Modelling of Energy Dissipation during Fracture of Concrete Notched Beams: Proportion of the Effective Crack and the Fracture Process Zone Consumption

The paper presents an analysis aiming at capturing the phenomenon of quasi-brittle fracture based on the record of the fracture tests on notched specimens. A method of separation of the energy amounts released for the crack advance and that dissipated within the volume of the sizeable nonlinear zone at the crack tip – the fracture process zone– is introduced. The approach is tested on selected data of published experimental campaigns accompanied with own conducted numerical simulations.

Energy Dissipation during Quasi-Brittle Fracture Associated with the Crack and the Fracture Process Zone Progression

The paper presents an analysis with an attempt to capture the phenomenon of quasi-brittle fracture based on the record of the fracture test on a notched specimen via separation the energy amounts released for the crack advance and dissipated within the volume of the sizeable nonlinear zone at the crack tip – the fracture process zone (FPZ). The described approach is tested on selected data of published experimental campaigns accompanied with own conducted numerical simulations.

Lattice Green’s Functions in Nonlinear Analysis of Defects

A method for analyzing problems involving defects in lattices is presented. Special attention is paid to problems in which the lattice containing the defect is infinite, and the response in a finite zone adjacent to the defect is nonlinear. It is shown that lattice Green’s functions allow one to reduce such problems to algebraic problems whose size is comparable to that of the nonlinear zone. The proposed method is similar to a hybrid finite-boundary element method in which the interior nonlinear region is treated with a finite element method and the exterior linear region is treated with a boundary element method. Method details are explained using an anti-plane deformation model problem involving a cylindrical vacancy.

Crack Propagation in Homogeneous and Bimaterial Sheets Under General In-Plane Loading: Nonlinear Analysis

The problem of non-coplanar crack propagation in homogeneous and bimaterial sheets is investigated within the framework of the nonlinear theory of plane stress and for the Generalized Neo-Hookean class of hyperelastic solids. The analysis is performed numerically using a boundary layer approach and the maximum energy release rate criterion. The influence of the large deformation effect on the limiting process associated with the concept of “infinitesimal virtual crack extension” is examined, together with the possible relation between the size of the nonlinear zone and the additional length parameter appearing in the linearized analysis of the interfacial crack propagation problem. As the virtual crack extension is gradually shortened to a size comparable to that of the nonlinear zone, a transition is observed between the nonunique value of the kink angle predicted by the linearized theory and a single “nonlinear” value, which is independent of the crack extension length but also independent of the far-field loading conditions. In the limit of homogeneous properties this angle is zero and is corroborated by experiments on natural rubber undergoing large deformations.