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SUMMARYThis paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows: A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework. An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated. An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem. The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN 2L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.

Abstract. In the present paper, three solutions are proposed to simulate fast phenomena with finite element method at best. At first, material constitutive laws of Johnson-Cook and Zerilli-Armstrong types are implemented. These well-known laws are efficient for the description of material behavior at high velocities, especially for material used in automotive or aeronautics industry. The second contribution of this paper is the coupling of an implicit Chung-Hulbert algorithm taking into account the inertial effects with a staggered scheme for solving the thermal problem. The last input of this paper is the use of EAS (Enhanced Assumed Strain) finite elements to better capture complex strain modes, especially bending that is not accurately evaluated with classical finite elements. These EAS finite elements are used in the scope of thermomechanical dynamic phenomena implemented in a modular C++ environment at the University of Liège in the home made software METAFOR.

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