On the instability, nonexistence and spatial behaviour of the one-dimensional response of a new class of elastic bodies

descriptionPublicationkeyboard_double_arrow_right Article 22 May 2021 English Publisher:Oxford University Press (OUP)Journal:IMA Journal of Applied Mathematics, volume 86, pages 565-576 (issn: 0272-4960, eissn: 1464-3634,

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Authors: Quintanilla de Latorre, Ramón; Rajagopal, Kumbakonam;

doi: 10.1093/imamat/hxab014

handle: 2117/347518

On the instability, nonexistence and spatial behaviour of the one-dimensional response of a new class of elastic bodies

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Abstract

Abstract In this note we consider 1D problems within the context of a new class of elastic bodies. Under suitable conditions on the constitutive equations we prove instability and nonexistence of solutions similar to those in place for the linearized theory. The last section is devoted to describing the spatial behavior of the solutions.

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
The University of Texas System
United States
Universitat Politècnica de Catalunya
Spain
Texas A&M University
United States

Keywords

linearized strain, :74 Mechanics of deformable solids::74B Elastic materials [Classificació AMS], Classificació AMS::80 Classical thermodynamics, Nonlinear elasticity, spatial behaviour, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Classificació AMS::74 Mechanics of deformable solids::74B Elastic materials, Elastic solid., Nonexistence of solutions, Thermoelasticity, Cauchy-Green tensor, :80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer [Classificació AMS], Elastic solid, Elastic solids -- Mathematics, Instability, Cauchy stress tensor, Spatial behaviour, Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer, Existence of solutions of dynamical problems in solid mechanics, nonexistence, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Sòlids elàstics -- Matemàtica, heat transfer::80A Thermodynamics and heat transfer, PDEs in connection with mechanics of deformable solids, Termoelasticitat, Stability of dynamical problems in solid mechanics, displacement instability

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