1 Nonlocal Constitutive Model for Simulating Localized Damage and Fracture of Viscoplastic Solids under High Energy Impacts Rashid K. Abu Al-Rub 1 Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA Anthony N. Palazotto 2 Department of Aeronautics and Astronautics, Air Force Institute of Technology, WPAFB, OH 45433-7765, USA Developing and applying theoretical and computational models that guide the development of design criteria and fabrication processes of high impact/ballistic-resistant material are essential. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening (localization) and the finite element computations are considerably affected by the mesh size and alignment and gives non-physical descriptions of the damaged regions and failure of solids. This study is concerned with the development of a novel coupled thermo-hypoelasto, thermo-viscoplastic, and thermo-viscodamage constitutive model within the laws of thermodynamics in which implicit and explicit intrinsic material length scale parameters are incorporated through the nonlocal gradient-dependent viscoplasticity and viscodamage constitutive equations. In this current model, the Laplacian of the effective viscoplastic strain rate and its coefficient, which introduces a missing length scale parameter, enter the constitutive equations besides the local effective viscoplastic strain. It is shown through simulating plugging fracture in ballistic penetration of high-strength steel circular plates by hardened blunt-nose cylindrical steel projectiles that the Laplacian coefficient parameter plays the role of a localization limiter during the penetration and perforation processes allowing one to obtain meaningful values for the ballistic limit velocity (or perforation resistance) independent of the finite element mesh density. For the corresponding local model, on the other hand, the ballistic limit continuously decreases as the mesh density increases and does not converge even for the finest mesh. 1. Introduction The effective use of existing computer codes and schemes in the direct simulation of impact problems is limited by the ability in obtaining mesh-independent deformation and fracture results [1]. During impact loading, especially by blunt-nose projectiles, large inelastic deformation and excessive damage associated with high strain rates lead, for a broad class of brittle and ductile materials, to degradation and fracture by strain localization and development of adiabatic shear banding [2]. Therefore, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element (or other numerical techniques) computations are considerably affected by the mesh size when using the classical (local) continuum plasticity and damage theories. This gives rise to non-physical descriptions of the material and structural failure, and unreliable computational tool that cannot be used in guiding the design of new generations of advanced impact/blast-resistant materials and structures. The issue of mesh sensitivity has been thoroughly investigated in the literature for many static, quasi- static, and dynamic problems. The mesh sensitivity in predicting damage, fracture, and failure is attributed to the absence of an intrinsic material length scale parameter in the constitutive description of the plasticity, damage, and fracture models. Such a length scale can improve the well-posed nature of the simulated (initial) boundary value problem and acts as a localization limiter. For the last three decades, several localization limiters or regularization approaches (i.e. as means of preserving the well-posed nature of the (initial) boundary value problems) that introduce explicit or implicit length scale measures have been proposed in the literature to accommodate this problem. They include but are not limited to: rate-dependent models, by including thermal effects and thermomechanical couplings, nonlocal integral 1 Assistant Professor, 3136 TAMU, College Station, TX 77843, e-mail: rabualrub@civil.tamu.edu . 2 Professor, Department of Aeronautics and Astronautics, Air Force Institute of Technology, WPAFB, OH 45433- 7765. 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference<BR> 19th 4 - 7 April 2011, Denver, Colorado AIAA 2011-2175 Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.