Quantum mechanics

Variational method

Engineering

Geotechnical engineering

Applied mathematics

Energy minimization

Set (abstract data type)

Computer science

Mathematical optimization

Variational principle

Geology

Data-driven

Physics

Finite element method

Mathematics

Brittle fracture

Computational mechanics

Mathematical analysis

Minification

Artificial intelligence

Geometry

Structural engineering

Calculus of variations

Point (geometry)

Fracture (geology)

Programming language

Test data

Mechanics

Fracture mechanics

Computer Methods in Applied Mechanics and Engineering

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.

Data-driven fracture mechanics