Explicit formulations of tangent stiffness tensors for isotropic materials

@article{citeulike:1613757, abstract = {A compact explicit expression for the tangent stiffness tensor is presented. Throughout the analysis, the formulation holds for general isotropic elastic materials and does not require solving eigenvector problems. On the theoretical side, a very simple solution of a tensor equation is obtained. Then the expressions for the derivatives of general symmetric isotropic tensor functions of a symmetric tensor are developed. On the computational side, particular attention is given to the consideration of the special case, Green elastic materials, in which the strain energy does not admit a closed-form expression in terms of principal invariants. Finally, a simple formulation of the tangent stiffness tensor for Ogden material model is supplied. Copyright {\copyright} 2006 John Wiley \& Sons, Ltd.}, address = {Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, People's Republic of China; Civil Engineering School, Hohai University, Nanjing, 210098, People's Republic of China}, author = {Dui, Guansuo and Wang, Zhengdao and Ren, Qingwen }, citeulike-article-id = {1613757}, doi = {10.1002/nme.1776}, journal = {International Journal for Numerical Methods in Engineering}, keywords = {tensor}, number = {4}, pages = {665--675}, posted-at = {2007-09-02 17:14:42}, priority = {2}, title = {Explicit formulations of tangent stiffness tensors for isotropic materials}, url = {http://dx.doi.org/10.1002/nme.1776}, volume = {69}, year = {2007} }

TY - JOUR ID - citeulike:1613757 L3 - citeulike-article-id:1613757 TI - Explicit formulations of tangent stiffness tensors for isotropic materials JF - International Journal for Numerical Methods in Engineering VL - 69 IS - 4 SP - 665 EP - 675 AD - Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, People's Republic of China; Civil Engineering School, Hohai University, Nanjing, 210098, People's Republic of China N2 - A compact explicit expression for the tangent stiffness tensor is presented. Throughout the analysis, the formulation holds for general isotropic elastic materials and does not require solving eigenvector problems. On the theoretical side, a very simple solution of a tensor equation is obtained. Then the expressions for the derivatives of general symmetric isotropic tensor functions of a symmetric tensor are developed. On the computational side, particular attention is given to the consideration of the special case, Green elastic materials, in which the strain energy does not admit a closed-form expression in terms of principal invariants. Finally, a simple formulation of the tangent stiffness tensor for Ogden material model is supplied. Copyright © 2006 John Wiley & Sons, Ltd. KW - tensor AU - Dui, Guansuo AU - Wang, Zhengdao AU - Ren, Qingwen PY - 2007/// UR - http://dx.doi.org/10.1002/nme.1776 ER -