Quasistatic evolution models for thin plates arising as low energy Gamma-limits of finite plasticity

2013/05/02 by Elisa Davoli, Davoli, Elisa · 1 citation
Computer Science · Engineering · Mathematics · #49J45) #74C05 (74G65 #74K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics #math.AP #msc:74C05 #msc:74K20

paper · pdf · doi:10.48550/arxiv.1305.0477

49 pages

arxiv created 2013/05/02 · openalex publication_date 2013/05/02 · arxiv updated 2013/05/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we deduce by Γ-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we study the case where the scaling factor of the elasto- plastic energy is of order ε^ (2α-2), with α>=3. We show that solutions to the three- dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on α.

Citations

• Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials
• 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

• Derivation of Kirchhoff-type plate theories for elastic materials with voids

Related

• Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: the limiting regimes
• Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure
• Quasistatic evolution for dislocation-free finite plasticity
• Quasistatic evolution problems for linearly elastic - perfectly plastic materials
• Globally stable quasistatic evolution in plasticity with softening