Implicit algorithms for multilayer J2-plasticity Original Research Article

In this paper two implicit algorithms for multilayer deviatoric plasticity based on the closest point projection iteration are introduced. The algorithmic elastoplastic tangents, in order to preserve the second-order convergence in Newton algorithms based on converged steps, are also developed. An implicit Mróz translation rule is formulated and serves as a basis for the construction of the traditional return mapping schemes. The main differences between the proposed procedures lay on a forward update of the active surface and the construction of the return mapping only at the end of the step or each time there is a surface update. The first option yields a scheme closer to that of a virtual bounding surface model and to that of explicit algorithms while the second one contributes with a mathematically more attractive and robust layout. Both of them allow a way to perform implicit unconditionally-stable, second-order-convergent multiaxial analysis using multilayer plasticity and they present an alternative to virtual bounding surface plasticity to which the examples are also compared.