用于微观组织模拟的高阶弹性插值函数
High-Order Elasticity Interpolants for Microstructure Simulation
摘要：
我们提出了一种新的配方的弹性材料的基础上，高阶插值，准确地拟合复杂的弹性行为，但仍然保守。所提出的高阶插值可以被视为径向基函数的高维扩展，并且它们允许弹性能量的导数的插值，特别是应力和刚度。给出了弹性模型的参数化方法，设计了一种基于训练数据的优化模型参数的算法。我们已经测试了我们的方法的二维微观结构的均匀化，我们表明，它成功地匹配复杂的行为，具有高精度。
英文摘要：
We propose a novel formulation of elastic materials based on high-order interpolants, which fits accurately complex elastic behaviors, but remains conservative. The proposed high-order interpolants can be regarded as a high-dimensional extension of radial basis functions, and they allow the interpolation of derivatives of elastic energy, in particular stress and stiffness. Given the proposed parameterization of elasticity models, we devise an algorithm to find optimal model parameters based on training data. We have tested our methodology for the homogenization of 2D microstructures, and we show that it succeeds to match complex behaviors with high accuracy.
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