Gradient polyconvex material models and their numerical treatment

0523776 - ÚTIA 2021 RIV GB eng J - Journal Article
Horák, M. - Kružík, Martin
Gradient polyconvex material models and their numerical treatment.
International Journal of Solids and Structures. Roč. 195, č. 1 (2020), s. 57-65. ISSN 0020-7683. E-ISSN 1879-2146
R&D Projects: GA ČR GA18-03834S
Institutional support: RVO:67985556
Keywords : Gradient polyconvexity * Microstructure formation * Nonlinear elasticity
OECD category: Applied mathematics
Impact factor: 3.900, year: 2020
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2020/MTR/kruzik-0523776.pdf https://www.sciencedirect.com/science/article/pii/S0020768320300949

Gradient polyconvex materials are nonsimple materials where we do not assume smoothness of the elastic strain but instead regularity of minors of the strain is required. This allows for a larger class of admissible deformations than in the case of second-grade materials.
We describe a possible implementation of gradient polyconvex elastic energies in nonlinear finite strain elastostatics. Besides, a new geometric interpretation of gradient-polyconvexity is given and it is compared with standard second-grade materials. Finally, we demonstrate application of the proposed approach using two different models, namely, a St.-Venant Kirchhoff material and a double well stored energy density.
Permanent Link: http://hdl.handle.net/11104/0308089