Fracture—how and why materials break—remains one of the most challenging problems in solid mechanics. Modeling both crack nucleation under multiaxial loading and contact phenomena—closure, sliding, and friction—within a single variational phase-field framework has long been difficult. Existing phase-field models typically treat either nucleation or contact, while nearly incompressible soft materials, such as elastomers and hydrogels, introduce additional challenges due to volumetric locking and suppressed crack opening in smeared models.
In this seminar, I present new mathematical and computational advances that (i) unify multiaxial crack nucleation and contact behavior within a single variational framework, and (ii) enable predictive three-dimensional simulations of large-deformation fracture in nearly incompressible hyperelastic materials. I also reveal a surprising finding: in certain anisotropic materials, a single load can produce multiple energetically admissible crack paths, with the observed path selected by tiny imperfections—providing the first numerical validation of a local energetic principle governing crack-path selection.
