复杂微结构非线性复合材料整体响应的数值计算方法
A numerical method for computing the overall response of nonlinear composites with complex microstructure
摘要：
用有限元法研究了非线性复合材料的局部和整体响应。我们提出了一种基于傅立叶级数的替代方法，该方法避免了网格化，并直接利用微观结构图像。它是基于一个线弹性和均匀的比较材料的格林函数的精确表达式。首先，弹性非均匀成分的情况下，被认为是一个迭代过程，提出解决自然出现的问题的Lippman-Schwinger方程。然后，该方法被扩展到非线性成分的逐步积分的时间。通过改变微结构的空间分辨率来评估该方法的准确性。该方法的灵活性使其能够用于各种各样的微结构。(C)1998年爱思唯尔科学股份有限公司
英文摘要：
The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.
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