New finite elements with embedded strong discontinuities for the modeling of failure in solids

This work is concerned with the development of new finite elements with embedded strong discontinuities for the numerical modeling of failure in solids, where a strong discontinuity is understood as a discontinuity in the displacement field, representing failure on the macroscopic scale. Singular fields characteristic for solids at failure, such as cracks or shearbands, are incorporated locally into the finite element formulation, resulting in an efficient implementation of these effects into standard finite element procedures.;The newly developed finite elements improve on the kinematical description of the strong discontinuities when compared to existing methods in the sense that stress locking can be avoided for non-constant separation modes, meaning that no stress transfer occurs between two parts of a single finite element separated by a fully softened strong discontinuity. This improvement allows also to capture better the localized dissipative mechanisms associated with the response of the singular fields characteristic for the failing material.;The contributions are developed within the infinitesimal theory for the quasistatic case and are subsequently extended to take into account geometric nonlinear effects. The frame indifference of the formulation within the finite deformation theory under superimposed rigid body motions appears as a challenging requirement directly influencing the developments of the new finite elements.;A series of numerical tests designed to evaluate the locking free and frame indifferent properties of the new elements are presented. Classical benchmark problems for concrete materials in the form of the three- and four-point bending test, together with simulations of the delamination in laminated composite materials and the shear band propagation for a slope failure are shown to illustrate the performance of the newly developed finite elements.;The modeling of dynamic fracture drastically increases the complexity of the numerical method when compared to the quasi-static case so that extensions of this finite element framework to take into account dynamic effects are rare. In this work a first attempt to model dynamic fracture is undertaken for the newly developed finite elements in the form of the numerical simulation of crack branching in brittle materials and failure mode transition in ductile materials.