Homotopy Shear Band Solutions in Gradient Plasticity

Abstract

Abstract Analytical shear band type solutions for finite domains are derived within the framework of gradient plasticity theory by employing the homotopy analysis method (HAM). Such types of solutions were available in the literature only for infinite domains in the nonlinear material softening regime and steady-state conditions, as well as for finite domains in the material hardening regime. HAM allows for solutions to be obtained for both hardening and softening material models, as well as for unsteady conditions periodic solutions are also derived. The HAM results are verified with numerical simulations, which show excellent agreement. Moreover, an error analysis is provided which guarantees the convergence of our series solution.