A Computational Framework via the Continuum Damage Mechanics Based Model for Brittle Damage, and Numerical Validation with Experiment Y. C. Miller * X. Zhou † , D. Sha ‡ , and K. K. Tamma § The modeling of brittle damage are traditionally based on empirical functions. The empirical function models for the brittle damage lack a theoretical basis for the proof of the satisfication for Clausius-Duhem inequality, and it has difficulty in incorporating with continuum mechanic based formulations from a computational perspective. Employing the Lemaitre continuum damage formulation approach, in this paper, we re-formulate the empirical function based brittle damage phenomenon into the continuum damage mechanics formulation to accurately model the mechanical behavior. The resulting formulation is validated with experimental results and achieve good agreement. I. Introduction Ceramic composite armor and ceramic/ductile multilayer material systems have been studied extensively to improve the ballistic protection of light armored vehicles. Ceramic armor provides the ability to reduce the total weight of the armor protection, increasing mobility and fuel efficiency, while maintaining the protection level of traditional metal armor. One drawback to ceramic armor is its inability to withstand multiple hits. To improve the multi-hit capability of ceramic armor, multilayered armor designs are being developed. These multilayered designs use a ceramic plate backed by a ductile material, such as a metal or a composite. Multilayered armor designs have proven to be successful against small arms fire and shell fragments, while reducing the armor’s areal density. In order to efficiently develop new improved designs, armor designers have turned to finite element modeling to assess the performance of material combinations. The difficulty and costs related to ballistic impact experiments and the complexity of analytical solutions has led to the increased use of finite element codes to model ballistic impact events. Impact events require simulating conditions under large deformation, high strain rates, varying stress states and complicated load history. Finite element modeling of advanced armor designs requires accurate material models for both brittle and ductile materials. Computations need to include accurate modeling of both the target and the projectile. Ceramic and metal armor systems have been investigated experimentally, analytically and numerically. Although experiments are the most accurate at capturing material behavior, they are expensive and are only accurate for the specific system being tested. Analytical methods can be used to predict material behavior without running experiments. Accurate analytical models are also limited to specific cases and require extensive material characterization. Numerical methods can provide a complete solution to impact problems and have proven to be effective at capturing the penetration process of projectiles. However, these methods require accurate material models, damage mechanics principles, and robust and effective numerical methods and computational algorithms. Obtaining parameters for these material models typically requires extensive experiments. A combination of experimental, analytical and numerical methods is required in order to model impact situations. Once accurate material models have been developed experimentally, numerical simulations may be the most efficient way to test different designs. Numerical simulations have been used to qualitatively understand impact of armor materials and to model experimental results. For all simulations, robust numerical methods and computational algorithms, * Captain, Instructor, United States Military Academy at West Point, Yvonne.Miller@usma.edu † Research Assistant Professor, Department of Mechanical Engineering, Univeristy of Minnesota, xiangmin.zhou@gmail.com ‡ Researcher, Department of Mechanical Engineering, Univeristy of Minnesota, sha@msi.umn.edu § Professor, to receive correspondence, Department of Mechanical Engineering, Univeristy of Minnesota, ktamma@umn.edu 1 of 14 American Institute of Aeronautics and Astronautics