Molecular mechanics of disordered solids

Abstract

Disordered solids are ubiquitous in engineering and everyday use. Although research has made considerable progress in the last decades, our understanding of the mechanics of these materials is, at best, in an embryonic state. Since the nature of disorder complicates the realization of physically meaningful continuum-mechanical models, particle-based molecular descriptions provide a powerful alternative. This paper reviews the numerical realization of classical molecular dynamics from an engineer’s perspective, starting with selecting potential functions, boundary conditions, time integration, and thermodynamic ensembles. Then, we discuss the concept of the potential energy landscape and the computational realization of the most suitable minimization methods. Subsequently, we discuss the algorithms necessary to numerically generate disordered materials, considering their thermodynamic properties and structural identification. We comprehensively and critically review computational methods and strategies available to mimic disordered materials on a molecular level and discuss some intriguing phenomena that are, to date, mostly ignored when applying models based on continuum-mechanical frameworks. We present the crucial difference between the shear response of a crystalline and a disordered structure. In this context, we elaborate on why it is beneficial to use an overdamped, athermal description to disentangle the complex deformation mechanics of disordered solids and comprehensively discuss the theory of the mechanics of disordered materials, including the problems of prediction and reversibility. Furthermore, we examine the fracture process on the nanoscale and investigate the response behavior to more complex deformation protocols. Finally, we provide critical conclusions, including challenges and future perspectives for engineers.