Gradient polyconvex material models and their numerical treatment

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:195

Article

Horak, Martin¹  Kruzik, Martin^1,2 

[1] Czech Tech Univ, Fac Civil Engn, Thakurova 7, CZ-16629 Prague 6, Czech Republic

[2] Czech Acad Sci, Inst Informat Theory & Automat, Pod Vodarenskou Vezi 4, CZ-18200 Prague 8, Czech Republic

关键词: Gradient polyconvexity;    Microstructure formation;    Nonlinear elasticity;    Numerical solution;   

DOI  :  10.1016/j.ijsolstr.2020.03.006

来源: Elsevier

【 摘 要 】

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 Saint Venant-Kirchhoff-material and a double-well stored energy density. (C) 2020 Elsevier Ltd. All rights reserved.

【 授权许可】

Free