Modeling of Progressive Damage in High Strain–Rate Deformations of Fiber-Reinforced Composites Romesh C. Batra and Noha M. Hassan Abstract We use the theory of internal variables, or equivalently of continuum damage mechanics, to develop a mathematical model involving three variables to describe the evolution of progressive damage in high strain–rate deformations of fiber-reinforced composites. The degradation of material parameters with the dam- age is considered. Values of material parameters in the postulated evolution laws of internal variables are determined from the test data. The delamination mode of fail- ure is simulated by hypothesizing a damage surface in terms of transverse normal and transverse shear stresses acting on an interface between two adjoining layers. When the stress state at a point on an interface lies on this surface, delamination is assumed to ensue from that point. Initial-boundary-value problems are numerically solved to validate the mathematical model by comparing computed results with test findings. A Figure of Merit, equal to the percentage of work done by external forces dissipated by all failure mechanisms, is introduced to characterize the performance of laminated composites under shock loads. 1 Introduction The failure mechanisms and processes on a micro-mechanical scale vary with the type of load, and are closely related to the ply-stacking sequence and properties of constituents, i.e., the matrix, the fiber, the interface, and the interphase between the fiber and the matrix (i.e., the treatment of the fiber prior to embedding it in the matrix, sometimes called the sizing of the fiber). Micro-level failure mechanisms include fiber breakage, fiber buckling, fiber splitting, fiber pullout, fiber/matrix R.C. Batra (  ) Department of Engineering Science and Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061 e-mail: rbatra@vt.edu N.M. Hassan Assistant Professor, Industrial Engineering Department, Alhosn University, P.O. Box: 38772, Abu Dhabi, UAE e-mail: n.hassan@alhosnu.ae I.M. Daniel et al. (eds.), Major Accomplishments in Composite Materials and Sandwich Structures: An Anthology of ONR Sponsored Research, c  Springer Science+Business Media B.V. 2009 89