Work

Discrete-to-continuum linearization in atomistic dynamics

Year: 2024

Type: article

Abstract: In the stationary case, atomistic interaction energies can be proved to $ \Gamma $-converge to classical elasticity models in the simultaneous atomistic-to-continuum and linearization limit [19,41]. The aim of this note is that of extending the convergence analysis to the dynamic setting. Moving within the framework of [41], we prove that solutions of the equation of motion driven by atomistic deformation energies converge to the solutions of the momentum equation for the corresponding continuum energy of linearized elasticity. By recasting the evolution problems in their equivalent energy-dissipation-inertia-principle form, we directly argue at the variational level of evolutionary $ \Gamma $-convergence [33,37]. This in particular ensures the pointwise in time convergence of the energies.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2024115

Authors: Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli

Institution: University of Vienna

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Awards: G1652504919, EXC 2044: Mathematik Münster: Dynamik – Geometrie – Struktur, G6938060324, G7207901211