Stewart Silling
Sandia National Laboratories

Upscaling Material Properties and Damage in Peridynamics

The peridynamic theory is an extension of the standard theory of solid mechanics that applies to discontinuous deformations and long-range forces. It is formulated in terms of integro-differential equations that include strong nonlocality, in contrast to the partial differential equations of the standard theory. Material models in the peridynamic theory contain a characteristic length scale called the “horizon” that represents the maximum interaction distance between material particles.

The availability of a length scale in the peridynamic equations offers an opportunity to explore multiscale mechanics and thermodynamics within a consistent mathematical framework. By adjusting the horizon, we can in principle apply the same integro-differential equations to small-scale phenomena such as material defects and to larger-scale mechanics of structures.

To exploit this potential for multiscale computation within peridynamics, accurate upscaling or coarse-graining of material properties is necessary. This talk will describe recent work on the systematic derivation of larger-scale material properties from smaller-scale mechanics. In the proposed method, the larger-scale degrees of freedom represent weighted mean displacements in the smaller-scale representation. The net force interactions between the larger-scale degrees of freedom represent the upscaled material properties. This method avoids the need for representative volume elements and can incorporate changes in damage. Theoretically, this upscaling process can be repeated many times to achieve very large increases in length scale using the same mathematical procedure at each successive step.
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