Nonlocal models with damage-dependent interactions motivated by internal time

Abstract : There are open questions concerning isotropic/anisotropic nonlocal models, as the possible evolution of internal length, as special treatments near boundaries and cracks. First, one makes nonlocal weight kernel function of information/wave propagation time normalized by an internal time and obtains strong localization with a non-spreading damage zone. The limit value of full damage is attained at a single point in 1D. Second, WKB approximation for wave propagation in 3D damaged media define interaction distances as solutions of an eikonal equation. This leads to the interpretation that damage, possibly anisotropic, curves the space in which the interaction distances are calculated.
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Rodrigue Desmorat, Fabrice Gatuingt, Milan Jirásek. Nonlocal models with damage-dependent interactions motivated by internal time. Engineering Fracture Mechanics, Elsevier, 2015, 142, pp.255-275. 〈10.1016/j.engfracmech.2015.06.015〉. 〈hal-01254354〉

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