A note on stress fields and crack growth in porous materials subjected to a contact load

Abstract

a b s t r a c tIn materials where inherent heterogeneities like cells and pores are relatively large compared to other relevant mechanical dimensions, such as the contact surface in indentation tests or the length of an existing crack, stress and strain fields predicted by classical continuum elasticity theories may become too harsh because of absence of internal lengths in the equations that characterize the underlying microstructure. To overcome this deficiency a gradient enhanced elasticity continuum theory may be applied, which include length parameters in the constitutive equations that limit the magnitude of deformation gradients and is able to capture internal length effects. In this study, microscopic stress fields in porous materials subjected to a cylindrical contact load are estimated with such a gradient enhanced continuum model. To judge the model's ability to capture the mechanical behavior in this class of materials, calculated stress fields in the contact region, given by the gradient theory, are contrasted with microscopic stress fields computed in discrete high-resolution finite element models of cellular wood-like structures having varying average pore sizes but identical macroscopic geometry and boundary conditions as the gradient model. X-ray computed tomography experiments on wood illustrate the phenomenon. It is observed, in both experiment and finite element models, that the region of high shear stresses, where a crack may grow despite a confining pressure, is located deeper down in the material than what is predicted in classical continuum theories. On the other hand, the gradient enhanced model produces remarkably similar stress/strain fields as the finite element models and experiment and is thus seemingly able to capture microstructural size effects.