Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials
Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials
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DOI：
10.1007/s11075-007-9063-9
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发表时间：
2007-02
影响因子：
2.1
通讯作者：
V. Rutka;Andreas Wiegmann
中科院分区：
文献类型：
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作者：
V. Rutka;Andreas Wiegmann
虚拟材料设计是指材料在计算机中的微观变化，然后对这种变化对材料宏观性能的影响进行数值评估。这一过程的目标是某种意义上的改进材料。在这里，我们给出了复合材料的有效弹性模量与夹杂形状的几何关系的例子。对于如何解决这类界面问题，一种新的方法避免了网格生成，即使在界面附近也能给出二阶精确结果。显式跳跃浸没界面方法是一种求解椭圆型偏微分方程组的有限差分方法，它在等距笛卡尔网格上工作，而不考虑方程参数和解的非网格对齐间断。在间断附近，通过增加涉及函数及其导数跳跃的修正项，对标准有限差分近似进行了修正。本文推导了具有分段常系数的二维线弹性的修正项，即复合材料的修正项。证明了该方法的数值收敛和逼近性质。
Virtual material design is the microscopic variation of materials in the computer, followed by the numerical evaluation of the effect of this variation on the material’s macroscopic properties. The goal of this procedure is an in some sense improved material. Here, we give examples regarding the dependence of the effective elastic moduli of a composite material on the geometry of the shape of an inclusion. A new approach on how to solve such interface problems avoids mesh generation and gives second order accurate results even in the vicinity of the interface. The Explicit Jump Immersed Interface Method is a finite difference method for elliptic partial differential equations that works on an equidistant Cartesian grid in spite of non-grid aligned discontinuities in equation parameters and solution. Near discontinuities, the standard finite difference approximations are modified by adding correction terms that involve jumps in the function and its derivatives. This work derives the correction terms for two dimensional linear elasticity with piecewise constant coefficients, i.e. for composite materials. It demonstrates numerically convergence and approximation properties of the method.