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- Title
Connecting Atomistic and Continuous Models of Elastodynamics.
- Authors
Braun, Julian
- 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.
- Subjects
ELASTODYNAMICS; MATHEMATICAL continuum; NONLINEAR elastic fracture; INTERATOMIC distances; BOUNDARY value problems
- Publication
Archive for Rational Mechanics & Analysis, 2017, Vol 224, Issue 3, p907
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-017-1091-6