热松弛热弹性周期材料的变分-渐近均匀化
Variational-asymptotic homogenization of thermoelastic periodic materials with thermal relaxation
摘要：
提出了一种多尺度渐近均匀化方法，用于求解具有周期性空间依赖单弛豫时间的热弹性周期微结构材料。将微位移场和微温度场的渐近展开式改写到变换后的Laplace空间，并表示为微结构长度尺度的幂级数，从而得到一组周期性单胞上的递归微分问题.这样的细胞问题的解决方案导致的扰动功能。然后定义了尺度放大和尺度缩小关系，后者允许用宏观场及其梯度来表示微观场。导出了无穷阶平均场方程。所提出的技术的效率进行了测试，在一个二维正交各向异性层状体与正交各向异性轴平行的层的方向，其中的机械和温度的本构性能得到很好的稳定。的均匀化介质的色散曲线，截断在一阶进行了比较与由Floquet-Bloch理论得到的非均匀连续介质的色散曲线。用两种不同的方法得到的结果显示出非常好的一致性。
英文摘要：
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement and the micro-temperature fields are rewritten on the transformed Laplace space and expressed as power series of the microstructural length scale, leading to a set of recursive differential problems over the periodic unit cell. The solution of such cell problems leads to the perturbation functions. Up-scaling and down-scaling relations are then defined, and the latter allow expressing the microscopic fields in terms of the macroscopic ones and their gradients. Average field equations of infinite order are also derived. The efficiency of the proposed technique was tested in relation to a bi dimensional orthotropic layered body with orthotropy axis parallel to the direction of the layers, where the mechanical and temperature constitutive properties were well stabilised. The dispersion curves of the homogenized medium, truncated at the first order are compared with the dispersion curves of the heterogeneous continuum obtained by the Floquet-Bloch theory. The results obtained with the two different approaches show a very good agreement.
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