Towards shock absorbing hyperelastic metamaterial design. (I) Macroscopic scale: Computational shock-capturing

Abstract

The work explores the computational modeling of propagating shocks in hyperelastic materials to be considered in the context of numerical analysis and design of mechanical energy absorbing materials. The computational approach can be classified as shock-capturing, since it aims at capturing the effects of the shock formation and propagation on the mechanical response in the solid, as opposed to the shock-fitting approach, an alternative focusing on determining the exact shock wave-front position in the propagation domain. Numerical simulation of the onset and propagation of discontinuous strain waves (mechanical shocks) across a solid is performed in that specific approach, and it is computationally assessed in different loading situations. The concept of extrinsic dissipation, arisen by breaking some of the polyconvexity aspects in hyperelastic materials, is recalled and exemplified via a large strains neo-Hookean polyconvex hyperelastic model which is perturbed in a number of different formats. The obtained mechanical responses, exhibiting propagating mechanical shocks, and the corresponding extrinsic dissipation, are explored together with the inherited computational issues, by means of numerical examples selected as representative for the aimed purposes. In a second stage, the problem of the dynamic impact of a rigid solid on low-density shock-absorbing specimens made of these perturbed hyperelastic materials is analyzed, and the amount and time-evolution of the resulting extrinsic dissipation are evaluated to characterize their performance for shock-absorbing purposes. Also, the exhibited property of shape recovery after impact is highlighted as a distinctive feature in front of alternative shock-absorbing materials. In the work, the analysis and numerical modeling are made at the single (macroscopic) scale, but the objective of the research is to constitute the first exploration of a more general setting, to be developed in future works: the multiscale design of shock-absorbing metamaterials.