Energy Dissipation in Nonlinearly Elastic Auxetic and Non-Auxetic Mechanical Metamaterials with Friction and Material Damping

Abstract

This study investigates the energy dissipation behavior of a frictional mechanical metamaterial made of thermoplastic polyurethanes (TPU) 95 A, a thermoplastic polyurethane exhibiting hyperelastic and viscoelastic properties. The metamaterial features a structured geometry designed to enhance energy dissipation through both internal material damping and frictional sliding interactions. Experimental compression tests, finite element simulations, and theoretical modeling are conducted to evaluate load–displacement relationships, hysteresis behavior, and peak force response under quasi-static uniaxial loading. A Mooney–Rivlin three-parameter model is employed to characterize the hyperelastic behavior of TPU 95 A, with loading and unloading experimental data incorporated to improve simulation accuracy. The results indicate that the metamaterial effectively dissipates energy across various deformation cycles, demonstrating its potential as a tunable and lightweight solution for repeated energy dissipation applications. This makes it a promising candidate for damping and impact absorption in engineering systems. This study provides new insights into the mechanics of frictional metamaterials and their ability to sustain repeated deformation while efficiently dissipating energy.