An adaptive approach for modeling a fiber‐matrix composite with the FE2 method
An adaptive approach for modeling a fiber‐matrix composite with the FE2 method
复制标题
使用 FE2 方法对纤维基复合材料进行建模的自适应方法
DOI：
10.1002/pamm.201710277
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Klinkel
中科院分区：
文献类型：
--
作者：
Praster;Klinkel
在具有复杂微观结构的材料中，宏观的材料行为是未知的。在这项工作中，考虑了纤维基复合材料与弹塑性纤维。微观尺度的均质化导致材料的宏观性质。在本工作中，这是在FE2公式的框架内实现的。它结合了两个嵌套的有限元模拟。在宏观尺度上，用有限元模拟边值问题，在每个积分点上进行二次有限元模拟，计算应力响应和材料切线模数。这种方法的一个巨大缺点是计算量大。当然，如果材料表现为线弹性，则不需要随之而来的均化。这激发了目前处理适应性方案的方法。提出了一种利用边界条件(BC)在微观尺度上不同的边界条件的指示方法。Dirichlet BC的均匀化高估了材料的切线模数，而Neumann BC低估了模数[2]。自适应建模的思想是在宏观结构的加载过程中使用这两个BC。首先从Neumann BC开始，导致了对位移响应的高估，从而导致了宏观尺度上边值问题的应变状态。在应变达到极限应变后，进行伴随的均质化。采用Dirichlet BCs进行伴随的均匀化。数值算例验证了该方法的有效性。(2017Wiley-VCH Verlag GmbH&Co.KGaA，Weinheim)
In materials with a complicated microstructre [1], the macroscopic material behaviour is unknown. In this work a Fiber‐Matrix composite is considered with elasto‐plastic fibers. A homogenization of the microscale leads to the macroscopic material properties. In the present work, this is realized in the frame of a FE2formulation. It combines two nested finite element simulations. On the macroscale, the boundary value problem is modelled by finite elements, at each integration point a second finite element simulation on the microscale is employed to calculate the stress response and the material tangent modulus. One huge disadvantage of the approach is the high computational effort. Certainly, an accompanying homogenization is not necessary if the material behaves linear elastic. This motivates the present approach to deal with an adaptive scheme. An indicator, which makes use of the different boundary conditions (BC) of the BVP on microscale, is suggested. The homogenization with the Dirichlet BC overestimates the material tangent modulus whereas the Neumann BC underestimates the modulus [2]. The idea for an adaptive modeling is to use both of the BCs during the loading process of the macrostructure. Starting initially with the Neumann BC leads to an overestimation of the displacement response and thus the strain state of the boundary value problem on the macroscale. An accompanying homogenization is performed after the strain reaches a limit strain. Dirichlet BCs are employed for the accompanying homogenization. Some numerical examples demonstrate the capability of the presented method. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)