CN113806989A - Finite element analysis method for stress-strain relationship of elastic material of sofa seat surface - Google Patents
Finite element analysis method for stress-strain relationship of elastic material of sofa seat surface Download PDFInfo
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- 238000004458 analytical method Methods 0.000 title claims abstract description 34
- 239000013013 elastic material Substances 0.000 title claims abstract description 27
- 239000006260 foam Substances 0.000 claims abstract description 178
- 229920000642 polymer Polymers 0.000 claims abstract description 119
- 239000004744 fabric Substances 0.000 claims abstract description 84
- 238000012360 testing method Methods 0.000 claims abstract description 65
- 239000002356 single layer Substances 0.000 claims abstract description 58
- 238000000034 method Methods 0.000 claims abstract description 20
- 238000004088 simulation Methods 0.000 claims abstract description 20
- 238000012669 compression test Methods 0.000 claims abstract description 12
- 239000000463 material Substances 0.000 claims description 30
- 241000628997 Flos Species 0.000 claims description 29
- 239000010410 layer Substances 0.000 claims description 24
- 238000007906 compression Methods 0.000 claims description 21
- 230000006835 compression Effects 0.000 claims description 18
- 238000005381 potential energy Methods 0.000 claims description 9
- 239000012858 resilient material Substances 0.000 claims description 7
- 238000009795 derivation Methods 0.000 claims description 6
- 230000005489 elastic deformation Effects 0.000 claims description 6
- 238000000926 separation method Methods 0.000 claims description 5
- 238000009864 tensile test Methods 0.000 claims description 4
- 238000005516 engineering process Methods 0.000 claims description 3
- 230000001131 transforming effect Effects 0.000 claims description 3
- 238000005457 optimization Methods 0.000 abstract description 3
- 239000004800 polyvinyl chloride Substances 0.000 description 11
- 229920000915 polyvinyl chloride Polymers 0.000 description 11
- 239000004814 polyurethane Substances 0.000 description 10
- 238000004364 calculation method Methods 0.000 description 4
- 239000004721 Polyphenylene oxide Substances 0.000 description 3
- 238000010586 diagram Methods 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
- 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
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010835 comparative analysis Methods 0.000 description 1
- 230000002349 favourable effect Effects 0.000 description 1
- 230000013011 mating Effects 0.000 description 1
- 238000011056 performance test Methods 0.000 description 1
- 229920002635 polyurethane Polymers 0.000 description 1
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- 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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- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Abstract
The invention discloses a finite element analysis method for stress-strain relationship of elastic material of a sofa seat surface, which is carried out according to the following steps: s1, fitting the stress-strain relation of the single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method based on an Ogden foam constitutive model of Ansys Workbench to obtain the test parameters of the single-layer polymer foam; s2, fitting the stress-strain relation of the single-layer fabric based on an Ogden constitutive model of Ansys Workbench to obtain the test parameters of the single-layer fabric; and S3, according to the testing parameters of the single-layer polymer foam and the testing parameters of the single-layer fabric, predicting the stress-strain relationship of the polymer foam and fabric combination by utilizing finite element simulation. The invention can effectively predict the stress-strain relationship of the sofa seat surface elastic material combination, thereby facilitating the subsequent improvement and optimization of the sofa seat surface 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 relationship of an elastic material of a sofa seat surface.
Background
The comfort of the sofa seat surface is closely related to the matching and combination of the elastic materials. Sofa companies and designers have historically relied primarily on uniaxial compression test analysis and worker experience in selecting a mating resilient material. However, the variety of elastic materials such as polymer foams, springs, bandages, fabrics and the like on the market is large, and it is difficult to systematically quantify the stress-strain relationship of a large number of elastic material combinations by means of only conventional uniaxial compression experiments. In recent years, finite element analysis is widely used for simulation of engineering mechanics due to its advantages such as intuitiveness and timeliness. The finite element analysis method can quantify a huge number of combined models through modeling and can also accurately analyze the stress of the combined models. Therefore, the finite element analysis method is of great significance for researching the stress-strain relationship of the elastic material of the sofa seat surface. In the field of seat comfort, the more attention is paid to the compressive yielding condition of single-layer polymer foam under a single shaft or multiple shafts, the stress-strain relationship of multi-layer polymer foam or polymer foam matched fabric combination is not researched much, and a simple and practical analysis method is lacked.
Disclosure of Invention
The invention aims to provide a finite element analysis method for the stress-strain relationship of an elastic material of a sofa seat surface. The invention effectively predicts the stress-strain relationship of the sofa seat surface elastic material combination, thereby facilitating the subsequent improvement and optimization of the sofa seat surface 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 relationship of the elastic material of the sofa seat surface is carried out according to the following steps:
s1, fitting the stress-strain relation of the single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method based on an Ogden foam constitutive model of Ansys Workbench to obtain the test parameters of the single-layer polymer foam;
s2, fitting the stress-strain relation of the single-layer fabric based on an Ogden constitutive model of Ansys Workbench to obtain the test parameters of the single-layer fabric;
and S3, according to the testing parameters of the single-layer polymer foam and the testing parameters of the single-layer fabric, predicting the stress-strain relationship of the polymer foam and fabric combination by utilizing finite element simulation.
In the above finite element analysis method of stress-strain relationship 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 thereof is the main stretching amount based on the levo cauchy-green 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. ofiInitial coefficient of shear modulus, αiBeing a fundamental parameter of the material, betaiIs compressibility factor, J is elastic volume ratio, λiIs the main elongation, and N is the order of the model;
simplifying the above equation, finding the principal direction of elongation λ for the strain potential W2Derivation of (a), nominal stress sigma in the direction of principal elongation lambda2The load direction is calculated as:
wherein: lambda [ alpha ]2Expressed as:
in the formula, lambda is the elongation in the stretching direction, L is the length of the polymer foam test piece in the axial pressure direction when the polymer foam test piece is not deformed, delta L is the axial pressure of the polymer foam test piece, and epsilon is the strain in the elongation direction;
elastic volume ratio J ═ λ1λ2λ3Formula 4;
in the form of a single-layer polymer foam, the Poisson's ratio viNeglect at λ in case of 01Direction sum lambda3The amount of stretching in the process, i.e. λ2＝λ，λ1＝λ3＝1；
Compressibility factor
In the formula, in Poisson's ratio viAt 0, the compressibility factor βiIs also 0;
the elastic volume ratio J is defined as λ during uniaxial compression test2The elongation ratio in the direction, and therefore the formula of the stress-strain relationship can be derived as follows:
in the formula, v0Expressed as the deformed volume of the polymer foam test piece, and v is the undeformed volume of the polymer foam test piece;
lambda of polymer foam during uniaxial compression2The elongation ratio in the direction is expressed as:
substituting equations 6 and 7 into equation 1, and then deriving the principal elongation direction for the strain potential, thus deriving the nominal stress-strain relationship for the polymer foam under uniaxial compression:
according to the finite element analysis method for the stress-strain relationship of the elastic material of the sofa seat surface, in the stress-strain relationship of the fitted single-layer polymer foam in the uniaxial compression test, the numerical value of the test parameter is continuously adjusted by the 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 the fitted uniaxial compression data is larger due to the fact that the polymer foam generates shear stress on the side wall and the bottom side edge of the disc when the polymer foam is pressed down under uniaxial compression by using the formula 8 is solved.
In the above finite element analysis method for the stress-strain relationship 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 the potential energy of elastic deformation, and the strain potential thereof is the main stretching amount based on the levocoxy-green tensor, and is given by the following formula:
the parameters are defined as follows: u. ofiInitial coefficient of shear modulus, αiIs a basic parameter of the material, J is the elastic volume ratio, lambdaiIs the main elongation, and N is the order of the model; dkIs an incompressible coefficient;
since the fabric is defined as a superelastic material, the superelastic material does not change its volume when compressed, i.e., J ═ λ1λ2λ3＝1；
Transforming the above formula to obtain:
when at λ2Lambda orthogonal to the direction of uniaxial extension in the direction1、λ3The following relationship is satisfied: lambda [ alpha ]1＝λ3＝λ2 -1/2，λ21+ epsilon, formula 12;
equation 11 is based on the strain potential energy of elongation change as in the Ogden foam constitutive model, and therefore equation 12 is taken to equation 11 and is aligned with λ2And (3) carrying out derivation:
and the formula 14 is a nominal stress-strain relation of the Ogden model and is used for fitting the stress-strain relation of the fabric so as to obtain simulation material parameters of the fabric.
In the finite element analysis method for the stress-strain relationship of the elastic material for the sofa seat surface, a layer of elastic foam with the thickness of 10mm is constructed in the combination of the polymer foam and the fabric to replace silk floss arranged between the polymer foam and the fabric, and the silk floss has the compressible property and is defined as low-elasticity foam, and the initial coefficient u of the shear modulus of the low-elasticity foami100pa, the basic parameter a of the materialiIs 1 and the compressibility factor is 0.
In the finite element analysis method for the stress-strain relationship of the elastic material of the sofa seat surface, the finite element simulation adopts hexahedral meshes, the finite element meshing technology is utilized to respectively mesh the polymer foam matching fabric combination, and the load step and the load subpart are arranged simultaneously to improve the convergence.
The finite element analysis method for the stress-strain relationship of the elastic material of the sofa seat surface is characterized in that: in Ansys Workbench, the contact of the fabric, the polymer foam and the uniaxial compression end is set as binding contact, namely, initial contact is kept between contact surfaces in a normal direction and a tangential direction, relative sliding or separation between the surfaces is not allowed, and the contact surfaces between the combination are prevented from being separated due to deformation.
Compared with the prior art, the invention has the following beneficial effects:
1. the method comprises the steps of defining polymer foam and fabric through an Ogden foam constitutive model and an Ogden constitutive model of Ansys Workbench, fitting the stress-strain relationship of single-layer polymer foam in a uniaxial compression test in the Ogden foam constitutive model to obtain the test parameters of the single-layer polymer foam, and fitting the stress-strain relationship of the single-layer fabric in the Ogden foam constitutive model to obtain the test parameters of the single-layer fabric; and then according to the testing parameters of the single-layer polymer foam and the testing parameters of the single-layer fabric, predicting the stress-strain relationship of the polymer foam and fabric combination by utilizing finite element simulation. Therefore, the method can predict the stress strain of a large number of multilayer polymer foam matched fabric combinations, and has the advantages of high prediction accuracy, simplicity and practicability.
2. In the stress-strain relationship of the single-layer polymer foam in the uniaxial compression test, the numerical values of the test parameters are continuously adjusted by an inverse analysis method until the target amount calculated by a finite element is matched with the test data, so that the problem that the initial parameters of the uniaxial compression data are large due to the fact that the polymer foam generates shear stress on the side wall and the bottom side edge of the disc when the single-layer polymer foam is pressed down by uniaxial compression is solved.
3. Because the modeling and material definition of the silk floss are difficult in finite element simulation, the invention utilizes a layer of low-elasticity foam to replace the silk floss between the polymer foam and the fabric, the structure is not much different from the actual structure, and the feasibility is realized.
4. Due to the fact that the large deformation of the polymer foam and fabric combination can cause the whole grids of the upper layer model and the lower layer model to be greatly distorted, and the change of material rigidity caused by distortion can easily cause the calculation result not to be converged, the method adopts hexahedron grids, utilizes a finite element grid division technology to respectively carry out grid division on the polymer foam and fabric combination, and meanwhile, a load step and a load sub-part are arranged to improve the convergence.
5. In the Ansys Workbench, the contact among the fabric, the polymer foam and the uniaxial compression end is set as binding contact, rather than friction (friction coefficient), and is carried out according to the fact that the polymer foam and the fabric combination do not slide in practical experiments, namely, the contact surfaces are in initial contact in the normal direction and the tangential direction, relative sliding or separation between the surfaces is not allowed, the contact surfaces between the combinations can be effectively prevented from being separated due to deformation, and the accuracy of analysis results is further ensured.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a single layer polymer foam stress strain fitting process;
FIG. 3 is a simplified schematic representation of a combination of a face fabric and a polymer foam;
FIG. 4 is a diagram illustrating the result of the meshing 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 comparing the finite element prediction results of Foam A + Foam B + Cloth + Silk walking with the test results;
FIG. 7 is a graph comparing the finite element prediction results of Foam A + Foam B + PU + Silk walking with the test results;
FIG. 8 is a graph comparing the finite element prediction results of Foam A + Foam B + PVC + Silk walking with the test results.
Detailed Description
The present invention will be further described with reference to the following examples and drawings, but the present invention is not limited thereto.
Example (b): the finite element analysis method of the stress-strain relationship of the elastic material of the sofa seat surface is carried out according to the following steps as shown in figure 1:
s1, fitting the stress-strain relation of the single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method based on an Ogden foam constitutive model of Ansys Workbench to obtain the test parameters of the single-layer polymer foam; wherein the polymer foams are respectively polyether polyol foams (density is 38 kg/m)3、25kg/m3) And polyurethane foam (density of 38 kg/m)3) The size of the single-layer polymer Foam test piece is 740mmx740mmx100mm, and the single-layer polyether polyol Foam with the density of 38kg/m3 is named as Foam A and the single-layer polyether polyol with the density of 25kg/m3Foam designated Foam B, single layer polyurethane Foam having a density of 38kg/m3 designated 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 the principal amount of stretch based on the levocoxy-green tensor, and is given by the following equation:
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. ofiInitial coefficient of shear modulus, αiBeing a fundamental parameter of the material, betaiIs compressibility factor, J is elastic volume ratio, λiIs the main elongation, and N is the order of the model;
simplifying the above equation, finding the principal direction of elongation λ for the strain potential W2Derivation of (a), nominal stress sigma in the direction of principal elongation lambda2The load direction is calculated as:
wherein: lambda [ alpha ]2Expressed as:
in the formula, lambda is the elongation in the stretching direction, L is the length of the polymer foam test piece in the axial pressure direction when the polymer foam test piece is not deformed, delta L is the axial pressure of the polymer foam test piece, and epsilon is the strain in the elongation direction;
elastic volume ratio J ═ λ1λ2λ3Formula 4;
in the form of a single-layer polymer foam, the Poisson's ratio viNeglect at λ in case of 01Direction sum lambda3The amount of stretching in the process, i.e. λ2＝λ，λ1＝λ3＝1；
Compressibility factor
In the formula, in Poisson's ratio viAt 0, the compressibility factor βiIs also 0;
the elastic volume ratio J is defined as λ during uniaxial compression test2The elongation ratio in the direction, and therefore the formula of the stress-strain relationship can be derived as follows:
in the formula, v0Expressed as the deformed volume of the polymer foam test piece, and v is the undeformed volume of the polymer foam test piece;
lambda of polymer foam during uniaxial compression2The elongation ratio in the direction is expressed as:
substituting equations 6 and 7 into equation 1, and then deriving the principal elongation direction for the strain potential, thus deriving the nominal stress-strain relationship for the polymer foam under uniaxial compression:
in the process of fitting a single layer of polymer foam, the error is caused by the fact that the polymer foam generates shear stress on the side walls and bottom side edges of the disk when the disk is pressed down, and this shear stress is not present in equation 8, resulting in a large initial parameter for fitting uniaxial compression data using equation 8. Therefore, in this embodiment, as shown in fig. 2, the values of the test parameters are continuously adjusted by inverse analysis until the target values calculated by the finite elements are matched with the test data, wherein the values obtained by fitting are shown in table 1:
TABLE 1
S2, fitting the stress-strain relation of the single-layer fabric based on an Ogden constitutive model of Ansys Workbench to obtain the test parameters of the single-layer fabric; the fabric is respectively PVC (polyvinyl chloride), PU (polyurethane) and Cloth, the size of the fabric test piece is 100mmx25mm, and the thickness is 2 mm.
Specifically, in the Ogden constitutive model of Ansys Workbench, the elasticity of a single-layer fabric is represented by the potential energy of elastic deformation, the strain potential of which is the main amount of stretch based on the levocauchy-green tensor, and is given by the following equation:
the parameters are defined as follows: u. ofiInitial coefficient of shear modulus, αiIs a basic parameter of the material, J is the elastic volume ratio, lambdaiIs the main elongation, and N is the order of the model; dkIs an incompressible coefficient;
since the fabric is defined as a superelastic material, the superelastic material does not change its volume when compressed, i.e., J ═ λ1λ2λ3＝1；
Transforming the above formula to obtain:
when at λ2Lambda orthogonal to the direction of uniaxial extension in the direction1、λ3Satisfy the following relationship：λ1＝λ3＝λ2 -1/2，λ21+ epsilon, formula 12;
equation 11 is based on the strain potential energy of elongation change as in the Ogden foam constitutive model, and therefore equation 12 is taken to equation 11 and is aligned with λ2And (3) carrying out derivation:
and the formula 14 is a nominal stress-strain relation of the Ogden model, and the formula can well fit the stress-strain relation of the fabric. The stress strain of the fabric obtained by the test is introduced into an Ogden constitutive model of Ansys Workbench, and test data is fitted by a fitting tool carried by the fabric to obtain simulation material parameters of the fabric, 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
And S3, according to the testing parameters of the single-layer polymer foam and the testing parameters of the single-layer fabric, predicting the stress-strain relationship of the polymer foam and fabric combination by utilizing finite element simulation. The uniaxial compression calculation simulation type of the polymer foam + fabric combination belongs to nonlinear large deformation, and the combination form of the fabric and the polymer foam is simplified in consideration of the convergence problem of the result, as shown in fig. 3. Due to the fact that the shear stress generated at the contact part of the polymer foam side wall and the fabric when the combination is compressed and deformed greatly is calculated by finite elements, the shear stress is generatedExcessive deformation of the polymer foam side fabric easily causes the problems of stress singularities and inconvergence of the results. Considering that the polymer foam side facing has less of an effect on the support of the sofa seat in the test, it is assumed that the effect of the polymer foam side facing on the sofa seat support is ignored. Meanwhile, according to the process method of modern sofa enterprises in producing and matching the elastic material of the sofa seat surface, a layer of silk floss with the thickness of about 20mm is added between double-layer polymer foam and the fabric 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 embodiment, in the combination of the polymer foam and the fabric, a layer of elastic foam with the thickness of 10mm is constructed to replace the silk floss arranged between the polymer foam and the fabric, and because of the compressibility of the silk floss, the elastic foam is defined as low-elasticity foam, and the initial coefficient u of the shear modulus isi100pa, the basic parameter a of the materialiIs 1 and the compressibility factor is 0.
The accuracy of the finite element simulation result depends on the density and quality of the model mesh to a great extent, the calculation accuracy is improved with the increase of the number of the meshes, but the calculation time is increased at the same time, so the reasonability of the number of the meshes should be paid attention to when dividing. Whether the analysis result is based on the result accuracy or the result convergence can be considered when determining the number of meshes, and a larger mesh is more favorable for the result convergence particularly for a nonlinear large deformation material. In this embodiment, the finite element simulation employs hexahedral mesh, and utilizes a finite element meshing technique to mesh the polymer foam and fabric combination, as shown in fig. 4. The method is characterized in that a loading step and a loading sub-part are arranged at the same time to improve convergence, and in the Ansys Workbench, the contact among the fabric, the polymer foam and the uniaxial compression end is set to be binding contact, namely, the contact surfaces are kept in initial contact in the normal direction and the tangential direction, the relative sliding or separation between the surfaces is not allowed, and the separation of the contact surfaces between the combination due to deformation is avoided.
In order to further verify the effectiveness of the invention, the applicant designs and prepares a mixture of Foam A + Foam B, Foam A + Foam C and Foam B + Foam C3 double-layer polymer foams, and prepares the double-layer polymer foams, silk floss and fabric into a combination of Foam A + Foam B + PVC + silk floss, Foam A + Foam C + PVC + silk floss, Foam B + Foam C + PVC + silk floss, FoA + Foam B + PU + silk floss, Foam A + Foam C + PU + silk floss, Foam B + silk floss, Foam A + Foam C + cloth + silk floss, Foam B + Foam C + cloth + silk floss and 9 double-layer polymer foams + fabric + silk floss.
The stress-strain relationship of the above combinations was tested using uniaxial compression, with reference to the American society for testing and materials Polymer foam test Standard (ASTM D3574-B1), on a TST-CD001 type mechanical tester, for single layer polymer foams, two layer polymer foam combinations, and two layer polymer foam + face stock + floss combinations. Each test is carried out for 3 times, a circular pressure plate with the diameter of 350mm is used for the test, the test piece is slowly pressed downwards at a constant speed of 100mm/min, pre-pressed to 80 percent at first, and then compressed to 65 percent of the thickness of the test piece.
Axial tensile test the PVC, PU and cloth 3 types were tested in a CMT6203 electronic universal testing machine, with reference to the specifications of the fabric in the GB/T3923.1-2013 standard for axial tensile properties. Each fabric test piece is tested for 5 times, the two ends of each fabric test piece are clamped by clamps, the clamping distance is 80mm, and a wood block is respectively fixed at the two ends to ensure that the two ends are fixed and do not slide. The axial stretching rate during loading is 100mm/min, and the upper limit of loading is 200N.
The test result shows that the axial tensile property of the PVC and the PU is obviously superior to that of the cloth, and the axial tensile strain of the PVC and the PU is obviously greater than that of the cloth after the stress values of the 3 fabrics exceed 0.5 Mpa. The uniaxial compression results show that the double-layer polymer foam combination and the double-layer polymer foam + fabric + silk floss combination can effectively improve the stress bearing capacity of the seat surface compared with 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 test data of PVC, PU and cloth 3 fabrics are obtained through a fitting tool in a finite element. Based on fitting parameters obtained by fitting, stress-strain relations of the matched 3 kinds of double-layer polymer foam, 9 kinds of double-layer polymer foam, plus material and silk floss under 12 combinations are respectively predicted in a finite element, and the prediction results are shown as
Tables 3-7 and FIGS. 5-8.
TABLE 3 (5% Strain)
TABLE 4 (10% Strain)
TABLE 5 (25% Strain)
TABLE 6 (50% Strain)
Table 7 (65% Strain)
As can be seen from the comparison of the stress strains of the bilayer polymer foam combinations in FIGS. 5-8 and tables 3-7, the relative error between the finite element prediction results and the test results for the bilayer polymer foam combinations was within 46.6%, and the relative error between the finite element prediction results and the test results for the bilayer polymer foam + face material + floss silk combination was within 64.7%. In the method of the present invention, the stress-strain relationship of a bi-layer polymer foam composition is predicted based on the material parameters of a single-layer polymer foam. And similarly, the stress-strain relation of the combination of the double-layer polymer foam, the fabric and the silk floss is predicted by depending on a reasonable prediction result of the combination of the double-layer polymer foam and a test result of the axial tension of the fabric. As seen from tables 3-7, at 5% strain, there is also a significant difference in the relative error between the finite element prediction results and the test results for the combination of the two-layer polymer foam + face material + floss silk due to the difference in the polymer foam. The comparative analysis result of finite element analysis and mechanical test shows that: the stress-strain relationship of the sofa seat surface elastic material combination can be effectively predicted by applying a finite element analysis method, and the result shows that when the strain of the sofa seat surface elastic material combination is 15-65%, the relative error between the finite element prediction result and the test result is 0-29%, which proves that the method has good prediction accuracy. And because the silk floss is difficult to model and define in finite element simulation, the invention utilizes a layer of low-elasticity foam to replace the silk floss between the polymer foam and the fabric, and the prediction result of the combination of the double-layer polymer foam, the fabric and the silk floss shows that the method has certain rationality.
In conclusion, the invention can effectively predict the stress-strain relationship of the sofa seat surface elastic material combination, thereby facilitating the subsequent improvement and optimization of the sofa seat surface elastic material, and having the advantages of simplicity and practicability.
Claims (7)
1. The finite element analysis method of the stress-strain relationship of the elastic material of the sofa seat surface is characterized in that: the method comprises the following steps:
s1, fitting the stress-strain relation of the single-layer polymer foam in a uniaxial compression test by using a nonlinear least square method based on an Ogden foam constitutive model of Ansys Workbench to obtain the simulation material parameters of the single-layer polymer foam;
s2, fitting the stress-strain relation of the single-layer fabric based on an Ogden constitutive model of Ansys Workbench to obtain the simulation material parameters of the single-layer fabric;
and S3, predicting the stress-strain relation of the polymer foam and fabric combination by utilizing finite element simulation according to the simulation material parameters of the single-layer polymer foam and the single-layer fabric.
2. A finite element analysis method of the stress-strain relationship of the resilient material of the sofa seat as claimed in claim 1, wherein: 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, the strain potential of which is the principal amount of stretch based on the levocoxy-green tensor, and is given by the following equation:
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. ofiInitial coefficient of shear modulus, αiBeing a fundamental parameter of the material, betaiIs compressibility factor, J is elastic volume ratio, λiIs the main elongation, and N is the order of the model;
simplifying the above equation, finding the principal direction of elongation λ for the strain potential W2Derivation of (a), nominal stress sigma in the direction of principal elongation lambda2The load direction is calculated as:
wherein: lambda [ alpha ]2Expressed as:
in the formula, lambda is the elongation in the stretching direction, L is the length of the polymer foam test piece in the axial pressure direction when the polymer foam test piece is not deformed, delta L is the axial pressure of the polymer foam test piece, and epsilon is the strain in the elongation direction;
elastic volume ratio J ═ λ1λ2λ3Formula 4;
in the form of a single-layer polymer foam, the Poisson's ratio viNeglect at λ in case of 01Direction sum lambda3The amount of stretching in the process, i.e. λ2＝λ，λ1＝λ3＝1；
Compressibility factor
In the formula, in Poisson's ratio viAt 0, the compressibility factor βiIs also 0;
the elastic volume ratio J is defined as λ during uniaxial compression test2The elongation ratio in the direction, and therefore the formula of the stress-strain relationship can be derived as follows:
in the formula, v0Expressed as the deformed volume of the polymer foam test piece, and v is the undeformed volume of the polymer foam test piece;
lambda of polymer foam during uniaxial compression2The elongation ratio in the direction is expressed as:
substituting equations 6 and 7 into equation 1, and then deriving the principal elongation direction for the strain potential, thus deriving the nominal stress-strain relationship for the polymer foam under uniaxial compression:
3. a finite element analysis method of the stress-strain relationship of the resilient material of the sofa seat as claimed in claim 2, wherein: 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 the fitting uniaxial compression data is larger due to the fact that the shear stress is generated on the side wall and the bottom side edge of the disc by the polymer foam when the single-layer polymer foam is pressed down under uniaxial compression is solved.
4. A finite element analysis method of the stress-strain relationship of the resilient material of the sofa seat as claimed in claim 1, wherein: in the Ogden constitutive model of Ansys Workbench, the elasticity of a single layer fabric is represented by the potential energy of elastic deformation, which is the main amount of stretch based on the levocauchy-green tensor, and is given by:
the parameters are defined as follows: u. ofiInitial coefficient of shear modulus, αiIs a basic parameter of the material, J is the elastic volume ratio, lambdaiIs the main elongation, and N is the order of the model; dkIs an incompressible coefficient;
since the fabric is defined as a superelastic material, the superelastic material does not change its volume when compressed, i.e., J ═ λ1λ2λ31, formula 10;
transforming the above formula to obtain:
when at λ2Lambda orthogonal to the direction of uniaxial extension in the direction1、λ3The following relationship is satisfied: lambda [ alpha ]1＝λ3＝λ2 -1/2，λ21+ epsilon, formula 12;
equation 11 is based on the strain potential energy of elongation change as in the Ogden foam constitutive model, and therefore equation 12 is taken to equation 11 and is aligned with λ2And (3) carrying out derivation:
and the formula 14 is a nominal stress-strain relation of the Ogden model and is used for fitting the stress-strain relation of the fabric so as to obtain simulation material parameters of the fabric.
5. A finite element analysis method of the stress-strain relationship of the resilient material of the sofa seat as claimed in claim 1, wherein: in the polymer foam and fabric combination, 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 silk floss has the compressible property and is defined as low-elasticity foam, and the initial coefficient u of the shear modulus of the silk flossi100pa, the basic parameter a of the materialiIs 1 and the compressibility factor is 0.
6. A finite element analysis method of the stress-strain relationship of the resilient material of the sofa seat as claimed in claim 1, wherein: the finite element simulation adopts hexahedral meshes, utilizes a finite element meshing technology to respectively mesh the polymer foam matched fabric combination, and simultaneously sets a load step and a load subsection so as to improve the convergence of the result.
7. The finite element analysis method of the stress-strain relationship of the resilient material of the sofa seat as set forth in claim 6, wherein: in Ansys Workbench, the contact of the fabric, the polymer foam and the uniaxial compression end is set as binding contact, namely, initial contact is kept between contact surfaces in a normal direction and a tangential direction, relative sliding or separation between the surfaces is not allowed, and the contact surfaces between the combination are prevented from being separated due to deformation.
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