Showing papers by "Rashid K. Abu Al-Rub published in 2006"

A Finite Strain Plastic-damage Model for High Velocity Impact using Combined Viscosity and Gradient Localization Limiters: Part I - Theoretical Formulation

Abstract: During dynamic loading processes, large inelastic deformation associated with high strain rates leads, for a broad class of ductile metals, to degradation and failure by strain localization. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element computations are considerably affected by the mesh size and alignment. This gives rise to a non-physical description of the localized regions. This article presents a theoretical framework to solve this problem with the aid of nonlocal gradient-enhanced theory coupled to viscoinelasticity. Constitutive equations for anisotropic thermoviscodamage (rate-dependent damage) mechanism coupled with thermo-hypoelasto-viscoplastic deformation are developed in this work within the framework of thermodynamic laws, nonlinear continuum mechanics, and nonlocal continua. Explicit and implicit microstructural length-scale measures, which preserve the well-posedness of the differential equations, are introduced through the use of the viscosity and gradient localization limiters. The gradient- enhanced theory that incorporates macroscale interstate variables and their high- order gradients is developed here to describe the change in the internal structure and to investigate the size effect of statistical inhomogeneity of the evolution related plasticity and damage. The gradients are introduced in the hardening internal state variables and are considered dependent on their local counterparts. The derived microdamage constitutive model is destined to be applied in the context of high velocity impact and penetration damage mechanics. The theoretical framework presented in this article can be considered as a feasible thermodynamic approach that enables to derive various gradient (visco) plasticity/(visco) damage theories

A Finite Strain Plastic-damage Model for High Velocity Impacts using Combined Viscosity and Gradient Localization Limiters: Part II - Numerical Aspects and Simulations

Abstract: In this companion article, we present within the finite element context the numerical algorithms for the integration of the thermodynamically consistent formulation of geometrically nonlinear gradi...

On the small and finite deformation thermo-elasto-viscoplasticity theory for strain localization problems: Algorithmic and computational aspects

Abstract: This work is focused on the numerical implementation of thermo-elasto viscoplastic constitutive equations in small and finite strain contexts using the FEM. A length-scale parameter is introduced implicitly through viscosity in order to address strain localization and material instability in the (initial) boundary value problems. According to the second law of thermodynamics a dissipation inequality described in the rotated material coordinate system is developed by Voyiadjis et al. (2004), which was used along with the principle of maximum dissipation to formulate a viscoinelastic model. In order to check the effectiveness of the present framework a set of numerical examples under strict deformation conditions are presented. These numerical examples prove the excellent performance of the present framework in describing the strain localization problem and in obtaining mesh-independent results.

Modeling and Simulation of Perforation of Steel Plates by Blunt Projectiles

Abstract: Due to the lack of the classical local continuum formulation to produce physically meaningful and numerically converging results within large deformation and strain localization computations, a thermodynamically motivated micro-damage formulation is proposed for highrate and temperature dependent materials. This model uses a combined viscosity and nonlocal gradient localization limiters in order to regularize the dynamic strain localization problems. The enhanced nonlocal gradient-dependent theory formulates a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical theories and the classical (local) continuum theories. They are successful in explaining the size effects encountered at the micron scale and in preserving the well-posedeness of the initial boundary value problem governing the solution of material instability triggering strain localization. Moreover, viscosity (rate dependency) allows the spatial difference operator in the governing equations to retain its hyperbolicity and the initial boundary value problem is well-posed. This is due to the incorporation of either explicit (via nonlocal theory) or implicit (via viscosity) intrinsic material length scale parameter in the constitutive description. Model capabilities are preliminarily illustrated for the dynamic localization of inelastic flow in adiabatic shear bands and the perforation of Weldox 460E steel plates with different thicknesses by deformable blunt projectiles at various impact speeds. The simulated shear band results well illustrated the potential of the proposed model in dealing with the well-known mesh sensitivity problem. Consequently the introduced implicit and explicit length scale measures are able to predict size effects in localization failures. The micro-damage model used to predict material behavior under dynamic loading conditions was earlier presented in Refs. 1 and 2. Thus, only the main equations will be given in the following. The model is based on the nonlocal gradient-dependent theory. It includes the von Mises yield criterion, the non-associated flow rules, isotropic and anisotropic strain hardening, strain rate hardening, softening due to adiabatic heating and anisotropic damage evolution, and finally a path dependent equation of state. The stress-strain rate relationship in the spatial and damaged configuration is given by