Data-driven fracture mechanics

Abstract

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step is identified as the point within the data set that best satisfies either the Kuhn-Tucker conditions stemming from the variational fracture problem or global minimization of a suitable energy functional, leading to data-driven counterparts of both the local and the global minimization approaches of variational fracture mechanics. Both formulations are tested on different test configurations with and without noise and for Griffith and R-curve type fracture behavior.

Accepted CMAME revised version, details added, conclusions did not change

References in corpus (6)

• Data-driven computational mechanics
• Model-Free Data-Driven Inelasticity
• Data Driven Computing with Noisy Material Data Sets
• Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers
• Data-Driven Finite Elasticity
• Mixed-Integer Programming Formulation of a Data-Driven Solver in Computational Elasticity

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