| A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green tensor |
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| 作者姓名： | TIAN Dongyan JIN Ming DUI Guansuo |
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| 作者单位： | Institute of Engineering Mechanics, School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, China |
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| 基金项目： | Supported by the school foundation of Beijing Jiaotong University (Grant No. TJ2002J0180) |
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| 摘 要： | A new approach for the derivation of the principal invariants of the stretch tensor with respect to the right Cauchy-Green tensor is presented in this paper. According to the definition of the derivation of tensor function, the three first-order derivatives for the principal invariants of the stretch tensor are obtained through derivation directly to the right Cauchy-Green tensor by incremental method. Then the three second-order derivatives are yielded by the derivation to the right Cauchy-Green strain tensor directly. Furthermore, an explicit expression of the tangent modulus of the general Varga material is given as an example.
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| 关 键 词： | continuum mechanics invariant strain energy tangent modulus. |
A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green tensor |
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| TIAN Dongyan,JIN Ming,DUI Guansuo.A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green tensor[J].Progress in Natural Science,2006,16(1):96-99. |
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| Authors: | TIAN Dongyan JIN Ming DUI Guansuo |
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| Institution: | Institute of Engineering Mechanics, School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, China |
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| Abstract: | A new approach for the derivation of the principal invariants of the stretch tensor with respect to the right Cauchy-Green tensor is presented in this paper. According to the definition of the derivation of tensor function, the three first-order derivatives for the principal invariants of the stretch tensor are obtained through derivation directly to the right Cauchy-Green tensor by incremental method. Then the three second-order derivatives are yielded by the derivation to the right Cauchy-Green strain tensor directly. Furthermore, an explicit expression of the tangent modulus of the general Varga material is given as an example. |
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| Keywords: | continuum mechanics invariant strain energy tangent modulus |
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