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Generalisation of Hooke's law for finite strain to include the elastic range of strain-hardening materials

机译:包含应变硬化材料的弹性范围的有限应变的胡克定律的推广

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摘要

The representation theorem for isotropic tensor-valued functions of symmetric second-order tensors is considered in the context of two parameters based on the Lode and Fromm parameters. A geometrical representation is established using the concept of a characteristic representation intensity function. It is shown that this geometrical representation identifies the only admissible form of the representation intensity function to be piecewise linear and continuous. This conclusion imposes a restriction on how the representation theorem can be used to formulate constitutive equations. The representation theorem is used to formulate a generalisation of Hooke's law for finite strain that is applicable to the initial elastic range of strain-hardening materials, including the elastic conditions at initial yield.
机译:在基于Lode和Fromm参数的两个参数的情况下,考虑对称二阶张量的各向同性张量值函数的表示定理。使用特征表示强度函数的概念来建立几何表示。结果表明,该几何表示将表示强度函数的唯一允许形式标识为分段线性和连续的。该结论对如何使用表示定理来构造本构方程施加了限制。表示定理用于对适用于应变硬化材料的初始弹性范围(包括初始屈服时的弹性条件)的有限应变的胡克定律进行概括。

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