Time-adaptive non-linear finite-element computations for thermo-mechanically coupled analysis in inelastic dynamical systems (original) (raw)

2016, Proceedings in applied mathematics & mechanics

An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations

International Journal of Solids and Structures, 2006

The so-called viscoplastic consistency model, proposed by Wang, Sluys and de Borst, is extended here to the integration of a thermoviscoplastic constitutive equation for J2 plasticity and adiabatic conditions. The consistency condition in this case includes not only strain rate but also the effect of temperature on the yield function. Using the backward Euler integration scheme to integrate the constitutive equations, an implicit algorithm is proposed, leading to generalized expressions of the classical return mapping algorithm for J2 plasticity, both for the iterative calculation of the plastic multiplier increment and for the consistent tangent operator when strain rate and temperature are considered also as state variables of the hardening equation. The model was implemented in a commercial finite element code and its performance is demonstrated with the numerical simulation of four Taylor impact tests.

Numerical Solution of Coupled Thermo-Elastic-Plastic Dynamic Problems

Mathematical Modelling of Engineering Problems, 2021

The article considers a numerical method for solving a two-dimensional coupled dynamic thermoplastic boundary value problem based on deformation theory of plasticity. Discrete equations are compiled by the finite-difference method in the form of explicit and implicit schemes. The solution of the explicit schemes is reduced to the recurrence relations regarding the components of displacement and temperature. Implicit schemes are efficiently solved using the elimination method for systems with a three diagonal matrix along the appropriate directions. In this case, the diagonal predominance of the transition matrices ensures the convergence of implicit difference schemes. The problem of a thermoplastic rectangle clamped from all sides under the action of an internal thermal field is solved numerically. The stress-strain state of a thermoplastic rectangle and the distribution of displacement and temperature over various sections and points in time have been investigated.

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