Continuum models for materials with lattice-like microstructure

Within the framework of the finite element method, a general technique is presented to compute the continuum constitutive matrix of an equivalent lattice-like microstructural material. The equivalency between the continuum and microstructural stiffness matrices produces an over-determined system which is solved using the Moore-Penrose generalized inverse procedure. Although the resulting solution is not exact, it is unique in the least-squares sense. The present study is limited to two-dimensional problems; however, the technique can easily be extended to three dimensions. Several specific examples are given to demonstrate the effectiveness and accuracy of the method.