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.

中文翻译：

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通过同心插值进行多尺度有限应变计算均质化

提出了一种在有限应变下高效计算均质超弹性材料的方法。在递归过程中将多个空间比例均匀化：从最小比例开始，很少执行高保真度FE计算。快照POD处理变形梯度波动的结果字段，从而生成缩减基数（RB）模型。借助于计算效率高的RB模型，可以创建大量均质化材料响应的样本集。该数据集为同心插值（CI）方案提供了支持，可对有效应力和刚度进行插值。然后，使用此CI替代均质材料定律，在更大的范围内调用相同的过程。在标准工作站上，几个小时内即可完成三级均质化过程。在便携式计算机上，几分钟之内即可评估生成的模型，以生成第四级结果。提供了开放源代码。