1-131 MATHEMATICAL MODELS OF WAVE PROPAGATION AND FRACTURE IN UNIDIRECTIONAL COMPOSITES * G. Osharovich a , M. Ayzenberg-Stepanenko b and V. D. Kubenko c a Bar-Ilan University, Ramat-Gan, Israel b Ben-Gurion University of the Negev, Beer-Sheva, Israel c Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine Abstract. Mathematical models and computer algorithms are developed to calculate dynamic stress concentration and fracture in a unidirectional composite. A plane problem is considered. The composite consists of a regular system alternating extensible (fiber) and pliable (adhesive) layers. A calculation technique is designed to precise computing dynamic stress discontinuities that appear under fracture. Results of fracture simulations are presented in the composite pre-stretched along the fibers. 1 INTRODUCTION Unidirectional layered composite plates having a wide range of applications may be required to endure intense dynamic loadings ([1-5]). A set of dynamic problem have been studied on the basis of the homogenization approach averaging local properties of microstructure (see e.g. [5-8]). Within such approach, features inherent in impact processes are, as a rule, explored by methods and models of solid dynamics. Those methods are well developed for analysis of a longwave spectrum, for which microstructure peculiarities, however, play a secondary role. Wave front gaps and high-gradient components responsible for dynamic stress concentrations and brittle fracture propagation in a composite have not yet been adequately examined and remain a subject of contemporary research (see e.g. [9-10]). Significant rise in influence of microstructure on the wave picture essentially restricts capabilities of analytical modeling. There exist a set of numerical approaches intended for comprehensive simulations of composite dynamics in practice [11-14]. The recent work [14] reviews new software upgrades that are extending the digital advantage in the composites marketplace. At the same time, explicit-time algorithms used in computer codes come across specific obstacles, which do not allow to calculate accurately wave fronts and high- gradient components. We mean the mesh dispersion responsible for the emergence of short-wave "parasite" oscillations at calculation of transient processes and, notably, of fracture dynamics in reinforced composites: breaking of fibers and cracking of adhesive result in appearing of multiple wave fronts and high-frequency oscillations. In this work, computational algorithms are designed on the basis of the mesh dispersion minimization (MDM) technique, which allows mesh dispersion drawbacks to be eliminated or significantly decreased. The idea behind MDM is to properly adjust the so-called domains of influence determined by continuous and discrete models. The MDM approach proposed in [15] and upgraded in [16] has recently been used in diverse dynamic problems: high-speed penetration of layered shields [17], impact indentation of a rigid body into an elastic medium [18], and resonant excitation of lattice structures [19]. _____________________________________________________________________ __ * This research was supported by The Israel Science Foundation, Grant No. 504/08, and the Center of Advanced Studies of Mathematics at Ben-Gurion University of the Negev.