A note on locking materials and gradient polyconvexity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00495918" target="_blank" >RIV/67985556:_____/18:00495918 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21110/18:00324723

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0218202518500513" target="_blank" >http://dx.doi.org/10.1142/S0218202518500513</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218202518500513" target="_blank" >10.1142/S0218202518500513</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A note on locking materials and gradient polyconvexity

Popis výsledku v původním jazyce

We use gradient Young measures generated by Lipschitz maps to define a relaxation of integral functionals which are allowed to attain the value +∞ and can model ideal locking in elasticity as defined by Prager in 1957. Furthermore, we show the existence of minimizers for variational problems for elastic materials with energy densities that can be expressed in terms of a function being continuous in the deformation gradient and convex in the gradient of the cofactor (and possibly also the gradient of the determinant) of the corresponding deformation gradient. We call the related energy functional gradient polyconvex. Thus, instead of considering second derivatives of the deformation gradient as in second-grade materials, only a weaker higher integrability is imposed. Although the second-order gradient of the deformation is not included in our model, gradient polyconvex functionals allow for an implicit uniform positive lower bound on the determinant of the deformation gradient on the closure of the domain representing the elastic body. Consequently, the material does not allow for extreme local compression.

Název v anglickém jazyce

A note on locking materials and gradient polyconvexity

Popis výsledku anglicky

We use gradient Young measures generated by Lipschitz maps to define a relaxation of integral functionals which are allowed to attain the value +∞ and can model ideal locking in elasticity as defined by Prager in 1957. Furthermore, we show the existence of minimizers for variational problems for elastic materials with energy densities that can be expressed in terms of a function being continuous in the deformation gradient and convex in the gradient of the cofactor (and possibly also the gradient of the determinant) of the corresponding deformation gradient. We call the related energy functional gradient polyconvex. Thus, instead of considering second derivatives of the deformation gradient as in second-grade materials, only a weaker higher integrability is imposed. Although the second-order gradient of the deformation is not included in our model, gradient polyconvex functionals allow for an implicit uniform positive lower bound on the determinant of the deformation gradient on the closure of the domain representing the elastic body. Consequently, the material does not allow for extreme local compression.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-04301S" target="_blank" >GA17-04301S: Pokročilé matematické metody pro disipativní evoluční systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

35

Strana od-do

2367-2401

Kód UT WoS článku

000449107200002

EID výsledku v databázi Scopus

2-s2.0-85052953158