Abstract:Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for micrometer-scale structural analyses. We develop a two-scale atomistic-continuum framework that couples a nonlinear finite-element boundary-value problem at the microscale to periodic molecular-statics cell problems at quadrature points. The scale transition is formulated by computational homogenization in the sense of Hill-Mandel energy equivalence. Instead of prescribing a continuum constitutive law on the lower scale, the atomistic cell is driven directly by the continuum deformation and returns volume-averaged stresses in work-conjugate form together with effective tangent moduli. Numerical examples for single-crystalline copper show pronounced tension-compression asymmetry, abrupt instability-driven defect nucleation, rapid stabilization under reversed cyclic loading, and localized elastic-plastic transition in cantilever bending. In all these strongly nonlinear scenarios, the coarse-scale Newton solver remains robust and recovers near-quadratic convergence in its final iterations. The two-scale framework thus extends potential-based atomistic modeling to structural length scales that are inaccessible to direct atomistic simulation in the present quasi-static, athermal setting.
| Subjects: | Numerical Analysis (math.NA) |
| MSC classes: | 74Q05, 74S05, 74M25, 74N05, 74N15, 65N30 |
| Cite as: | arXiv:2605.25286 [math.NA] |
| (or arXiv:2605.25286v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25286 arXiv-issued DOI via DataCite (pending registration) |
From: Bernhard Eidel [view email]
[v1]
Sun, 24 May 2026 22:52:31 UTC (9,754 KB)
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