Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials
| Autor: | Thomas Blesgen, Ada Amendola |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Scheme (programming language)
Computer science Crystal plasticity Parameterized complexity Cosserat theory Micropolar materials Numerical simulations Preconditioning Quaternions 02 engineering and technology Plasticity 01 natural sciences 0203 mechanical engineering 0103 physical sciences Applied mathematics Quaternion 010301 acoustics computer.programming_language Holonomic Mechanical Engineering Numerical analysis Condensed Matter Physics 020303 mechanical engineering & transports Mechanics of Materials Finite strain theory Benchmark (computing) computer |
| Popis: | This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with microstructure. Two improvements are made in contrast to earlier approaches: First, the micro-rotations are parameterized with the help of an Euler–Rodrigues formula related to quaternions. Secondly, as main result, a novel two-pass preconditioning scheme for searching the energy-minimizing solutions based on the limited memory Broyden–Fletcher–Goldstein–Shanno quasi-Newton method is proposed that consists of a predictor step and a corrector-iteration. After outlining the necessary adaptations to the model, numerical simulations compare the performance and efficiency of the new and the old algorithm. The proposed numerical model can be effectively employed for studying the mechanical response of complicated materials featuring large size effects. |
| Databáze: | OpenAIRE |
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