Strain gradient plasticity modeling and finite element simulation of Lüders band formation and propagation

Abstract

An analytical solution of the problem of the propagation of a Luders band in an isotropic strain gradient plasticity medium is provided based on a softening–hardening constitutive law. A detailed description is given of the plastic strain distribution in the finite size band front. The solution is shown to be harmonic in the band front and exponential in the band tail. Particular attention is paid to the conditions to be applied at the interface between both regions. This solution is then used to validate finite element simulations of the Luders band formation and propagation in a plate in tension. The approach is shown to suppress the spurious mesh dependence exhibited by conventional finite element simulations of the Luders behavior and to provide a finite width band front in agreement with the experimental observations from strain field measurements.