当视界趋于零时，基于键的周波学不收敛于超弹性
Bond-based peridynamics does not converge to hyperelasticity as the horizon goes to zero
摘要：
基于键的周向动力学是固体力学中的一种非局部连续介质模型，其中变形能量通过涉及参考构型和变形构型中的点对的二重积分来计算。当视界（粒子间的最大相互作用距离）趋于零时，如何计算该模型的Γ-极限是已知的，并且该极限是定义在索伯列夫空间中的（局部）向量变分问题，属于（经典）超弹性中出现的类型。在本文中，我们在模型中加入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周期力学模型的Γ-极限。特别是，Mooney-Rivlin材料无法通过该限度程序回收。
英文摘要：
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 Γ-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 Γ-limits of the bond-based peridynamics model. In particular, Mooney-Rivlin materials are not recoverable through this limit procedure.
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