Description of impact energy dissipation in fibrous composite materials using a nonlinear dynamic degenerate model

Abstract

Abstract To design effective energy-absorbing shields made of modern composite materials (e.g., fibrous composite panels), it is necessary to use deformable materials whose important feature is the largest possible dissipation of impact energy. Rheological properties of these materials differ significantly from dissipative and elastic properties described by the Hooke and Kelvin linear models. Moreover, the range of material deformation at the place of impact is so wide that the above-mentioned models are not sufficient to properly describe the process of energy dissipation. The value of dissipated energy is also important for the determination of the lifespan of dissipative and elastic elements subjected to cyclic dynamic loading and made of modern structural materials (fatigue phenomena). The authors proposed a dynamic model in which the rheological properties of the material are described by two spring parameters c, c 0 and one parameter of viscous damping k 0 in the configuration used in the so-called rheological standard model (Zener model). In addition, the model introduces the element of dry friction described by the appropriate function h(x). In addition, it was assumed that the non-linear element present in this model describes the effect of the occurrence of dry friction hSign(dx/dt) in the tested material, the value of which h is not constant but depends to some extent on the level of material deformation (variable x) is described by the relevant function. In this way, a non-linear third-order equation was obtained describing the motion of the so-called degenerate system. The developed method was tested on a computer system.