On strength analysis of highly porous materials within the framework of the micropolar elasticity

We discuss the finite element approach to modelling of static deformations of porous materials such as foams, beam lattices, and others within the linear micropolar elasticity. It is known that the micropolar elasticity may be used for microstructured solids and fluids since it can forecast size-effect near geometrical singularities such as holes, notches, small contact areas of two solids. Within the micropolar elasticity the translational and rotational interactions of the material particles can be taken into account. Here we present the recent developments in the theory of finite elements calculations for micropolar solids in order to capture the stress behaviour in the vicinity of geometric singularities such as holes, notches, imperfections or contact areas. The fundamental equations of the micropolar continuum are presented. The FEM implementation in micropolar elasticity is given. The new 8-node hybrid micropolar isoparametric element and its implementation in ABAQUS are introduced. The solutions of few 3D benchmark problems of the micropolar elasticity are given. Among them are analysis of stresses and couple stresses near notches and holes, contact problem of parabolic stamp and half space. The main attention is paid to modelling of interaction between a biodegradable porous implant and a trabecular bone. Comparison of classical and micropolar solutions is carefully discussed. Comparison of classical and micropolar solutions is discussed. Numerical tests have shown that couple stress appears almost in the vicinity of geometrical singularities. It is shown that micropolar elasticity allows to obtain better results for domains with microstructures and singularities than classical theory of elasticity.