Bond-Based Peridynamics Does Not Converge to Hyperelasticity as the Horizon Goes to Zero

被引：16
作者：
Bellido, J. C. [1 ,2 ]
Cueto, J. [1 ,2 ]
Mora-Corral, C. [3 ]
机构：
[1] Univ Castilla La Mancha, Dept Matemat, ETSI Ind, Ciudad Real 13071, Spain
[2] Univ Castilla La Mancha, INEI, Ciudad Real 13071, Spain
[3] Univ Autonoma Madrid, Fac Ciencias, Dept Matemat, Madrid 28049, Spain
来源：
JOURNAL OF ELASTICITY | 2020年 / 141卷 / 02期
关键词：
Bond-based peridynamics; Hiperelasticity; Gamma-convergence as the horizon goes to zero; NONLOCAL VARIATIONAL-PROBLEMS; NAVIER EQUATION; FUNCTIONALS; EXISTENCE; LIMIT; MODEL;
D O I：
10.1007/s10659-020-09782-9
中图分类号：
T [工业技术];
学科分类号：
08 ;
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 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.
引用
收藏
页码：273 / 289
页数：17
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