用渐近均匀化方法确定异向材料广义热力学参数
Determining parameters in generalized thermomechanics for metamaterials by means of asymptotic homogenization
摘要：
制造方法的进步使得能够设计具有定制微结构的所谓超材料。微观结构影响材料的响应在一个长度尺度，在这里我们模拟这种行为，使用广义热力学。应变梯度理论作为一个高阶理论与热力学建模为一阶理论。开发非均质材料的多物理场模型确实是一个挑战，即使是广义热力学中的这个“最简单”的模型也会导致数十个参数被确定。我们开发了一个计算模型，通过使用一个给定的微观结构，建模为一个周期性的域，并通过渐近均匀化数值计算的所有参数。有限元法（FEM）的援助下，开源代码（FEniCS）。模型问题中孔洞对称随机分布的算例验证了该方法的有效性，并为在何种尺度下需要考虑复合材料的广义热弹性提供了一个实例。
英文摘要：
Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized thermomechanics. Strain gradient theory is employed as a higher-order theory with thermodynamics modeled as a first-order theory. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this ``simplest'' model in generalized thermomechanics causes dozens of parameters to be determined. We develop a computational model by using a given microstructure, modeled as a periodic domain, and numerically calculate all parameters by means of asymptotic homogenization. Finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Some example with symmetric and random distribution of voids in a model problem verifies the method and provides an example at which length-scale we need to consider generalized thermoeleasticity in composite materials.
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