We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a micro-object (defect) and a macro-object (crack) modeled in two dimensions. The corresponding nonlinear optimization problem subject to inequality constraints at the crack is considered within a gene...

Crack propagation modeling in quasi-brittle materials such as concrete is essential for improving the reliability and load-bearing capacity assessment. Crack propagation explains many failure characteristics of concrete structures using the fracture mechanics approach. This approach could better explain the softening behavior of concrete structures. A great effort has been made in developing nu...

We consider a Mode III lattice with an interface layer where the dynamic crack growth is caused by a localised sinusoidal wave. In the wave–fracture scenario, the ‘feeding wave’ (here also called the knife wave) delivers energy to the moving crack front, while the dissipative waves carry a part of this energy away from the front. The questions addressed here are: What are the conditions of exis...

The dynamic fracture behavior of layered architectures is experimentally studied. Specifically, crack penetration, trapping, and branching at an interface are examined. A newly introduced optical technique called Digital Gradient Sensing (DGS) that quantifies elasto-optic effects due to a non-uniform state of stress is extended to perform full-field measurements during the fracture event using ...

Polymethylmethacrylate (PMMA) bone cement is a polymeric material that is widely used as a structural orthopedic material. However, it is not an ideal material for bone grafting due to its fragility. Carbon nanotubes (CNTs) have been introduced in order to reinforce PMMA resulting in a composite material which exhibits improved tensile properties, increased fatigue resistance and fracture tough...

Colloidal dispersions are known to display a fascinating network of cracks on drying. We probe the fracture mechanics of free-standing films of aqueous polymer-particle dispersions. Thin films of the dispersion are cast between a pair of plain steel wires and allowed to dry under ambient conditions. The strain induced on the particle network during drying is relieved by cracking. The stress whi...

Crack deflection and the subsequent growth of delamination cracks can be a potent source of energy dissipation during the fracture of layered ceramics. In this study, multilayered ceramics that consist of silicon nitride (Si3N4) layers separated by boron nitride/silicon nitride (BN/Si3N4) interphases have been manufactured and tested. Flexural tests reveal that the crack path is dependent on th...

In the present paper, we investigate the influence of corrosion driving forces and interfacial toughness for a coated material subjected to mechanical loading. If the protective coating is cracked, the substrate material may become exposed to a corrosive media. For a stress corrosion sensitive substrate material, this may lead to detrimental crack growth. A crack is assumed to grow by anodic di...

Bamboo, as a natural hierarchical cellular material, exhibits remarkable mechanical properties including excellent flexibility and fracture toughness. As far as bamboo as a functionally graded bio-composite is concerned, the interactions of different constituents (bamboo fibers; parenchyma cells; and vessels.) alongside their corresponding interfacial areas with a developed crack should be of h...

The mechanics of cracking in fiber-reinforced ceramic matrix composites (CMCs) under general loadings remains incomplete. The present paper addresses one outstanding aspect of this problem: the development of matrix cracks in unidirectional plies under shear loading. To this end, we develop a model based on potential energy differences upstream and downstream of a fully bridged steady-state mat...