Computational simulation of deformation behavior of 2D-lattice continuum

Finite element methods for an elastic Cosserat continuum obeying micropolar theory and couple stress theory are developed and applied to the simulation of stress concentration around a circular hole in a lattice continuum plate, in which the lattice continuum is the continuum model for materials with lattice-like microstructure. In the formulation of the finite element method based on couple stress theory, a new method consisting of a kind of selective reduced integration is proposed to remedy the over-constraint problem which arises in the penalty method of constraining the micro- and macrorotation vectors. The proposed finite element methods are validated by comparing the numerical solutions of stress concentration around a circular hole in a uniform tension field to the exact solutions for the isotropic materials obeying both micropolar theory and couple stress theory. Subsequently, the proposed method is applied to the lattice continuum, which is a continuous model of discrete lattice structure obeying couple stress theory such as cancellous bone with trabecular architecture, to analyze the dependence of the stress concentration factor on the microstructural parameters. In the range where the dimensions of the structural parameters are comparable to the hole radius, the stress concentration factor rises when the principal direction of the lattice structure is aligned along the tensile direction, whereas it falls when these directions form an oblique angle. The proposed finite element methods are applicable in investigation of the deformation behavior of materials with microstructures. (C) 1998 Elsevier Science Ltd. All rights reserved.