A note on locking materials and gradient polyconvexity

Result code in 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>
Alternative codes found
RIV/68407700:21110/18:00324723
Result on the web
<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>

Result language
angličtina
Original language name
A note on locking materials and gradient polyconvexity
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-04301S" target="_blank" >GA17-04301S: Advanced mathematical methods for dissipative evolutionary systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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