CN113806989B - Finite element analysis method for stress-strain relation of sofa seat elastic material - Google Patents
Finite element analysis method for stress-strain relation of sofa seat elastic material Download PDFInfo
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- 239000013013 elastic material Substances 0.000 title claims abstract description 35
- 238000004458 analytical method Methods 0.000 title claims abstract description 32
- 239000006260 foam Substances 0.000 claims abstract description 175
- 229920000642 polymer Polymers 0.000 claims abstract description 112
- 239000004744 fabric Substances 0.000 claims abstract description 82
- 238000012360 testing method Methods 0.000 claims abstract description 58
- 239000002356 single layer Substances 0.000 claims abstract description 56
- 238000000034 method Methods 0.000 claims abstract description 24
- 238000004088 simulation Methods 0.000 claims abstract description 18
- 238000012669 compression test Methods 0.000 claims abstract description 13
- 241000628997 Flos Species 0.000 claims description 32
- 230000006835 compression Effects 0.000 claims description 26
- 238000007906 compression Methods 0.000 claims description 26
- 239000010410 layer Substances 0.000 claims description 25
- 239000000463 material Substances 0.000 claims description 23
- 230000005489 elastic deformation Effects 0.000 claims description 6
- 238000005381 potential energy Methods 0.000 claims description 6
- 238000000926 separation method Methods 0.000 claims description 6
- 238000005516 engineering process Methods 0.000 claims description 4
- 238000010008 shearing Methods 0.000 claims description 3
- 238000005457 optimization Methods 0.000 abstract description 3
- 239000004814 polyurethane Substances 0.000 description 11
- 239000004800 polyvinyl chloride Substances 0.000 description 10
- 229920000915 polyvinyl chloride Polymers 0.000 description 10
- 238000004364 calculation method Methods 0.000 description 4
- 238000009864 tensile test Methods 0.000 description 4
- 239000004721 Polyphenylene oxide Substances 0.000 description 3
- 229920000570 polyether Polymers 0.000 description 3
- 229920005862 polyol Polymers 0.000 description 3
- 150000003077 polyols Chemical class 0.000 description 3
- 229920005830 Polyurethane Foam Polymers 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 239000000203 mixture Substances 0.000 description 2
- 239000011496 polyurethane foam Substances 0.000 description 2
- 230000001419 dependent effect Effects 0.000 description 1
- 230000000994 depressogenic effect Effects 0.000 description 1
- 238000011056 performance test Methods 0.000 description 1
- 229920002635 polyurethane Polymers 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 239000002023 wood Substances 0.000 description 1
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
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Abstract
The invention discloses a finite element analysis method of stress-strain relation of a sofa seat elastic material, which comprises the following steps: s1, an Ogden foam constitutive model based on Ansys Workbench is used for fitting a stress-strain relation of single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method to obtain test parameters of the single-layer polymer foam; s2, fitting a stress-strain relation of the single-layer fabric on the basis of an Ogden constitutive model of Ansys Workbench to obtain test parameters of the single-layer fabric; s3, predicting the stress-strain relation of the polymer foam matched fabric combination by utilizing finite element simulation according to the test parameters of the single-layer polymer foam and the test parameters of the single-layer fabric. The invention can effectively predict the stress-strain relation of the sofa seat elastic material combination, thereby facilitating the subsequent improvement and optimization of the sofa seat elastic material and having the advantages of simplicity and practicability.
Description
Technical Field
The invention relates to the field of sofa performance test, in particular to a finite element analysis method for stress-strain relation of a sofa seat elastic material.
Background
The comfort of the sofa seat surface is closely related to the matching combination of the elastic materials. Sofa enterprises and designers have been traditionally primarily dependent on uniaxial compression test analysis and worker experience in selecting to match elastomeric materials. However, the elastic materials such as polymer foam, springs, bandages, fabrics and the like on the market are various, and the stress-strain relation of a huge number of elastic material combinations is difficult to systematically quantify only by means of the traditional uniaxial compression experiment. In recent years, finite element analysis is widely applied to simulation of engineering mechanics due to the advantages of intuitiveness, timeliness and the like. The finite element analysis method can quantify a large number of combined models through modeling, and meanwhile, the finite element analysis method can accurately analyze the stress of the combined models. Therefore, the finite element analysis method is of great significance in researching the stress-strain relation of the sofa seat elastic material. In the field of seat comfort, a great deal of attention is paid to the compressive yielding condition of single-layer polymer foam under single axis or multiple axes, but the research on the stress-strain relation of multi-layer polymer foam or polymer foam matched fabric combination is not much, and a simple and practical analysis method is lacked.
Disclosure of Invention
The invention aims to provide a finite element analysis method for stress-strain relation of a sofa seat elastic material. The invention effectively predicts the stress-strain relation of the sofa seat elastic material combination, thereby facilitating the subsequent improvement and optimization of the sofa seat elastic material and having the advantages of simplicity and practicability.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: the finite element analysis method of the stress-strain relation of the sofa seat elastic material comprises the following steps:
S1, an Ogden foam constitutive model based on Ansys Workbench is used for fitting a stress-strain relation of single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method to obtain test parameters of the single-layer polymer foam;
s2, fitting a stress-strain relation of the single-layer fabric on the basis of an Ogden constitutive model of Ansys Workbench to obtain test parameters of the single-layer fabric;
s3, predicting the stress-strain relation of the polymer foam matched fabric combination by utilizing finite element simulation according to the test parameters of the single-layer polymer foam and the test parameters of the single-layer fabric.
In the finite element analysis method of the stress-strain relation of the elastic material of the sofa seat surface, in the Ogden foam constitutive model of Ansys Workbench, the elasticity of the single-layer polymer foam is represented by the potential energy of elastic deformation, and the strain energy potential is based on the main stretching amount of the left Kexil-Grin tensor and is given by the following formula:
the above formula is based on an axial tensile test on a single layer polymer foam, the parameters of which are defined as follows: u i is the initial coefficient of shear modulus, alpha i is the basic parameter of the material, beta i is the compressible coefficient, J is the elastic volume ratio, lambda i is the main elongation, and N is the order of the model;
Simplified above, the derivative of the strain energy potential W in the main elongation direction λ 2, the nominal stress σ calculated in the main elongation direction λ 2 load direction is:
wherein: lambda 2 is expressed as:
wherein lambda is the elongation in the stretching direction, L is the length in the axial compression direction when the polymer foam test piece is not deformed, deltaL is the axial compression of the polymer foam test piece, and epsilon is the strain in the stretching direction;
The elastic volume ratio j=λ 1λ2λ3, formula 4;
Wherein in the deformation of the single layer polymer foam, the amount of stretching in the λ 1 direction and in the λ 3 method is ignored with poisson's ratio v i being 0, i.e. λ 2＝λ,λ1＝λ3 =1;
Compressibility factor
Where, in the case where poisson's ratio v i is 0, compressible coefficient β i is also 0;
From the uniaxial compression test, the elastic volume ratio J is defined as the elongation ratio in the direction of lambda 2, so that the formula of the stress-strain relationship can be deduced, and the process is as follows:
Wherein v 0 represents the volume of the polymer foam test piece after deformation, and v represents the volume of the polymer foam test piece after deformation;
the elongation ratio in the lambda 2 direction of the polymer foam upon uniaxial compression is expressed as:
substituting equations 6 and 7 into equation 1, and then deriving the principal elongation direction from the strain energy potential, the nominal stress-strain relationship of the polymer foam under uniaxial compression is deduced:
In the finite element analysis method for the stress-strain relation of the elastic material of the sofa seat surface, in the stress-strain relation of the fitting single-layer polymer foam in the uniaxial compression test, the numerical value of the test parameter is continuously adjusted by an inverse analysis method until the target amount calculated by the finite element is matched with the test data, so that the problem that the initial parameter of fitting uniaxial compression data by using the formula 8 is larger because the polymer foam generates shearing stress on the side wall and the bottom side edge of the disc during uniaxial compression and pressing is solved.
In the finite element analysis method of the stress-strain relation of the elastic material of the sofa seat surface, in the Ogden constitutive model of Ansys Workbench, the elasticity of the single-layer fabric is represented by potential energy of elastic deformation, and the strain energy potential is based on the main stretching amount of the left Kexil-Grin tensor and is given by the following formula:
The parameters are defined as follows: u i is the initial coefficient of shear modulus, alpha i is the basic parameter of the material, J is the elastic volume ratio, lambda i is the main elongation, and N is the order of the model; d k is the incompressible coefficient;
Since the fabric is defined as a super-elastic material, the volume of the super-elastic material does not change when being compressed, namely j=λ 1λ2λ3 =1;
the above-mentioned method is modified to obtain:
When uniaxially stretched in the direction of lambda 2, lambda 1、λ3 orthogonal thereto satisfies the following relationship: lambda 1＝λ3＝λ2 -1/2,λ2 =1+epsilon, formula 12;
Equation 11 is a strain potential based on a change in elongation as in the Ogden foam constitutive model, and therefore, equation 12 is taken into equation 11 and derivative of λ 2:
Equation 14 is a nominal stress-strain relationship of the Ogden model, which is used to fit the stress-strain relationship of the fabric, thereby obtaining simulated material parameters of the fabric.
In the finite element analysis method of the stress-strain relation of the elastic material of the sofa seat surface, a layer of 10mm thick elastic foam is constructed to replace silk floss arranged between the polymer foam and the fabric in the combination of the polymer foam and the fabric, and the initial coefficient u i of the shear modulus of the silk floss is 100pa, the basic parameter alpha i of the material is 1, and the compressibility coefficient is 0 because of the compressibility performance of the silk floss and is defined as low elastic foam.
According to the finite element analysis method for the stress-strain relation of the sofa seat elastic material, hexahedral grids are adopted in the finite element simulation, the polymer foam collocation fabric combination is respectively subjected to grid division by utilizing a finite element grid division technology, and meanwhile, the load steps and the load carrier parts are arranged to improve the convergence.
The finite element analysis method for the stress-strain relation of the elastic material of the sofa seat surface is characterized by comprising the following steps of: in Ansys Workbench, the contact of the fabric, the polymer foam and the uniaxial compression end is set to be binding contact, namely, the contact surfaces keep initial contact in the normal direction and the tangential direction, relative sliding or separation between the surfaces is not allowed, and the contact surfaces between the combinations are prevented from being separated due to deformation.
Compared with the prior art, the invention has the following beneficial effects:
1. According to the invention, polymer foam and fabric are defined through an Ogden foam constitutive model and an Ogden constitutive model of Ansys Workbench respectively, a stress-strain relation of single-layer polymer foam in a uniaxial compression test is fitted in the Ogden foam constitutive model, test parameters of the single-layer polymer foam are obtained, and a stress-strain relation of the single-layer fabric is fitted in the Ogden constitutive model, so that test parameters of the single-layer fabric are obtained; and then predicting the stress-strain relation of the polymer foam matched fabric combination by utilizing finite element simulation according to the test parameters of the single-layer polymer foam and the test parameters of the single-layer fabric. Therefore, the method can predict the stress strain of the huge number of multi-layer polymer foam collocation fabric combinations, and has the advantages of high prediction accuracy, simplicity and practicability.
2. In the stress-strain relation of the fitting single-layer polymer foam in the uniaxial compression test, the numerical value of the test parameter is continuously adjusted by an inverse analysis method until the target quantity calculated by the finite element is matched with the test data, so that the problem that the initial parameter of fitting uniaxial compression data by using 8 is larger because the polymer foam generates shearing stress on the side wall and the bottom side edge of the disc when the uniaxial compression is pressed down is solved.
3. Because of the difficulty in modeling and material definition of silk floss in finite element simulation, the invention replaces the silk floss between polymer foam and fabric with a layer of foam with low elasticity, and the structure is not much different from the actual structure, thus having feasibility.
4. Because the large deformation of the combination of the polymer foam and the fabric can cause the large deformation of the overall grids of the upper and lower models, the change of the rigidity of the material generated by the deformation is very easy to cause the non-convergence of the calculation result, the invention adopts the hexahedral grid, utilizes the finite element grid division technology to respectively carry out the grid division on the combination of the polymer foam and the fabric, and simultaneously sets the load step and the load carrier part so as to improve the convergence.
5. In Ansys Workbench, the contact of the fabric, the polymer foam and the uniaxial compression end is set as binding contact, but friction (friction coefficient) is not set, and the contact is carried out according to the fact that the polymer foam and the fabric are not in sliding in practical experiments, namely, the contact surfaces are kept in initial contact in the normal direction and tangential direction, relative sliding or separation between the surfaces is not allowed, separation of the contact surfaces between the combinations due to deformation can be effectively avoided, and further accuracy of analysis results is guaranteed.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a schematic illustration of a monolayer polymer foam stress strain fit process;
FIG. 3 is a simplified schematic diagram of a combination of a facing and a polymer foam;
FIG. 4 is a diagram of meshing results and boundary conditions;
FIG. 5 is a graph comparing the finite element prediction results of Foam A+foam B with the test results;
FIG. 6 is a graph of Foam A+Foam B+Cloth+ SILK WADDING finite element predictions versus test results;
FIG. 7 is a graph comparing the finite element prediction results of Foam A+Foam B+PU+ SILK WADDING with the test results;
FIG. 8 is a graph comparing the finite element prediction results of Foam A+foam B+PVC+ SILK WADDING with the test results.
Detailed Description
The invention is further illustrated by the following examples and figures, which are not intended to be limiting.
Examples: the finite element analysis method of the stress-strain relation of the sofa seat elastic material is carried out according to the following steps as shown in figure 1:
S1, an Ogden foam constitutive model based on Ansys Workbench is used for fitting a stress-strain relation of single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method to obtain test parameters of the single-layer polymer foam; wherein the polymer foams are polyether polyol Foam (density 38kg/m 3、25kg/m3) and polyurethane Foam (density 38kg/m 3), respectively, the size of the single-layer polymer Foam test piece is 740mmx740mmx100mm, the single-layer polyether polyol Foam with density 38kg/m3 is named Foam A, the single-layer polyether polyol Foam with density 25kg/m3 is named Foam B, and the single-layer polyurethane Foam with density 38kg/m3 is named Foam C.
Specifically, in the Ogden foam constitutive model of Ansys Workbench, the elasticity of a single layer polymer foam is represented by the potential energy of elastic deformation, which is based on the principal amount of stretch of the left-hand Cauchy-Green tensor and is given by:
the above formula is based on an axial tensile test on a single layer polymer foam, the parameters of which are defined as follows: u i is the initial coefficient of shear modulus, alpha i is the basic parameter of the material, beta i is the compressible coefficient, J is the elastic volume ratio, lambda i is the main elongation, and N is the order of the model;
Simplified above, the derivative of the strain energy potential W in the main elongation direction λ 2, the nominal stress σ calculated in the main elongation direction λ 2 load direction is:
wherein: lambda 2 is expressed as:
wherein lambda is the elongation in the stretching direction, L is the length in the axial compression direction when the polymer foam test piece is not deformed, deltaL is the axial compression of the polymer foam test piece, and epsilon is the strain in the stretching direction;
The elastic volume ratio j=λ 1λ2λ3, formula 4;
Wherein in the deformation of the single layer polymer foam, the amount of stretching in the λ 1 direction and in the λ 3 method is ignored with poisson's ratio v i being 0, i.e. λ 2＝λ,λ1＝λ3 =1;
Compressibility factor
Where, in the case where poisson's ratio v i is 0, compressible coefficient β i is also 0;
From the uniaxial compression test, the elastic volume ratio J is defined as the elongation ratio in the direction of lambda 2, so that the formula of the stress-strain relationship can be deduced, and the process is as follows:
Wherein v 0 represents the volume of the polymer foam test piece after deformation, and v represents the volume of the polymer foam test piece after deformation;
the elongation ratio in the lambda 2 direction of the polymer foam upon uniaxial compression is expressed as:
substituting equations 6 and 7 into equation 1, and then deriving the principal elongation direction from the strain energy potential, the nominal stress-strain relationship of the polymer foam under uniaxial compression is deduced:
The reason for the error in fitting the single layer polymer foam is that the polymer foam will create shear stress to the disk side and bottom edges as the disk is depressed, whereas the absence of this shear stress in equation 8 results in a larger initial parameter for fitting the uniaxial compression data using equation 8. Thus, in this embodiment, the values of the test parameters are continuously adjusted by inverse analysis as shown in fig. 2 until the target values calculated by the finite element match the test data, wherein the fitting results in the values shown in table 1:
TABLE 1
S2, fitting a stress-strain relation of the single-layer fabric on the basis of an Ogden constitutive model of Ansys Workbench to obtain test parameters of the single-layer fabric; wherein the fabrics are PVC (polyvinyl chloride), PU (polyurethane) and Cloth (Cloth), the size of the fabric test piece is selected to be 100mmx25mm, and the thickness is 2mm.
Specifically, in the Ogden constitutive model of Ansys Workbench, the elasticity of a single layer of fabric is represented by the potential energy of elastic deformation, and the strain energy potential is based on the principal stretching amount of the Leuchy-Green tensor and is given by the following formula:
The parameters are defined as follows: u i is the initial coefficient of shear modulus, alpha i is the basic parameter of the material, J is the elastic volume ratio, lambda i is the main elongation, and N is the order of the model; d k is the incompressible coefficient;
Since the fabric is defined as a super-elastic material, the volume of the super-elastic material does not change when being compressed, namely j=λ 1λ2λ3 =1;
the above-mentioned method is modified to obtain:
When uniaxially stretched in the direction of lambda 2, lambda 1、λ3 orthogonal thereto satisfies the following relationship: lambda 1＝λ3＝λ2 -1/2,λ2 =1+epsilon, formula 12;
Equation 11 is a strain potential based on a change in elongation as in the Ogden foam constitutive model, and therefore, equation 12 is taken into equation 11 and derivative of λ 2:
equation 14 is the nominal stress-strain relationship of the Ogden model, which can fit the stress-strain relationship of the fabric well. The stress strain of the fabric obtained by the test is imported into an Ogden constitutive model of Ansys Workbench, test data are fitted through a fitting tool of the Ogden constitutive model, and simulation material parameters of the fabric are obtained, as shown in table 2:
| u1(MPa) | α1 | d1 | u2(MPa) | α2 | d2 | |
| PVC | 0.512 | 3.903 | 0 | 0.512 | 3.903 | 0 |
| PU | 0.064 | 8.748 | 0 | 721.79 | 0.007 | 0 |
| Cloth | 0.161 | 26.532 | 0 |
TABLE 2
S3, predicting the stress-strain relation of the polymer foam matched fabric combination by utilizing finite element simulation according to the test parameters of the single-layer polymer foam and the test parameters of the single-layer fabric. The uniaxial compression calculation simulation type of the polymer foam plus shell fabric combination belongs to nonlinear large deformation, and the combination form of the shell fabric and the polymer foam is simplified in consideration of the problem of convergence of the result, as shown in fig. 3. The shear stress generated at the contact part of the side wall of the polymer foam and the shell fabric and the excessive deformation of the side surface of the polymer foam are easy to cause the problems of stress singular points and non-convergence of the result when the finite element calculates the combined compression large deformation. Considering that the side panels of the polymer foam have less effect on the support of the sofa seating surface during testing, it is assumed that the effect of the side panels of the polymer foam on the support of the sofa seating surface is ignored. Meanwhile, according to the technical method of modern sofa enterprises when producing and collocating sofa seat surface elastic materials, a layer of silk floss with the thickness of about 20mm is added between double-layer polymer foam and fabric so as to increase the softness of the seat surface, and because the silk floss is difficult to model and define materials in finite element simulation, in the combination of the polymer foam collocating fabric, a layer of 10 mm-thick elastic foam is constructed to replace the silk floss arranged between the polymer foam and the fabric, and the elastic foam is defined as low-elastic foam due to the compressibility of the silk floss, the initial coefficient u i of the shear modulus of the silk floss is 100pa, the basic parameter alpha i of the material is 1, and the compressibility coefficient is 0.
The accuracy of the finite element simulation result depends greatly on the density and quality of the model grids, and the calculation accuracy is improved along with the increase of the number of grids, but the calculation time is increased at the same time, so that the rationality of the number of grids should be paid attention to in the dividing process. In determining the number of grids, whether the analysis result is based on the result accuracy or the result is based on the convergence can be considered, and particularly for nonlinear large deformation materials, larger grids are more beneficial to the convergence of the result. The finite element simulation in this embodiment adopts hexahedral mesh, and utilizes finite element mesh division technology to respectively perform mesh division on the polymer foam collocation fabric combination, as shown in fig. 4. And meanwhile, a load step and a load carrier part are arranged to improve convergence, and the contact of the fabric, the polymer foam and the single-shaft compression end is set to be binding contact in Ansys Workbench, namely, the contact surfaces keep initial contact in the normal direction and the tangential direction, relative sliding or separation between the surfaces is not allowed, and the separation of the contact surfaces between the combinations due to deformation is avoided.
To further verify the effectiveness of the present invention, applicants have formulated a Foam-in-Foam composition of Foam A+foam B, foam A+foam C, foam B+foam C3 double-layer polymer Foam, a Foam-in-Foam, silk floss, and a facestock into a Foam-in-Foam composition of 9 double-layer polymer foams +silk floss, foam A+foam B+PVC+silk floss, foam A+foam C+PVC+silk floss, foam A+foam B+PU+silk floss, foam A+foam C+PU+silk floss, foam B+foam C+PU+silk floss, foam A+foam B+cloth, foam A+silk floss, foam C+silk floss, foam B+foam C+cloth+silk floss.
The stress-strain relationship of the above combinations was tested using uniaxial compression, and single layer polymer foam, double layer polymer foam combinations, and double layer polymer foam + shell + silk floss combinations were tested on a TST-CD001 type mechanical tester, with reference to the american society for testing and materials polymer foam test standard (astm d 3574-B1). Each test was performed 3 times using a round platen with a diameter of 350mm, and the test piece was slowly pressed down at a constant speed of 100mm/min, pre-pressed to 80% and then compressed to 65% of its thickness.
Axial tensile testing the PVC, PU and cloth 3 types were tested in a CMT6203 electronic Universal tester with reference to the specification of the axial tensile properties of standard GB/T3923.1-2013 fabrics. Each fabric test piece is tested for 5 times, two ends of the fabric test piece are clamped by using clamps, the clamping distance is 80mm, and in order to ensure that the two ends are fixed and do not slide, a wood block is fixed at each of the two ends. The axial stretching speed is 100mm/min during loading, and the upper limit of the loading is 200N.
The test results show that the axial tensile properties of PVC and PU are obviously better than those of cloth, and the axial tensile strain of PVC and PU is obviously greater than that of cloth after the stress value of 3 fabrics exceeds 0.5 Mpa. The uniaxial compression result shows that the double-layer polymer foam combination and the double-layer polymer foam plus fabric plus silk floss combination can effectively improve the capability of bearing stress of the seat surface relative to the single-layer polymer foam.
Further, fitting parameters of Foam A, foam B and Foam C3 single-layer polymer foams are obtained through an inverse analysis method, and fitting parameters of PVC, PU and cloth 3 fabric test data are obtained through a fitting tool in a finite element. Based on fitting parameters obtained by fitting, the stress-strain relation of the matched 3 double-layer polymer foams and 9 double-layer polymer foams, plus fabric and silk floss under 12 combinations is respectively predicted in finite elements, and the predicted results are as follows
Tables 3-7 and FIGS. 5-8.
Table 3 (5% stress)
Table 4 (10% stress)
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Table 5 (25% stress)
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Table 6 (50% stress)
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Table 7 (65% stress)
As can be seen by comparing the stress strain of the two-layer polymer foam combinations of FIGS. 5-8 and tables 3-7, the relative error of the two-layer polymer foam combination finite element prediction results and the test results is within 46.6%, and the two-layer polymer foam + shell fabric + silk floss combination finite element prediction results and the test results relative error is within 64.7%. In the method of the present invention, the stress-strain relationship of the combination of the two-layer polymer foam is predicted based on the material parameters of the single-layer polymer foam. And the stress-strain relation of the double-layer polymer foam, the fabric and the silk floss combination is predicted, and the reasonable double-layer polymer foam combination prediction result and the fabric axial tensile test result are relied on. As seen in tables 3-7, there is also a significant difference in the relative error between the double layer polymer foam + shell + silk floss combined finite element prediction results and the test results at 5% strain due to the difference in polymer foam. The comparison analysis results of the finite element analysis and the mechanical test show that: the stress-strain relation of the elastic material combination of the sofa seat surface can be effectively predicted by using the finite element analysis method, and the result shows that when the strain of the elastic material combination of the sofa seat surface is 15% -65%, the relative error of the finite element prediction result and the test result is 0% -29%, so that the invention has good prediction accuracy. And because modeling and material definition are difficult to carry out on silk floss in finite element simulation, the method utilizes a layer of low-elasticity foam to replace the silk floss between polymer foam and fabric, and the prediction result of the combination of double-layer polymer foam, fabric and silk floss shows that the method has certain rationality.
In summary, the invention can effectively predict the stress-strain relation of the combination of the elastic materials of the sofa seat surface, thereby facilitating the subsequent improvement and optimization of the elastic materials of the sofa seat surface, and has the advantages of simplicity and practicability.
Claims (3)
1. The finite element analysis method for the stress-strain relation of the elastic material of the sofa seat surface is characterized by comprising the following steps of: the method comprises the following steps:
s1, an Ogden foam constitutive model based on Ansys Workbench is used for fitting a stress-strain relation of single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method to obtain simulation material parameters of the single-layer polymer foam;
s2, fitting a stress-strain relation of the single-layer fabric on the basis of an Ogden constitutive model of Ansys Workbench to obtain simulation material parameters of the single-layer fabric;
S3, predicting the stress-strain relation of the polymer foam matched fabric combination by utilizing finite element simulation according to the simulation material parameters of the single-layer polymer foam and the single-layer fabric;
In the Ogden foam constitutive model of the Ansys Workbench, the elasticity of a single layer polymer foam is represented by the potential energy of elastic deformation, which is based on the principal amount of stretch of the Leuchy-Green tensor and is given by:
A formula 1;
The parameters are defined as follows: u i is the initial coefficient of shear modulus, α i is the basic parameter of the material, β i is the compressible coefficient, J is the elastic volume ratio, N is the order of the model;
The elastic volume ratio j=λ 1λ2λ3, formula 4;
Wherein in the single layer polymer foam deformation, the stretching amounts in the λ 1 direction and the λ 3 direction are ignored with poisson's ratio v i being 0, i.e., λ 1＝λ3 =1;
Compressibility factor
Where, in the case where poisson's ratio v i is 0, compressible coefficient β i is also 0;
From the uniaxial compression test, the elastic volume ratio J is defined as the elongation ratio in the direction of lambda 2, so that the formula of the stress-strain relationship can be deduced, and the process is as follows:
Wherein v 0 represents the volume of the polymer foam test piece after deformation, and v represents the volume of the polymer foam test piece after deformation; l is the length in the axial pressure direction when the polymer foam test piece is not deformed, and DeltaL is the axial pressure of the polymer foam test piece;
the elongation ratio in the lambda 2 direction of the polymer foam upon uniaxial compression is expressed as:
wherein ε is the strain in the compressive direction;
substituting the formula 6 and the formula 7 into the formula 1, and then solving the derivative of the main extension direction lambda 2 for the strain energy W, so as to push out the nominal stress-strain relation of the polymer foam under uniaxial compression, and fitting the stress-strain relation of the single-layer polymer foam in the uniaxial compression test;
In the stress-strain relation of the fitting single-layer polymer foam in the uniaxial compression test, the numerical value of the test parameter is continuously adjusted by an inverse analysis method until the target amount calculated by the finite element is identical with the test data, so as to solve the problem that the initial parameter of fitting uniaxial compression data by using the formula 8 is larger because the polymer foam generates shearing stress on the side wall and the bottom side edge of the disc when the uniaxial compression is pressed down;
In the Ogden constitutive model of the Ansys Workbench, the elasticity of a single layer of fabric is represented by the potential energy of elastic deformation, which is based on the principal stretching of the left cauchy-green tensor and is given by:
The parameters are defined as follows: u i is the initial coefficient of shear modulus, alpha i is the basic parameter of the material, J is the elastic volume ratio, and N is the order of the model; d k is the incompressible coefficient;
Since the fabric is defined as a super-elastic material, the volume of the super-elastic material does not change when being compressed, namely J=λ 1λ2λ3 =1, and the formula 10;
the above-mentioned method is modified to obtain:
When uniaxially stretched in the direction of lambda 2, lambda 1、λ3 orthogonal thereto satisfies the following relationship: lambda 1＝λ3＝λ2 -1/2,λ2 =1+epsilon, epsilon being the strain in the stretching direction; formula 12;
Equation 11 is a strain potential based on a change in elongation as in the Ogden foam constitutive model, and therefore, equation 12 is taken into equation 11 and derivative of λ 2:
Equation 14 is a nominal stress-strain relationship of the Ogden model, which is used for fitting the stress-strain relationship of the fabric, so as to obtain simulated material parameters of the fabric;
The finite element simulation adopts hexahedral grids, and utilizes the finite element grid division technology to respectively carry out grid division on polymer foam collocation fabric combination, and simultaneously sets load steps and load sub-steps so as to improve the convergence of the result.
2. The method for finite element analysis of stress-strain relationship of sofa seat elastic material according to claim 1, wherein the method comprises the following steps: in the combination of polymer foam and fabric, a layer of elastic foam with the thickness of 10mm is constructed to replace silk floss arranged between the polymer foam and the fabric, and the initial coefficient u i of the shear modulus of the silk floss is 100pa, the basic parameter alpha i of the material is 1, and the compressibility coefficient is 0 due to the compressibility of the silk floss and is defined as low-elasticity foam.
3. The method for finite element analysis of stress-strain relationship of sofa seat elastic material according to claim 1, wherein the method comprises the following steps: in Ansys Workbench, the contact of the fabric, the polymer foam and the uniaxial compression end is set to be binding contact, namely, the contact surfaces keep initial contact in the normal direction and the tangential direction, relative sliding or separation between the surfaces is not allowed, and the contact surfaces between the combinations are prevented from being separated due to deformation.
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