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**An efficient 3D implicit approach for the thermomechanical simulation of elastic-viscoplastic materials submitted to high strain rate and damage.**
*(English)*
Zbl 1352.74369

Summary: This 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\(^{2}\)L, University of Liège, Belgium) named Metafor.

}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\(^{2}\)L, University of Liège, Belgium) named Metafor.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74C20 | Large-strain, rate-dependent theories of plasticity |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

74R05 | Brittle damage |

### Keywords:

damage; high strain rate; implicit time integration; constitutive law integration scheme; thermo-elasto-viscoplastic material behavior; impact
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\textit{P. P. Jeunechamps} and \textit{J. P. Ponthot}, Int. J. Numer. Methods Eng. 94, No. 10, 920--960 (2013; Zbl 1352.74369)

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