The standard benchmark problem of a notched plate in tension. The notch is either "meshed-in" or represented using an initial damage field. A Mode-I type of crack emanates from the notch.

The standard benchmark problem of a notched plate under shear load. The notch is either "meshed-in" or represented using an initial damage field. A Mode-II type of crack emanates from the notch.

Row 1: Three dimensional soil desiccation simulations in a film-substrate system.

Row 2: Two dimensional crack morphologies obtained with different constructions of stochastic fracture properties.

The Kalthoff-Winkler experiment simulated using the phase-field cohesive fracture model. The elastodynamics problem is solved using an explicit central-difference operator. The phase-field is shown on the left, and the field of maximum principal stress is shown on the right.

The stochastic random field is decomposed using the Karhunen-Loeve expansion. The first 10 eigenvectors with the largest eigenvalues are shown on the left. The crack propagation with random fracture properties constructed using the KL-expansion is shown on the right.

The simulation result of a ductile aluminum-alloy specimen. The compressible Neo-Hookean hyperelasticity model and the plasticity model are used. The fracture toughness is coupled with the effective plastic strain by introducing a novel coalescence dissipation in the total potential. The resulting load-deflection curve is also reasonable close to the experimental data after calibration.