Effective yield criterion accounting for microvoid coalescence in a porous solid
A. Amine Benzerga (Texas A&M University), Jean-Baptiste Leblond (University Pierre et Marie Curie)
Symposium in honor of Rod Clifton on the occasion of his 75th Birthday
Mon 2:40 - 4:00
Salomon 101
Thomason posed a limit analysis problem for a square-prismatic unit cell containing a square-prismatic microvoid. This geometry was meant to represent a space-filling unit cell for a doubly periodic distribution of micro-voids. He used two sets of velocity fields which are both compatible with a uniaxial straining mode for the whole cell, a kinematics that is ubiquitous during the coalescence of neighboring voids in a rate-independent solid. However, Thomason did not obtain a closed-form solution to the problem he posed. Instead, he derived numerical solutions to which he proposed an empirical fit. The latter has since been widely used in the mechanics and material science communities alike. Here, we revisit the above problem focusing on a cylindrical unit cell containing a coaxial cylindrical void and subject to axisymmetric triaxial loading. We obtain a closed-form solution to the limit analysis problem, i.e., a fully analytical expression of the effective yield function. The latter can be used concurrently with a Gurson-like yield function in numerical simulations of ductile fracture. In addition, the availability of a fully analytical solution to the above 30-year old problem is a first step toward generalizations to plastic anisotropy and more general loading states.