Cavitation in elastomeric solids: I --- A defect-growth theory

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

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2011 vol. 59 p. 1464 - 1487

0022-5096

It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (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 extit{defects}. Then, by means of a novel iterated homogenization procedure, extit{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 spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton-Jacobi equations, in which the initial size of the cavities plays the role of ``time´´ and the applied load plays the role of ``space´´. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.