On strong ellipticity for implicit and strain-limiting theories of elasticity

DOI10.1177/1081286514544254OpenAlexW2115636002MaRDI QIDQ5136821

Tina Mai, Jay R. Walton

Publication date: 27 November 2020

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1081286514544254

zbMATH Keywords

strong ellipticityimplicit theories of elasticitystrain-limiting elasticity

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX)

Related Items (8)

Ellipticity of gradient poroelasticity ⋮ Generalized Multiscale Finite Element Treatment of a Heterogeneous Nonlinear Strain-limiting Elastic Model ⋮ Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity ⋮ Finite element simulation of quasi-static tensile fracture In nonlinear strain-limiting solids with the phase-field approach ⋮ Finite element model for a coupled thermo-mechanical system in nonlinear strain-limiting thermoelastic body ⋮ Global existence of solutions for the one-dimensional response of viscoelastic solids within the context of strain-limiting theory ⋮ On monotonicity for strain-limiting theories of elasticity ⋮ A finite-element discretization of some boundary value problems for nonlinear strain-limiting elastic bodies

Cites Work

• On a new class of models in elasticity
• Sufficient conditions for strong ellipticity for a class of anisotropic materials
• On strong ellipticity for isotropic hyperelastic materials based upon logarithmic strain
• On the failure of ellipticity of the equations for finite elastostatic plane strain
• The elasticity of elasticity
• A numerical study of a plate with a hole for a new class of elastic bodies
• Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack
• Non-Linear Elastic Bodies Exhibiting Limiting Small Strain
• Conspectus of concepts of elasticity
• The Convexity Properties of a Class of Constitutive Models for Biological Soft Issues
• A Note on Plane Strain and Plane Stress Problems for a New Class of Elastic Bodies
• On the inhomogeneous shearing of a new class of elastic bodies
• On a new class of electroelastic bodies. I
• On a new class of electro-elastic bodies. II. Boundary value problems
• On the response of non-dissipative solids
• Nonlinear problems of elasticity

This page was built for publication: On strong ellipticity for implicit and strain-limiting theories of elasticity