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Stress and strain mapping tensors and general work-conjugacy in large strain continuum mechanics

机译：大应变连续力学中的应力和应变映射张量和一般功共轭

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摘要

In this paper we show that mapping tensors may be constructed to transform any arbitrary strain measure in any other strain measure. We present the mapping tensors for many usual strain measures in the Seth-Hill family and also for general, user-defined ones. These mapping tensors may also be used to transform their work-conjugate stress measures. These transformations are merely geometric transformations obtained from the deformation gradient and, hence, are valid regardless of any constitutive equation employed for the solid. Then, advantage of this fact may be taken in order to simplify the form of constitutive equations and their numerical implementation and thereafter, perform the proper geometric mappings to convert the results -stresses, strains and constitutive tangents- to usually employed measures and to user-selectable ones for input and output We herein provide the necessary transformations. Examples are the transformation of small strains formulations and algorithms to large deformations using logarithmic strains.
机译：在本文中，我们表明可以构造映射张量来转换任何其他应变量度中的任意应变量度。我们介绍了Seth-Hill系列中许多常用应变量度以及用户定义的一般量度的映射张量。这些映射张量也可以用于转换其共轭应力测量值。这些变换仅仅是从变形梯度获得的几何变换，因此，无论用于实体的本构方程如何，这些变换都是有效的。然后，可以利用这一事实的优势来简化本构方程的形式及其数值实现，然后执行适当的几何映射以将结果（应力，应变和本构切线）转换为通常采用的度量并转换为用户用于输入和输出的可选变量我们在此提供必要的转换。示例是使用对数应变将小应变公式和算法转换为大变形。

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