Explicit formulations of tangent stiffness tensors for isotropic materials

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 q 2006 John Wiley & Sons, Ltd