{"paper":{"title":"A calibration method for estimating critical cavitation loads from below in 3D nonlinear elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jonathan H. B. Deane, Jonathan J. Bevan","submitted_at":"2017-07-26T16:45:58Z","abstract_excerpt":"In this paper we give an explicit sufficient condition for the affine map $u_\\lambda(x):=\\lambda x$ to be the global energy minimizer of a general class of elastic stored-energy functionals $I(u)=\\int_{\\Omega} W(\\nabla u)\\,dx$ in three space dimensions, where $W$ is a polyconvex function of $3 \\times 3$ matrices. The function space setting is such that cavitating (i.e., discontinuous) deformations are admissible. In the language of the calculus of variations, the condition ensures the quasiconvexity of $I(\\cdot)$ at $\\lambda \\mathbf{1}$, where $\\mathbf{1}$ is the $3 \\times 3$ identity matrix. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08532","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}