SOME INVERSE PROBLEMS IN PENETRATION MECHANICS G. Ben-Dor, A. Dubinsky, and T. Elperin Department of Mechanical Engineering, Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, Beer-Sheva, Israel Many empirical and semi-empirical models that are widely used in impact dynamics employ the dependencies between the impact (initial) velocity and the depth of penetration (DOP). These dependencies are often obtained by statistical processing of experimental results and are not based on the theoretical models of penetration. In this study we develop an approach that allows using such phenomenological correlations for determining the dependencies of forces acting on a penetrator versus the instantaneous DOP and the instantaneous velocity. The developed approach can be also useful in other fields of mechanics. Keywords: Concrete; Granular media; High speed; Impact; Penetration. INTRODUCTION Inverse problems often occur in various fields of science and are a subject of numerous studies (see e.g., Denisov, 1994; Ramm, 2005 and references therein). Solution of the inverse problems for ordinary differential equations (ODEs) implies determining either the right-hand side of ODEs or their coefficients (including the case when they are functions of the independent variable), using the known solution. However, inverse problems of different type also occur in applied sciences, and particular in penetration mechanics (Ambroso et al., 2005; Eisler et al., 1998; Katsuragi and Durian, 2007; Kennedy, 1976; Pilyugin, 2004). Comprehensive theoretical foundations for investigating these problems have not been developed as yet. It is convenient to describe the essence of these problems without dwelling on a particular application. Let y = x y 0  be a solution of the first-order ODE with the initial condition y = y 0 for x = 0. Let us consider for y =˜ y the set of x 1 and y 0 , which satisfy the equation ˜ y = x 1 y 0 . It is assumed that the empirical dependence x 1 y 0  ≡ x 1 y 0  -˜ y = 0 is known. Consider the problem of recovering the ODE, which includes the unknown functions such that the solution of this ODE implies the dependence, x 1 y 0  = 0. In the case when ODE describes penetration of a striker Received April 16, 2010; Accepted June 4, 2010 Correspondence: Tov Elperin, Department of Mechanical Engineering, Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel; E-mail: elperin@.bgu.ac.il 468 Mechanics Based Design of Structures and Machines, 38(4): 468–480, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 1539-7734 print/1539-7742 online DOI: 10.1080/15397734.2010.501274 Communicated by N.Banichuk.