Cargando…

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavio...

Descripción completa

Detalles Bibliográficos
Autores principales: Alexandrov, Sergei, Lang, Lihui, Lyamina, Elena, Date, Prashant P.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6747840/
https://www.ncbi.nlm.nih.gov/pubmed/31454883
http://dx.doi.org/10.3390/ma12172725
_version_ 1783451987540443136
author Alexandrov, Sergei
Lang, Lihui
Lyamina, Elena
Date, Prashant P.
author_facet Alexandrov, Sergei
Lang, Lihui
Lyamina, Elena
Date, Prashant P.
author_sort Alexandrov, Sergei
collection PubMed
description The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.
format Online
Article
Text
id pubmed-6747840
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-67478402019-09-27 Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers Alexandrov, Sergei Lang, Lihui Lyamina, Elena Date, Prashant P. Materials (Basel) Article The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field. MDPI 2019-08-26 /pmc/articles/PMC6747840/ /pubmed/31454883 http://dx.doi.org/10.3390/ma12172725 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Alexandrov, Sergei
Lang, Lihui
Lyamina, Elena
Date, Prashant P.
Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers
title Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers
title_full Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers
title_fullStr Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers
title_full_unstemmed Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers
title_short Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers
title_sort solution behavior near envelopes of characteristics for certain constitutive equations used in the mechanics of polymers
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6747840/
https://www.ncbi.nlm.nih.gov/pubmed/31454883
http://dx.doi.org/10.3390/ma12172725
work_keys_str_mv AT alexandrovsergei solutionbehaviornearenvelopesofcharacteristicsforcertainconstitutiveequationsusedinthemechanicsofpolymers
AT langlihui solutionbehaviornearenvelopesofcharacteristicsforcertainconstitutiveequationsusedinthemechanicsofpolymers
AT lyaminaelena solutionbehaviornearenvelopesofcharacteristicsforcertainconstitutiveequationsusedinthemechanicsofpolymers
AT dateprashantp solutionbehaviornearenvelopesofcharacteristicsforcertainconstitutiveequationsusedinthemechanicsofpolymers