A generalized theory of stress and strain tensor measures in the classical continuum mechanics is discussed: the main axioms of the theory are proposed, the general formulas for new tensor measures are derived, arid an energy conjugate theorem is formulated to distinguish the complete Lagrangian class of measures. As a subclass, a simple Lagrangian class of energy conjugate measures of stresses and finite strains is constructed in which the families of holonomic and corotational measures are distinguished. The characteristics of holonomic and corotational measures are studied by comparing the tensor measures of the simple Lagrangian class with one another and with logarithmic measures. For the simple Lagrangian class and its families, their completeness and closure are shown with respect to the choice of a generating pair of energetically conjugate measures. The applications of the new tensor measures in modeling the properties of plasticity, viscoelasticity, and shape memory are mentioned.

中文翻译：

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经典连续体力学中的应力和应变测度的广义理论

讨论了经典连续力学中的应力和应变张量测度的广义理论：提出了该理论的主要公理，推导了新张量测度的通用公式，并制定了能量共轭定理来区分完整的拉格朗日类。措施。作为一个子类，构建了简单的拉格朗日应力和有限应变能量共轭测度类，其中区分了完整的和整洁的测度族。通过比较简单拉格朗日类的张量量度和对数量度，研究了完整和整齐量度的特征。对于简单的拉格朗日阶层及其家庭，关于生成一对能量共轭量度的选择，显示了它们的完整性和闭合性。提到了新的张量度量在建模可塑性，粘弹性和形状记忆特性中的应用。