Shocks and induced discontinuities in materials with internal state variables - Applications to finite linear viscoelasticity
type: Item
instance of: scholarly article
title: Shocks and induced discontinuities in materials with internal state variables - Applications to finite linear viscoelasticity
zbMATH Open document ID: 0586.73048
DOI: 10.1007/BF01176356
author: Peter J. Chen
author: Paul. B. Bailey
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: In this paper, we derive the coupled governing differential equations of shock amplitudes and induced discontinuities in materials with internal state variables. For the special case of finite linear viscoelasticity and weak shocks and under physically reasonable conditions, two examples of the solutions of the coupled equations are given. In the first example, the solutions of the shock and the induced discontinuity approach finite non-zero values in an oscillatory manner, very much akin to the forced vibrations of spring-mass-damper systems. In the second example, both solutions decay monotonically to zero.
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 74M20
zbMATH DE Number: 3940838
zbMATH Keywords: theory of singular surfaces
zbMATH Keywords: reduced form of equations
zbMATH Keywords: numerical solutions
zbMATH Keywords: compression shock
zbMATH Keywords: necessary condition for existence of steady shock
zbMATH Keywords: coupled governing differential equations
zbMATH Keywords: shock amplitudes
zbMATH Keywords: induced discontinuities
zbMATH Keywords: internal state variables
zbMATH Keywords: finite linear viscoelasticity
zbMATH Keywords: weak shocks
MaRDI profile type: Publication
cites work: Q4146306
cites work: Growth and Decay of One-Dimensional Shock Waves in Fluids with Internal State Variables
cites work: On the growth of one-dimensional shock waves in materials with memory
cites work: Q5848416
Recommended article: On the local and global behavior of weak shocks and induced discontinuities in a class of materials with internal state variables
Recommended article: The behavior of induced discontinuities behind curved shocks in isotropic linear elastic materials
Recommended article: Q5291248
Recommended article: On induced discontinuities in a class of linear materials with internal state parameters
Recommended article: Existence and stability of viscoelastic shock profiles
Recommended article: Shock Structure in Viscoelastic Materials
Recommended article: Stability of shock profiles in viscoelasticity with non‐convex constitutive relations
Recommended article: Dynamics of discontinuities in elastic solids
Recommended article: Existence of Shock Profiles for Viscoelastic Materials with Memory
Recommended article: Q4013038
description: scientific article; zbMATH DE number 3940838