This study is concerned with a new,explicit approach by means of which forms of the large strain elastic potential for multiaxial rubberlike elasticity may be obtained based on data for a single deformation mode.As a ...This study is concerned with a new,explicit approach by means of which forms of the large strain elastic potential for multiaxial rubberlike elasticity may be obtained based on data for a single deformation mode.As a departure from usual studies,here for the first time errors may be estimated and rendered minimal for all possible deformation modes and,furthermore,failure behavior may be incorporated.Numerical examples presented are in accurate agreement with Treloar＇s well-known data.展开更多
By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduce...By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multi axial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders （Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII： experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251-288 （1951））. Good agreement is achieved with these extensive data.展开更多
An explicit, exact approach is proposed to obtain multi-axial elastic potentials for isotropic rubber-like materials undergoing large incompressible deformations. By means of two direct, explicit procedures, this appr...An explicit, exact approach is proposed to obtain multi-axial elastic potentials for isotropic rubber-like materials undergoing large incompressible deformations. By means of two direct, explicit procedures, this approach reduces the problem of determining multi-axial poten- tials to that of determining one-dimensional elastic potentials. To this end, two one-dimensional potentials for uniaxial case and simple shear case are respectively determined via spline inter- polation and, then, the two potentials are extended to generate a multi-axial elastic potential using a novel method based on certain logarithmic invariants. Eventually, each of the multi-axial potentials will exactly match the finite strain data from four benchmark tests.展开更多
An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is esta...An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.展开更多
A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-s...A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.展开更多
基金the support of the start-up fund from the Education Committee of China through Shanghai University(Grant S.15-B002-09-032)the fund for research innovation from Shanghai University(Grants S.10-0401-12-001)the fund from Natural Science Foundation of China(Grants 11372172,11472164)
文摘This study is concerned with a new,explicit approach by means of which forms of the large strain elastic potential for multiaxial rubberlike elasticity may be obtained based on data for a single deformation mode.As a departure from usual studies,here for the first time errors may be estimated and rendered minimal for all possible deformation modes and,furthermore,failure behavior may be incorporated.Numerical examples presented are in accurate agreement with Treloar＇s well-known data.
基金Project supported by the National Natural Science Foundation of China(No.11372172)the 211-Plan of the Education Committee of China(No.A.15-B002-09-032)the Research Innovation Fund of Shanghai University(No.A.10-0401-12-001)
文摘By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multi axial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders （Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII： experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251-288 （1951））. Good agreement is achieved with these extensive data.
基金supported by the fund for innovative research from Shanghai University(No.A10-0401-12-001)the startup fund from the 211-project of the Education Committee of China through Shanghai University(No.A15-B002-09-032)
文摘An explicit, exact approach is proposed to obtain multi-axial elastic potentials for isotropic rubber-like materials undergoing large incompressible deformations. By means of two direct, explicit procedures, this approach reduces the problem of determining multi-axial poten- tials to that of determining one-dimensional elastic potentials. To this end, two one-dimensional potentials for uniaxial case and simple shear case are respectively determined via spline inter- polation and, then, the two potentials are extended to generate a multi-axial elastic potential using a novel method based on certain logarithmic invariants. Eventually, each of the multi-axial potentials will exactly match the finite strain data from four benchmark tests.
文摘An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.
文摘A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.
