Many engineering materials, such as composites, bonded materials and geophysical materials, are generally modeled as nonhomogeneous continua and usually assumed to be piecewise homogeneous for simplicity. However, in some of these materials the mechanical properties do vary continuously and the continuity has to be considered. For examples, hydraulic fracturing of geophysical materials, interface crack problems in bonded materials [1,2], functionally graded materials [3] and so on, the continuity of the material properties should be considered undoubtedly in analysis.
There have been a number of papers that studied the nonhomogeneous problem [4][5][6]. However, the analytical approach used by these studies can only deal with unbounded media and simple distribution of material properties, such as linear form, power form or exponential form. For a great deal of finite dimensional structural components and/or various distributions of material properties, it is difficult, if not impossible, to find the analytical solution. Therefore, numerical methods have to be developed. In numerical methods, the most versatile method is the Finite Element Method (FEM) and it has been used to solve many practical problems. However, almost all of these finite element approaches mainly concentrated on homogeneous materials or piecewise homogeneous materials. The finite element formulation relating to nonhomogeneous materials with continuously varying properties was very few. In this paper, we propose a more simple and more versatile finite element formulation. The concept of isoparametric transformation is adopted for simulating the variations of the material properties in individual finite elements. The continuity requirement of the material properties is satisfied. The feasibility and the versatility of this method are verified by examples.