Data-Driven nonlocal mechanics: Discovering the internal length scales of materials
Nonlocal effects permeate most microstructured materials, including granular media, metals and foams. The quest for predictive nonlocal mechanical theories with well-defined internal length scales has been ongoing for more than a century since the seminal work of the Cosserats. We present here a novel framework for the nonlocal analysis of material behavior, which bypasses the need to define any internal length scale. This is achieved by extending the Data-Driven paradigm in mechanics, originally introduced for simple continua, into generalized continua. The problem is formulated directly on a material data set, comprised of higher-order kinematics and their conjugate kinetics, which are identified from experiments or inferred from lower scale computations. The case of a micropolar continuum is used as a vehicle to introduce the framework, which may also be adapted to strain-gradient and micromorphic media. Two applications are presented: a micropolar elastic plate with a hole, which is used to demonstrate the convergence properties of the method, and the shear banding problem of a triaxially compressed sample of quartz sand, which is used to demonstrate the applicability of the method in the case of complex history-dependent material behavior.
© 2021 Elsevier. Received 29 January 2021, Revised 30 April 2021, Accepted 5 July 2021, Available online 23 August 2021. Partial support for this research was provided by US ARO funding through the Multidisciplinary University Research Initiative (MURI) Grant No. W911NF-19-1-0245. This support is gratefully acknowledged. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.