The dynamic behavior of non-monotonic relaxation: Examination of select loading cases resulting in negative Prony coefficients

Non-monotonic viscoelastic relaxation has been exhibited in various materials while undergoing multi-step loading protocols. This paper introduces negative General Maxwell Coefficients as a means of modeling non-monotonic relaxation. The resulting relaxation functions are material and compression protocol dependent and based on empirical material study. Using this approach, the dynamic behavior of a material exhibiting an increasing relaxation function is examined. The results indicate a capacity to amplify displacements associated with dynamic excitation under the assumption that the dynamic behavior is sufficiently small compared to the loading protocol. Such behavior is strongly indicative of a potential metamaterial. An application in enhanced acoustic re-scatter is proposed and studied based on analysis and understanding of the phenomena. • Negative Prony multipliers are introduced in the General Maxwell Model to enable the simulation of non-monotonic relaxation. • Inverse relaxation functions induce stiffening under quasi-static loading and amplified displacement under dynamic loading. • Acoustic re-scattering is shown to be enhanced by use of disordered non-monotonic materials.