Many problems in the modelling of materials call for a synthesis of approaches used at both the atomistic and the continuum levels. One notable implementation of this type of strategy is in the construction of local constitutive relations which serve to provide a microscopic underpinning for the energetics of phenomena ranging from interfacial debonding to dislocation nucleation. The need for atom- istics in the formulation of such local constitutive approaches is twofold; first, atomistics can serve as the basis of the constitutive phenomenology itself; secondly, atomistics can be used to make quantitative tests of the assumptions which underlie the continuum framework. The present work demonstrates this strategy through the examples of two types of continuum models: the Peierls framework used in the analysis of dislocation nucleation in solids and the type of model used to describe interfacial debonding. Using atomistics within the framework of the embedded-atom method, we test each of the central assumptions in the Peierls- type analysis separately. The insights of this analysis are then combined to test the energetics predicted by the Peierls dislocation model as a whole via consideration of the Lomer dislocation in aluminium. These calculations demonstrate that the local constitutive framework leads to significant errors for rapidly varying slip and opening distributions and yield suggestions for the further refinement of continuum models.

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Journal Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties
Miller, R, & Phillips, R. (Rob). (1996). Critical analysis of local constitutive models for slip and decohesion. Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties, 73(4), 803–827. doi:10.1080/01418619608243690