Approaching and overcoming the limitations of the multiscale Capriccio method for simulating the mechanical behavior of amorphous materials

Abstract

The Capriccio method is a computational technique for coupling finite element (FE) and molecular dynamics (MD) domains to bridge their length scales and to provide boundary conditions typically employed in large-scale engineering applications. Earlier studies showed that strain inconsistencies between the coupled domains are caused by the coupling region’s (bridging domain, BD) resistance to spatial motion. Thus, this work examines influences of coupling parameters on strain convergence in Capriccio-coupled setups to study the mechanical behavior of solid amorphous materials. To this end, we employ a linear elastic 1D setup, imitating essential features of the Capriccio method, including force-transmitting anchor points (AP), which couple the domains via linear elastic springs. To assess the effect of more complex interactions in 3D models versus 1D results, we use an interdimensional mapping scheme, allowing qualitative and quantitative comparisons. For validation, we employ both an inelastic polystyrene MD model and a predominantly elastic silica glass MD model, each coupled to a corresponding FE material description. Our 1D results demonstrate that decreasing the conventionally high AP stiffness, along with other less significant measures, diminishes this motion resistance, revealing an optimal ratio between the material stiffness of the coupled domains and the cumulative AP stiffness. The 3D silica setup confirms that these measures ensure decent domain adherence and sufficiently low strain incompatibilities to study the mechanical behavior of elastic models. However, these measures turn out limited and may not ensure sufficient accuracy for studying the deformation and fracture behavior of Capriccio-coupled inelastic models. To overcome this, we employ a modified coupling approach, revising the Capriccio method’s AP concept by introducing a much lower so-called molecular statics stiffness during the FE calculation and a higher AP stiffness during only the MD calculation. Initial results on the 1D setup indicate that essential coupling limitations can be overcome, albeit with the risk of oscillatory strain amplifications depending on the BD’s design. This novel approach may enable a more accurate analysis of the mechanical behavior of coupled inelastic amorphous materials. We recommend evaluating its performance in 3D alongside additional methodological extensions. Overall, our results outline the current limitations of the Capriccio method and lay the groundwork for its targeted extension to study the mechanical behavior and, in particular, fracture phenomena in inelastic amorphous materials.