论文标题
通过使用扩展的Noether的形式主义，在力学中采用基于能量的方法
Energy based methods applied in mechanics by using the extended Noether's formalism
论文作者
论文摘要
物理系统由字段方程建模；这些是空间和时间上的偏微分方程的耦合。场方程通常由平衡方程和本构方程给出，其中前者是公理给出的，后者是热力学得出的。这种方法在热力学和电磁学中很有用，但是一旦将其应用于损害机制中，就会出现挑战。为了得出管理方程式，另一种方法是基于一个被称为扩展的Noether形式主义的变异框架。它的正式介绍依赖于数学概念，限制了其在应用机制中用作现场理论的使用。在这项工作中，我们通过使用张量代数和常规的连续性力学命名来证明扩展Noether的形式主义的力量。我们证明了广义连续性损伤力学中场方程的推导，特别是在应变梯度弹性的情况下。
Physical systems are modeled by field equations; these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former are axiomatically given and the latter are thermodynamically derived. This approach is useful in thermomechanics and electromagnetism, yet challenges arise once we apply it in damage mechanics for generalized continua. For deriving governing equations, an alternative method is based on a variational framework known as the extended Noether's formalism. Its formal introduction relies on mathematical concepts limiting its use in applied mechanics as a field theory. In this work, we demonstrate the power of extended Noether's formalism by using tensor algebra and usual continuum mechanics nomenclature. We demonstrate derivation of field equations in damage mechanics for generalized continua, specifically in the case of strain gradient elasticity.
