经典场的应力理论
Stress theory for classical fields
摘要：
经典的场论与拉格朗日和欧拉方法的连续介质力学被拥抱下的几何设置的纤维束。基流形可以是连续介质力学的体流形、空间流形或时空流形。纤维丛的可微截面表示系统的构形，包含它们的构形空间被赋予无穷维流形的结构。位形空间的余切丛的元素被解释为广义力，一个表示定理意味着存在一个表示力的应力对象，非唯一。的属性的应力的研究，以及在目前的一般设置的本构关系的作用。
英文摘要：
Classical field theories together with the Lagrangian and Eulerian approaches to continuum mechanics are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, space manifold, or space-time. Differentiable sections of the fiber bundle represent configurations of the system and the configuration space containing them is given the structure of an infinite dimensional manifold. Elements of the cotangent bundle of the configuration space are interpreted as generalized forces and a representation theorem implies that there exist a stress object representing forces, non-uniquely. The properties of stresses are studies as well as the role of constitutive relations in the present general setting.
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