Cavitation instabilities in soft solids: A defect-growth theory and applications to elastomers

O. LOPEZ-PAMIES; T. NAKAMURA; M. I. IDIART

Puerto España

Congreso; XII Pan American Congress of Applied Mechanics; 2012

American Academy of Mechanics

This work introduces a new theory to study the phenomenon of cavitation in soft solids that simultaneously: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as the homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. Then, by means of a novel iterated homogenization procedure, exact solutions are constructed for such a problem. These include solutions for the change in size of the underlying cavities as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal cavities suddenly grow into finite sizes — can be readily determined.In addition to the theory, we will also present a corresponding effective numerical approach to study cavitation instabilities in nonlinear elastic solids. Here, the basic idea is to examine — by means of a 3D finite element model — the mechanical response under affine boundary conditions of a block of nonlinear elastic material that contains a single infinitesimal defect at its center. The occurrence of cavitation is identified as the event when the initially small defect suddenly grows to a much larger size in response to sufficiently large applied loads.Applications of the theory and finite-element simulations to the case of isotropic solids containing a random isotropic distribution of vacuous defects will be presented.