论文标题
非局部多凸能在非局部超弹性中的最小化器
Minimizers of Nonlocal Polyconvex Energies in Nonlocal Hyperelasticity
论文作者
论文摘要
我们发展了一种基于迪里奇（Dirichlet）边界条件下非局部梯度的媒介问题中能量功能最小化的存在理论。该模型与Peridynanic模型具有许多特征，也适用于非局部固体力学，尤其是非线性弹性。这种非本地梯度是在较早的工作中引入的，灵感来自Riesz的分数梯度，但适用于有界域。能量整体上的主要假设是多凸度。因此，我们将经典案例的相应结果调整到这种非局部情况下，特别是Piola的身份，决定因素的一部分和决定因素的弱连续性的整合。证据利用了每个非本地梯度都是经典梯度的事实。与经典弹性相反，这种存在结果与空化和断裂兼容。
We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz' fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola's identity, the integration by parts of the determinant and the weak continuity of the determinant. The proof exploits the fact that every nonlocal gradient is a classical gradient. Contrary to classical elasticity, this existence result is compatible with cavitation and fracture.
