Again anti-plane shear

Abstract

We reconsider anti-plane shear deformations of the form $\phi (x)=(x_1,x_2,x_3+u(x_1,x_2))$ 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.

References in corpus (4)

• Geometry of logarithmic strain measures in solid mechanics
• Remarks on Analytic Solutions in Nonlinear Elasticity and Anti-Plane Shear Problem
• Analytical Solutions to General Anti-Plane Shear Problems In Finite Elasticity
• Duality in G. Saccomandi's Challenge on Analytical Solutions to Anti-plane Shear Problem in Finite Elasticity

Cited by in corpus (2)

• Shear, pure and simple
• Global bifurcation of anti-plane shear fronts