Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

The prediction of fracture in thin-walled structures is decisive for a wide range applications. Modeling methods such as the phase-field method usually consider cracks to be constant over thickness which, especially load cases involving bending, an imperfect approximation. In this contribution, phenomena along direction structural elements (plates or shells) are addressed with modeling approach. For purpose, new, so called “mixed-dimensional” model introduced, which combines representing displacement field two-dimensional shell midsurface continuum describing crack three-dimensional solid space. proposed uses two separate finite element discretizations, where transfer variables between coupled two- and fields performed at integration points turn need have corresponding geometric locations. governing equations mixed-dimensional deduced consistent manner from total energy functional them also being compared existing standard models. resulting has advantage reduced computational effort due while still able accurately arbitrary through-thickness evolutions well partly broken shells elements. Amongst others, higher accuracy numerical efficiency tested validated by comparing simulation results new those obtained models using numerous representative examples.