DISCRETE-TO-CONTINUUM LINEARIZATION IN ATOMISTIC DYNAMICS

Friedrich M, Seitz M, Stefanelli U (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Discrete and Continuous Dynamical Systems American Institute of Mathematical Sciences (AIMS)

Book Volume: 45

Pages Range: 847-874

Journal Issue: 3

DOI: 10.3934/dcds.2024115

Abstract

In the stationary case, atomistic interaction energies can be proved to Γ-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 Γ-convergence [33, 37]. This in particular ensures the pointwise in time convergence of the energies.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Friedrich, M., Seitz, M., & Stefanelli, U. (2025). DISCRETE-TO-CONTINUUM LINEARIZATION IN ATOMISTIC DYNAMICS. Discrete and Continuous Dynamical Systems, 45(3), 847-874. https://doi.org/10.3934/dcds.2024115

MLA:

Friedrich, Manuel, Manuel Seitz, and Ulisse Stefanelli. "DISCRETE-TO-CONTINUUM LINEARIZATION IN ATOMISTIC DYNAMICS." Discrete and Continuous Dynamical Systems 45.3 (2025): 847-874.

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