An adaptive FE2 method for the thermomechanical behaviour of a SMA‐Fiber matrix composite
An adaptive FE2 method for the thermomechanical behaviour of a SMA‐Fiber matrix composite
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用于 SMAâFiber 基复合材料热机械行为的自适应 FE2 方法
DOI：
10.1002/pamm.201800163
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Klinkel
中科院分区：
文献类型：
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作者：
Praster M;Klinkel
这篇文章涉及形状记忆合金（SMA）增强基体的多尺度分析。复杂的微观结构允许完全离散的宏观结构，因为使用了FE 2方法。与经典材料不同，SMA在加载和卸载情况下具有更复杂的行为，具有高温依赖性。宏观问题的微观结构由线弹性矩阵和随机纤维分布组成。复合材料的应力响应与变形、纤维取向和温度呈非线性关系。由于纤维的非线性行为，在每个积分点处采用嵌套均匀化。这就是所谓的FE2方法。FE2方法的一个缺点是在每一个积分点和每一步迭代中求解边值问题的计算量很大。这促使本工作引入一个指标，它确定是否需要一个伴随的同质化。由于温度依赖性，在宏观尺度上，解决了耦合的热机械问题。在第一个均匀化步骤中，用Neumann边界条件求解RVE的边值问题。这导致对菌株的高估。SMA将保持线性弹性，直到达到相变条件。该公式类似于弹塑性材料的经典屈服条件，但这里使用的是应变而不是应力准则。根据相变条件，温度依赖性指标被定义并公式化为SMA纤维线性行为的极限应变。当达到极限应变时，首先需要伴随的均匀化。
This contribution deals with the multiscale analysis of a reinforced matrix with shape‐memory‐alloys (SMA). The complicated micro‐structure permits a full discretized macro‐structure, due to that an FE2approach is used. Unlike classic materials, the SMA has more complex behavior with a high‐temperature dependency in the loading and unloading case. The micro‐structure of the macroscopic problem consists of a linear‐elastic matrix and a random fiber distribution. The stress response of the composite depends non‐linearly on the deformation, the fiber orientation and the temperature. Due to the non‐linear behavior of the fiber a nested homogenized is employed at each integration point. This results in the so‐called FE2method. One disadvantage of the FE2method is the high computational effort by solving the boundary value problem (BVP) in every integration point and every iteration step. This motivates the present work to introduce an indicator, which determines whether an accompanying homogenization is needed. Due to the temperature dependency, on the macro‐scale, a coupled thermo‐mechanical problem is solved. In the first homogenization step, the BVP of the RVE is solved with Neumann Boundary conditions. This leads to an overestimation of the strains. The SMA will remain linear elastic until the phase transition condition is reached. The formulation is similar to the classical yield condition of elasto‐plastic materials, however, here a strain instead a stress creteria is used. From the phase transition condition, the temperature dependent indicator is defined and formulated as a limit strain for the linear behavior of the SMA‐fibers. The accompanying homogenization is firstly needed when the limit strain is reached.