On local intrinsic dimensionality of deformation in complex materials

Abstract We propose a new metric called s -LID based on the concept of Local Intrinsic Dimensionality to identify and quantify hierarchies kinematic patterns in heterogeneous media. measures how outlying grain’s motion is relative its nearest neighbors displacement state space. To demonstrate merits over conventional measure strain, we apply it data individual grain motions set deforming granular materials. Several insights into evolution failure are uncovered. First, reveals hierarchy concurrent deformation bands that prevails throughout loading history. These structures vary not only dominance but also spatial scales. Second, nascent stages pre-failure regime, uncovers system-spanning, criss-crossing bands: microbands for small embryonic-shearbands at large , with former being dominant. At opposite extreme, fully formed shearbands dominate microbands. The novel uncovered from contradict common belief causal sequence where subset coalesce and/or grow form shearbands. Instead, suggests sample lead-up governed by complex symbiosis among these different coexisting structures, which amplifies promotes progressive Third, probed this transition microband-dominated regime shearband-dominated systematically suppressing rotations. found particle rotation be an essential enabler regime. When rotations completely suppressed, prevented: coexist parity.