Conti, Sergio and Dolzmann, Georg (2018) An adaptive relaxation algorithm for multiscale problems and application to nematic elastomers. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 113. pp. 126-143. ISSN 0022-5096, 1873-4782
Full text not available from this repository. (Request a copy)Abstract
The relaxation of nonconvex variational problems involving free energy densities W which depend on the deformation gradient is frequently characterized by a hierarchy of structures at different and well-separated length scales. A wide range of these structures can be characterized as the superposition of one-dimensional oscillations on different length scales which are referred to as laminates of finite order. During a finite element simulation, the relaxed energy W-qc needs to be evaluated in each time step in each Gauss point in the triangulation. In this paper, an algorithmic scheme is presented that allows for the efficient computation of an approximation of the relaxed energy based on laminates of finite order in a large number of points. As an application, the relaxed energy for thin sheets of anisotropic nematic elastomers is studied in detail. (C) 2018 Elsevier Ltd. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | INCREMENTAL STRESS POTENTIALS; SINGLE-CRYSTAL ELASTOMERS; ONE CONVEX ENVELOPES; DIRECTOR REORIENTATION; DISLOCATION-STRUCTURES; VARIATIONAL-PROBLEMS; ENERGY MINIMIZATION; EFFECTIVE BEHAVIOR; PLASTICITY; MICROSTRUCTURE; Numerical relaxation; Phase transformation; Quasiconvexity; Nematic elastomers |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Mar 2020 13:57 |
| Last Modified: | 10 Mar 2020 13:57 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14767 |
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