A geometrically-exact Finite Element Method for micropolar continua with finite deformations

Micropolar theory is a weakly non-local higher-order continuum theory based on the inclusion of independent (micro-)rotational degrees of freedom. Subsequent introduction of couple-stresses and an internal length scale mean the micropolar continuum is therefore capable of modelling size effects. This paper proposes a non-linear Finite Element Method based on the spatial micropolar equilibrium equations, but using the classical linear micropolar constitutive laws defined in the reference configuration. The method is verified rigorously with the Method of Manufactured Solutions, and quadratic Newton-Raphson convergence of the minimised residuals is demonstrated

Interaction of shear cracks in microstructured materials modeled by couple-stress elasticity

The interaction of two colinear in-plane shear cracks is investigated within the context of couple-stress elasticity. This theory introduces characteristic material length scales that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. An exact solution of the boundary value problem is obtained through integral transforms and singular integral equations. The main goal is to explain the size effects that are experimentally observed in fracture of brittle microstructured materials. Two basic configurations are considered: a micro-macrocrack interaction, and a micro-microcrack interaction. Numerical results are presented illustrating the effects of couple-stresses on the stress intensity factor and the energy release rate. It is shown that significant deviations from the predictions of the standard LEFM occur when the geometrical lengths of the problem become comparable to the characteristic material length of the couple-stress theory revealing that in such cases it is inadequate to analyze fracture problems employing only classical elasticity considerations

Shear crack growth in brittle materials modeled by constrained Cosserat elasticity

The propagation of in-plane shear cracks is investigated in brittle microstructured materials modeled by the constrained Cosserat elasticity. This theory introduces characteristic material lengths in order to describe the scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. An exact solution is obtained based on integral transforms and the Wiener-Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the loading profile, the propagation velocity, and the characteristic material lengths of Cosserat elasticity. It is shown that depending on the Cosserat microstructural lengths the limiting crack propagation velocity can be significantly lower than the classical Rayleigh limit. Moreover, strengthening effects are observed when the characteristic material lengths become comparable to the geometrical lengths of the problem, a behavior that has been experimentally verified in fracture of ceramics

Simulation of strain localisation with an elastoplastic micropolar material point method

The thickness of shear bands, which form along slip surfaces during certain modes of geotechnical failure, depends directly on the size of the soil particles. Classical continuum models, however, are invariant to length scale, so the strain localisation zone cannot converge to a finite size when employing numerical techniques such as the finite element method. Instead, the present approach adopts the micropolar (Cosserat) continuum, a weakly non-local higher-order theory which incorporates a characteristic length and allows independent rotations of the material micro-structure as well as transmission of couple stresses. As a result, strain can localise naturally in micropolar continua to form realistic finitesized shear bands. By extending an elastic finite-strain micropolar implementation of the material point method (a numerical method well-suited to modelling large deformation problems) with an elasto-plastic constitutive model suitable for geomaterials, this novel combined approach will provide a powerful tool to analyse numerically challenging localisation problems in geotechnics