A lower bound for the void coalescence load in nonlinearly elastic\n solids

2019/06/25 by Victor Cañulef-Aguilar, Cañulef-Aguilar, Victor, Duvan Henao +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1906.10360

openalex publication_date 2019/06/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

The problem of the sudden growth and coalescence of voids in elastic media is\nconsidered. The Dirichlet energy is minimized among incompressible and\ninvertible Sobolev deformations of a two-dimensional domain having n\nmicrovoids of radius \ε. The constraint is added that the cavities\nshould reach at least certain minimum areas v₁,...,v_n after the\ndeformation takes place. They can be thought of as the current areas of the\ncavities during a quasistatic loading, the variational problem being the way to\ndetermine the state to be attained by the elastic body in a subsequent time\nstep. It is proved that if each v_i is smaller than the area of a disk\nhaving a certain well defined radius, which is comparable to the distance, in\nthe reference configuration, to either the boundary of the domain or the\nnearest cavity (whichever is closer), then there exists a range of external\nloads for which the cavities opened in the body are circular in the\n\ε \→ 0 limit.\n

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