Many‐scale finite strain computational homogenization via Concentric Interpolation
Many‐scale finite strain computational homogenization via Concentric Interpolation
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DOI：
10.1002/nme.6454
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发表时间：
2020-06
影响因子：
2.9
通讯作者：
Oliver Kunc;F. Fritzen
中科院分区：
文献类型：
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作者：
Oliver Kunc;F. Fritzen
提出了一种有限应变下超弹性材料的高效计算均匀化方法。在一个递归过程中，多个空间尺度均匀化：从最小尺度开始，很少进行高保真的有限元计算。得到的变形梯度波动场通过快照POD进行处理，得到降基（RB）模型。利用计算效率高的RB模型，建立了一组均质材料响应的大样本。该数据集为同心插值（CI）方案提供支持，插值有效应力和刚度。然后，在下一个更大的尺度上调用相同的程序，该CI代表均质化物质定律。三尺度均质过程在标准工作站几个小时内完成。生成的模型在几分钟内在笔记本电脑上进行评估，以生成第四尺度的结果。提供开源代码。
A method for efficient computational homogenization of hyperelastic materials under finite strains is proposed. Multiple spatial scales are homogenized in a recursive procedure: starting on the smallest scale, few high fidelity FE computations are performed. The resulting fields of deformation gradient fluctuations are processed by a snapshot POD resulting in a reduced basis (RB) model. By means of the computationally efficient RB model, a large set of samples of the homogenized material response is created. This data set serves as the support for the Concentric Interpolation (CI) scheme, interpolating the effective stress and stiffness. Then, the same procedure is invoked on the next larger scale with this CI surrogating the homogenized material law. A three‐scale homogenization process is completed within few hours on a standard workstation. The resulting model is evaluated within minutes on a laptop computer in order to generate fourth‐scale results. Open source code is provided.