Reducing the severity of an impact to a structure or a multibody system is a significant aspect of engineering design. This requires the knowledge of variations of the resulting contact forces and also how these contact forces can be reduced. This paper presents an optimization methodology for the selection of proper parameters in the contact/impact force models so as to minimize the maximum value of the contact force. A two-particle model of an impact between two solids is considered, and then generalized to the impact analysis between two bodies of a multibody system. The concept of effective mass is presented in order to compensate for the effect of joint forces or impulses. The system is reduced to a single degree-of-freedom mass-spring-damper vibro-impact system. A single differential equation of motion in the direction of relative indentation of local contact surfaces is derived. Different contact force models of hysteresis form including linear and nonlinear models are described. An optimization problem is then formulated and solved by using the method of modified feasible direction for constrained minimization. A numerical integrator is used at every design iteration to obtain the system dynamic response for a given set of design variables. The objective function is to minimize the peak acceleration of the system equivalent mass resulting from the contact force. Comparison of the system with optimal parameters and non-optimal one shows that the peak contact force is greatly reduced for the optimal one. Since these parameters reflect the material properties (stiffness and damping) of the impacting bodies or surfaces, suitable materials may then be selected based upon the information provided by this optimization procedure. It is observed that the materials, which have good crashworthiness properties should posses capability of dissipating impact energy both in the forms of permanent indentation and internal damping friction. Based upon the analysis of the impact responses, mechanism of energy dissipation, and the typical force-indentation diagram for the high energy absorption materials obtained from experiments, a new contact force model is proposed which could precisely describe the impact response of high energy-absorption materials.

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