Assessing the Capriccio method via one-dimensional systems for coupled continuum-particle simulations in various uniaxial load cases using a novel interdimensional comparison approach

This contribution investigates sources of insufficiencies observed with the Capriccio method for concurrent continuum-particle coupling using a novel comparison technique. This approach maps the deformation states of three-dimensional (3D) coupled domains into a concise one-dimensional (1D) representation, which allows for a separate evaluation of the domain strains in a unified representation, enabling facile comparisons of the domain states during deformation. For the investigation, we employ both a 1D coupled system resembling the most relevant features of the full 3D Capriccio method as well as a corresponding 3D setup. Our analysis explores interactions between different material models in finite element (FE) and molecular dynamics (MD) domains. Based on various load cases studied in the 1D setup, we identify a resistance of the coupling region to spatial movement as the fundamental cause of strain convergence problems when applying the staggered solution scheme. Using the developed mapping approach, examination of the corresponding 3D setup reveals that these strain inconsistencies are even exacerbated by adverse relaxation effects in viscous MD models, particularly when coupled to a corresponding viscoelastic–viscoplastic FE model, leading to divergence from optimal strain. Our findings confirm that smaller strain increments in combination with larger load step numbers significantly improve strain convergence in all domains. Overall, this indicates the need for detailed sensitivity analysis of coupling parameter influences to reduce the identified motion resistance of the coupling region. Based on promising results in 1D, we further recommend exploring monolithic solving schemes for 3D systems to achieve optimal strain convergence for all types of Capriccio-based coupled particle and continuum material models. Moreover, our systematic approach of system definition and interdimensional comparison may serve as a model to assess other domain-decomposition coupling techniques.