微结构固体中孤立波的演变及非光滑孤立波

Abstract

A new free energy function was given with all quadratic terms of macro strain and micro deformation, as well as cubic terms of macro strain. A new model for description of the longitudinal wave propagation in microstructured solids was established by means of the new free energy function and Mindlin’s microstructure theory. Based on the dynamical system theory for singular traveling wave systems developed recently, all bifurcations of phase portraits of the traveling wave systems were analyzed, and the periodic wave solutions, the solitary wave solutions, the quasi peakon solutions, the peakon solutions and the compacton solutions were given. The obtained peakon and compacton solutions effectively prove that non-smooth solitary waves such as the peakon and the compacton can form and exist in microstructured solids under certain conditions. The results further exceed the conclusion that only smooth solitary waves can exist in microstructured solids.