Application of fractional continuum mechanics to rate independent plasticity

From Discrete Visco-Elasticity to Continuum Rate-Independent Plasticity: Rigorous Results

We show that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a viscoelastic crystal lattice with quenched disorder. The constitutive structure changes as a result of two concurrent limiting procedures: the vanishing-viscosity limit and the discrete-to-continuum limit. In the course of these limits a non...

Rate Independent Crystal Plasticity

The problem of non-uniqueness in the selection and determination of the amount of shear on the active slip systems has plagued the rate-independent crystal plasticity theories for several years. A new large deformation rate-independent crystal plasticity theory is fromulated which overcomes this long standing problem. The model has been implemented in a commerical finite element program ABAQUS/...

Thermodynamics of rate-independent plasticity

We show that the singular dissipative potential of the phenomenological rate-independent plasticity can be obtained by homogenization of a micro-model with quadratic dissipation. The essential ingredient making this reduction possible is a rugged energy landscape at the micro-scale, generating under external loading a regular cascade of subcritical bifurcations. Such landscape may appear as a r...

New implementation of a non-associated flow rule in rate-independent plasticity

One of the new research fields in plasticity is related to choosing a proper non-associated flow rule (NAFR), instead of the associated one (AFR), to predict the experimental results more accurately. The idea of the current research is derived from combining von Mises and Tresca criteria in the places of yield and plastic potential surfaces in rate-independent plasticity.  This idea is implemen...

Introduction to Continuum Mechanics