An efficient implicit approach for the thermomechanical behavior of materials submitted to high strain rates

Abstract

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.

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

“…To integrate this equation in time, we choose to use the implicit α ‐generalized algorithm family . This family of algorithms consists in weighting the momentum conservation Equation between two successive time stations noted 0 (associated to time t ) and 1 (associated to time t + Δ t ) with two user‐defined parameters α F and α M : …”

Implicit 2D Numerical Simulation of Materials Submitted to High Strain Rates Including Fracture

“…Implicit staggered thermomechanical algorithm. The main feature of this paper is the use of unconditionally stable implicit staggered thermomechanical algorithms including inertial effects [2] with erosion element method [3] to time integrate the conservation equations, in lieu of the traditional conditionally stable explicit algorithm generally used for impact problems [4].…”

“…With M the mass matrix, x the nodal acceleration vector, , int mec F the vector of internal mechanical forces and , ext mec F the vector of external mechanical forces. For the time integration of this equation, the Chung-Hulbert or alpha-generalized algorithm family [2,6] is selected. This algorithm consists in weighting accelerations and forces between time step n and time step n+1:…”