论文标题
一种用于计算具有复杂微结构的非线性复合材料的总体响应的数值方法
A numerical method for computing the overall response of nonlinear composites with complex microstructure
论文作者
论文摘要
非线性复合材料的局部和整体响应通过有限元方法进行了经典研究。我们提出了一种基于傅立叶系列的替代方法，该方法避免了网格划分并直接使用微结构图像。它基于线性弹性和均匀比较材料的绿色功能的确切表达。首先，考虑了弹性非均匀成分的情况，并提出了一种迭代程序来解决该问题自然出现的Lippman-Schwinger方程。然后，该方法通过时间分步积分扩展到非线性成分。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可以用于各种微观结构。 （c）1998 Elsevier Science S.A.
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.
