An Iterated Homogenization Method to Study Cavitation in Hyperelastic Solids

O. LOPEZ-PAMIES; M. I. IDIART

Filadelfia (PA)

Conferencia; SIAM Conference on Mathematical Aspects of Materials Science; 2010

Society for Industrial and Applied Mathematics

We propose a novel formulation to study cavitation in solids that: (i) is applicable to large classes of nonlinear elastic materials, (ii) allows for 3D general loading conditions with arbitrary triaxility, (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate, and (iv) is, at the same time, computationally tractable. The proposed framework is based on an iterated homogenization method that allows for the construction of exact solutions for the mechanical response of nonlinear elastic materials containing random distributions of initially infinitesimal cavities (or defects). The relevant analysis reduces to the study of Hamilton-Jacobi equations in which the initial size of the cavities plays therole of time and the applied load plays the role of space.