Reduced basis hybrid computational homogenization based on a mixed incremental formulation
Reduced basis hybrid computational homogenization based on a mixed incremental formulation
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DOI：
10.1016/j.cma.2013.03.007
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发表时间：
2013-06-15
影响因子：
7.2
通讯作者：
Leuschner, Matthias
中科院分区：
文献类型：
--
作者：
Fritzen, Felix;Leuschner, Matthias
提出了一种新的计算机辅助微异质材料均化的简化基方法。以非均匀变换场分析 (NTFA) [1,2] 的主要特征为出发点。 NTFA 方法的缺点是其仅限于微观尺度上的简单本构模型。第二个缺点是，当近似塑性应变的折减基具有增加的尺寸时，可能会损失精度。这两个问题都与模态活度系数的简单演化规律有关，模态活度系数是均质材料的新的宏观内部变量。在本贡献中，提出了 NTFA 的推广，其中新内部变量的演化源自混合增量变分公式。该推导纯粹基于微观机械考虑。该修改允许在微观尺度上使用任意通用标准材料 [3]，包括晶体粘塑性。此外，均匀响应的保真度现在与近似塑性应变场的简化基础直接相关。非线性粘性材料和单晶塑性的数值例子概述了所提出的多尺度方法的准确性。 (c) 2013 Elsevier B.V. 保留所有权利。
A new reduced basis method for the computer assisted homogenization of microheterogeneous materials is proposed. Key features of the Nonuniform Transformation Field Analysis (NTFA) [1,2] are taken as a point of departure. A short-coming of the NTFA method is its limitation to simple constitutive models on the microscale. A second disadvantage is the possible loss of accuracy when the reduced basis approximating the plastic strains has increasing dimension. Both issues are related to the simple evolution law for the mode activity coefficients, which are the new macroscopic internal variables of the homogenized material. In the present contribution a generalization of the NTFA is proposed in which the evolution of the new internal variables is derived from a mixed incremental variational formulation. The derivation is based on purely micro-mechanical considerations. The modification allows for arbitrary Generalized Standard Materials [3] on the microscopic scale including, e.g., crystal visco-plasticity. Additionally, the fidelity of the homogenized response is now directly linked to the reduced basis approximating the plastic strain field. Numerical examples for nonlinear viscous materials and single crystal plasticity outline the accuracy of the proposed multi-scale method. (c) 2013 Elsevier B.V. All rights reserved.