A New Variational Approach to Linearization of Traction Problems in Elasticity

2018/11/26 by Francesco Maddalena, Danilo Percivale, Franco Tomarelli
Computer Science · Engineering · Mathematics · #Contact Mechanics and Variational Inequalities #Elastic energy #Elasticity (physics) #Energy functional #Linearization #Maxima and minima #Nonlinear Partial Differential Equations #Nonlinear system #Theory of computation #Topology Optimization in Engineering #Traction (geology) #math.AP #math.OC #msc:49J45 #msc:74K30 #msc:74K35 #msc:74R10

paper · pdf · doi:10.1007/s10957-019-01533-8

published as J Optim Theory Appl (2019) 182: 383 · arXiv admin note: text overlap with arXiv:1810.01339

arxiv created 2018/11/26 · openalex created_date 2018/12/11 · openalex publication_date 2019/05/17 · arxiv updated 2019/07/01 · openalex updated_date 2026/08/06

Abstract

A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with respect to the weak convergence of strains when a suitable small parameter tends to zero. This functional exhibits a gap that makes it different from the classical linear elasticity functional. Nevertheless a suitable compatibility condition on the force field ensures coincidence of related minima and minimizers. Here we show some relevant properties of the new functional and prove stronger convergence of minimizing sequences for suitable choices of nonlinear elastic energies.

Citations

• The Gap Between Linear Elasticity and the Variational Limit of Finite Elasticity in Pure Traction Problems
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity
• A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence

Cited by

• The Gap Between Linear Elasticity and the Variational Limit of Finite Elasticity in Pure Traction Problems