Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in the reference and deformed configurations. It is known how to calculate the {\Gamma}-limit of this model when the horizon (maximum interaction distance between the particles) tends to zero, and the limit turns out to be a (local) vector variational problem defined in a Sobolev space, of the type appearing in (classical) hyperelasticity. In this paper, we impose frame-indifference and isotropy in the model and find that very few hyperelastic functionals are {\Gamma}-limits of the bond-based peridynamics model. In particular, Mooney-Rivlin materials are not recoverable through this limit procedure.

中文翻译：

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当地平线趋于零时，基于键的近场动力学不会收敛到超弹性

基于键的近场动力学是固体力学中的非局部连续介质模型，其中变形的能量通过涉及参考和变形配置中的点对的双积分计算。已知当视界（粒子之间的最大相互作用距离）趋于零时如何计算该模型的 {\Gamma}-极限，并且该极限结果是在 Sobolev 空间中定义的（局部）向量变分问题，出现在（经典）超弹性中的类型。在本文中，我们在模型中强加了框架无差异和各向同性，发现很少有超弹性泛函是基于键的近场动力学模型的 {\Gamma} 极限。特别是，Mooney-Rivlin 材料无法通过此限制程序恢复。