| Abstract: |
| The modeling of cavitation in nonlinear elastostatics typically rests upon the minimization of an energy functional comprising a bulk term, accounting for strain concentration, and a surface term proportional to the area of the cavity boundaries. Motivated by studies on void stability and the search for a regularizing effect, we propose a variational model featuring a surface term that depends on the curvature of the cavity boundaries. The rigorous formulation employs oriented varifolds on the deformed configuration and is based on a suitable coupling between these varifolds and the underlying deformation. Our main findings ensure the well-posedness of the resulting free-discontinuity problem and identify first-order necessary conditions for minimality. |
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