Micropolar hyperelasticity: constitutive model, consistent linearization and simulation of 3D scale effects
Micropolar hyperelasticity: constitutive model, consistent linearization and simulation of 3D scale effects
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DOI：
10.1007/s00466-012-0679-9
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发表时间：
2012-01
影响因子：
4.1
通讯作者：
S. Bauer;W. Dettmer;D. Perić;M. Schäfer
中科院分区：
文献类型：
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作者：
S. Bauer;W. Dettmer;D. Perić;M. Schäfer
这项研究描述了三维有限应变和有限曲率微极超弹性的计算框架。该模型基于非线性运动学设置，并具有在热力学一致框架内推导的适当的超弹性材料定律。材料正切算子是通过一致线性化得到的。采用牛顿-拉夫森过程的隐式有限元方法来计算节点位移和旋转。给出了许多数值例子。结果表明：(i) 该方法能够捕获有限变形中的 3D 长度尺度效应，(ii) 该方法稳健且计算效率高，(iii) 所提出的微极元正切呈现牛顿-拉夫森过程的渐近二次收敛。结果表明，经典的 Neo-Hooke 型材料行为在所提出的微极性设置中恢复为特例。
This study describes a computational framework for three-dimensional finite strain and finite curvature micropolar hyperelasticity. The model is based on the non-linear kinematic setting and features an appropriate hyperelastic material law which is derived within the thermodynamically consistent framework. The material tangent operator is obtained by consistent linearization. An implicit finite element method with a Newton-Raphson procedure is employed for the computation of the nodal displacements and rotations. A number of numerical examples is presented. The results demonstrate (i) that the methodology is capable of capturing 3D length scale effects in finite deformation, (ii) that it is robust and computationally efficient and (iii) that the proposed micropolar element tangent renders asymptotically quadratic convergence of the Newton-Raphson procedure. It is shown that the classical Neo-Hooke type material behaviour is recovered as a special case within the proposed micropolar setting.