COMPUTATIONAL SIMULATION OF DEFORMATION-BEHAVIOR OF 2D-LATTICE CONTINUUM

Finite element methods for an elastic Cosserat continuum obeying micro polar theory and couple stress theory are developed and applied to the simulation of stress concentration around a circular hole in a lattic e continuum plate, in which the lattice continuum is the continuum mod el for materials with lattice-like microstructure. In the formulation of the finite element method based on couple stress theory, a new meth od consisting of a kind of selective reduced integration is proposed t o remedy the over-constraint problem which arises in the penalty metho d of constraining the micro- and macrorotation vectors. The proposed f inite element methods are validated by comparing the numerical solutio ns 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 propose d method is applied to the lattice continuum, which is a continuous mo del of discrete lattice structure obeying couple stress theory such as cancellous bone with trabecular architecture, to analyze the dependen ce of the stress concentration factor on the microstructural parameter s. In the range where the dimensions of the structural parameters are comparable to the hole radius, the stress concentration factor rises w hen 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 i nvestigation of the deformation behavior of materials with microstruct ures. (C) 1998 Elsevier Science Ltd. All rights reserved.