Nonlocal models with damage-dependent interactions motivated by internal time

• The paper addresses the possible evolution of internal material length.
• Nonlocal weight kernel function of wave propagation time normalized by an internal time.
• Strong localization with a non-spreading damage zone.
• Pure geometric extension to 3D from WKB approximation for wave propagation in damaged media.
• Defines Nonlocal Eikonal damage framework for isotropic and anisotropic damage models.

The paper addresses open questions concerning isotropic/anisotropic nonlocal models: possible evolution of internal length and special treatments near boundaries and cracks. First, the nonlocal weight is considered as function of information/wave propagation time normalized by an internal time, which leads to localization with a non-spreading damage zone. The limit value of full damage is attained at a single point in 1D. Second, the WKB approximation for wave propagation in 3D damaged media defines interaction distances as solutions of an eikonal equation. This motivates the interpretation that damage, possibly anisotropic, curves the space in which the interaction distances are calculated.