Multiscale coupling in function space-weak coupling between molecular dynamics and continuum mechanics. (English) Zbl 1176.74179
Summary: We present a function space-oriented coupling approach for the multiscale simulation of non-linear processes in mechanics using finite elements and molecular dynamics concurrently. The key idea is to construct a transfer operator between the different scales on the basis of weighted local averaging instead of using point wise taken values. The local weight functions are constructed by assigning a partition of unity to the molecular degrees of freedom (Shepard’s approach). This allows for decomposing the micro scale displacements into a low-frequency and a high-frequency part by means of a weighted L2-projection. Numerical experiments illustrating the stabilizing effect of our coupling approach are given.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74A25 | Molecular, statistical, and kinetic theories in solid mechanics |
Software:
PUMAReferences:
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