A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of jacobians

Alexey Miroshnikov; Athanasios E. Tzavaras

doi:10.4310/CMS.2012.v10.n1.a5

A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of jacobians

Alexey Miroshnikov^*, Athanasios E. Tzavaras

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter.

Original language	English (US)
Pages (from-to)	87-115
Number of pages	29
Journal	COMMUNICATIONS IN MATHEMATICAL SCIENCES
Volume	10
Issue number	1
DOIs	https://doi.org/10.4310/CMS.2012.v10.n1.a5
State	Published - Mar 2012
Externally published	Yes

Keywords

Elasticity
Polyconvex
Variational approximation

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4310/CMS.2012.v10.n1.a5

Cite this

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title = "A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of jacobians",

abstract = "We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter.",

keywords = "Elasticity, Polyconvex, Variational approximation",

author = "Alexey Miroshnikov and Tzavaras, {Athanasios E.}",

year = "2012",

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doi = "10.4310/CMS.2012.v10.n1.a5",

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AU - Tzavaras, Athanasios E.

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N2 - We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter.

AB - We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter.

KW - Elasticity

KW - Polyconvex

KW - Variational approximation

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U2 - 10.4310/CMS.2012.v10.n1.a5

DO - 10.4310/CMS.2012.v10.n1.a5

M3 - Article

AN - SCOPUS:84855434929

SN - 1539-6746

VL - 10

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JF - COMMUNICATIONS IN MATHEMATICAL SCIENCES

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A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of jacobians

Abstract

Keywords

ASJC Scopus subject areas

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