x'y'+b1,5y'2+b1,6x'3+b1,7x'2y'+b1,8x'y'2+b1,9y'3 (16)
σyy'＝b2,0+b2,1x'+b2,2y'+b2,3x'2+b2,4x'y'+b2,5y'2+b2,6x'3+b2,7x'2y'+b2,8x'y'2+b2,9y'3 (17)
τxy'＝b3,0+b3,1x'+b3,2y'+b3,3x'2+b3,4x'y'+b3,5y'2+b3,6x'3+b3,7x'2y'+b3,8x'y'2+b3,9y'3 (18)
By utilizing the equal stress of the study objects ABDE and BCD on the BD side, 12 constant coefficients can be determined, and the remaining 6 unknown constant coefficients. Using y '═ 0, σ'y0 or y ═ 0, σ'xthe 3 constant coefficients can be determined by using the D point to satisfy the existing peak stress criterion (e.g., moore's criterion, Griffth's criterion), and using the formula (10):
The study object BCD stress solution can be obtained.
From the above solving process, the solution has multi-solution characteristics.
step 6, determining a subsequent destruction angle of the research object by combining a material peak intensity criterion (such as a molar coulomb criterion, a Griffth criterion and the like), and determining a subsequent destruction path by combining displacement monitoring, namely determining a potential destruction surface; on the basis of detailed analysis of stress characteristics, the deformation characteristics of a research object can be researched by combining a constitutive equation, comparison analysis is carried out on the calculated deformation and the field monitoring by combining the field monitoring, the behavior characteristics of the research object are determined, and prediction and forecast of material damage are implemented according to a critical state dynamic movement rule.
The above examples are merely illustrative, and are not intended to limit the embodiments of the present invention. In addition to the above embodiments, the present invention has other embodiments. All technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the claims of the present invention.
Claims (5)
1. A material damage prediction method based on critical state dynamic movement is characterized by comprising the following steps:
step 1, determining a critical state point or line of the current material damage based on theoretical research, numerical analysis and field judgment, determining a damage area and a non-damage area, measuring the macroscopic geometric characteristics of a research object, and establishing a geometric description equation corresponding to the macroscopic geometric characteristics;
Step 2, analyzing the specific gravity distribution characteristics of the research object, and establishing a specific gravity equation of the research object in the research area;
Step 3, analyzing the boundary condition stress characteristics of a damaged area and a non-damaged area of the research object, and establishing a boundary condition stress equation corresponding to the boundary condition stress characteristics;
Step 4, dividing the research object into regular different areas to research according to the characteristics of the research object, separating a damaged area from a non-damaged area, analyzing continuous and discontinuous physical mechanical quantities, and establishing a discontinuous physical mechanical quantity solving method; in the physical mechanical quantity continuous area, the corresponding stress must be continuous;
Step 5, selecting a stress expression equation, wherein the stress expression equation meets a force, stress or bending moment balance equation corresponding to a damaged area and a non-damaged area of a research object; at the critical state point or line, the corresponding peak intensity criterion of the material is satisfied, and each constant coefficient is calculated;
step 6, combining the material peak intensity criterion, the subsequent damage path of the research object can be determined, namely the potential damage surface is determined; on the basis of detailed analysis of stress characteristics, the deformation characteristics of a research object are researched by combining the constitutive equation, comparison analysis is carried out on the calculated deformation and the field monitoring by combining the field monitoring, the behavior characteristics of the research object are determined, and prediction and forecast of material damage are implemented according to the dynamic movement rule of a critical state.
2. The method according to claim 1, wherein the method comprises:
in the step 1, under the condition that the research object is in a two-dimensional geometric configuration, a critical state point of the current material damage is determined based on two-dimensional theoretical research, numerical analysis and field judgment, a damaged area and a non-damaged area are determined, simultaneously, the macroscopic geometric characteristics of the research object are measured, and a geometric description equation corresponding to the macroscopic characteristics is established.
3. The method according to claim 1, wherein the method comprises:
in step 2, in the case where the object of investigation is of a two-dimensional geometric configuration, the specific gravity of the investigation region includes the specific gravity γ in the X-axis directionw,xAnd specific gravity Y in the Y-axis directionw,y(ii) a In the case of a three-dimensional geometric configuration of the object under investigation, the specific gravity of the investigation region includes the specific gravity γ in the direction of the X-axisw,xSpecific gravity Y in the Y-axis directionw,yand specific gravity in Z-axis directionw,z。
4. the method according to claim 1, wherein the method comprises:
In the step 3, if the damage area is broken, according to the boundary condition of the breakage; otherwise, the damaged region and the non-damaged region all comply with the boundary condition stress characteristics.
5. the method according to claim 1, wherein the method comprises:
In step 4, the shear stress and the driving slip stress are discontinuous in the transition type landslide failure rear region mainly including the compression shear failure, but the compression stress and the counter pressure stress of the vertical sliding surface are continuous.
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