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Connecting Atomistic and Continuous Models of Elastodynamics

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Abstract

We prove the long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the interatomic distances tend to zero. Here, the continuum energy density is given by the Cauchy–Born rule. The models considered allow for general finite range interactions. To control the stability of large deformations we also prove a new atomistic Gårding inequality.

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Authors and Affiliations

  1. Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, UK

    Julian Braun

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  1. Julian Braun
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Correspondence to Julian Braun.

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Communicated by C. Le Bris

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Braun, J. Connecting Atomistic and Continuous Models of Elastodynamics. Arch Rational Mech Anal 224, 907–953 (2017). https://doi.org/10.1007/s00205-017-1091-6

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  • DOI: https://doi.org/10.1007/s00205-017-1091-6

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