Invariants of the Stretch Tensors and their Application to Finite Elasticity Theory
Invariants of the Stretch Tensors and their Application to Finite Elasticity Theory
复制标题
拉伸张量的不变量及其在有限弹性理论中的应用
DOI：
10.1177/108128028481
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发表时间：
2002
影响因子：
2.6
通讯作者：
D. Steigmann
中科院分区：
文献类型：
--
作者：
D. Steigmann
变形梯度极分解中拉伸张量的主不变量与其平方的主不变量，即柯西-格林变形张量，呈一一对应关系。这些关系被用来得到第一组不变量对变形梯度的导数。后者将极分解中的拉伸和旋转因子作为变形梯度的显式函数表示出来，并推导出各向同性弹性材料的应力和弹性模量的新公式。
The principal invariants of the stretch tensors in the polar decomposition of the deformation gradient stand in one-to-one relation to the principal invariants of their squares, the Cauchy—Green deformation tensors. These relations are used to obtain the derivatives of the first set of invariants with respect to the deformation gradient. The latter generate expressions for the stretch and rotation factors in the polar decomposition as explicit functions of the deformation gradient, and lead to new formulae for the stress and elastic moduli for isotropic elastic materials.