Again anti-plane shear

2018/03/01 by Jendrik Voss, Voss, Jendrik, Herbert Baaser +5
Engineering · #Analysis of PDEs (math.AP) #Composite Material Mechanics #Dynamics and Control of Mechanical Systems #Elasticity and Material Modeling #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1803.00265

openalex publication_date 2018/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reconsider anti-plane shear deformations of the form φ(x)=(x₁, x₂, x₃+u(x₁,x₂)) based on prior work of Knowles and relate the existence of anti-plane shear deformations to fundamental constitutive concepts of elasticity theory like polyconvexity, rank-one convexity and tension-compression symmetry. In addition, we provide finite-element simulations to visualize our theoretical findings.

Citations

• Convexity conditions and existence theorems in nonlinear elasticity

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