Localised failure in quasibrittle materials is due mainly to the effects of combined shear and compression. Once the cohesion strength is reached, shear tractions generate slip and aggregate interlocking that cause dilatancy inducing crack opening. Further damage reduces the cohesion and dilatancy so that eventually only a residual friction state remains. The energy dissipated due to friction and interlocking needs to be considered in the constitutive law. Initially, a Mohr-Coulomb yield surface with a tension cut-off will be investigated. A compression cap will be included when the modelled interfaces are not appropriately aligned and compressive failure must be controlled. The evolution of the yield surface and the appropriate flow rules to be used in the interface/particle model, are questions which will be examined. The particle/interface model with plasticity concentrated at the interface nodes, which can produce the correct volumetric expansion, will also be studied. A composite model has been developed to represent the heterogeneity of concrete consisting of coarse aggregates, mortar matrix and the mortar-aggregate interface. The constituents of concrete are modelled using triangular elements with six interface nodes along their sides. Fracture is captured through a constitutive softening-fracture law at the interface nodes, which bound the elastic domain inside each element. The inelastic displacement at an interface node represents the crack opening, which is associated to the conjugate internodal force by a single branch softening law. The path-dependent softening behaviour is derived in irreversible rate formulation within a quasi-prescribed displacement control. At each event in the loading history, all equilibrium solutions for the prescribed mesh can be obtained and the critical equilibrium path with the minimum increment of external work adopted. The crack profile develops restrictively to the interface boundaries of the defined mesh. No re-meshing is carried out. Solutions to the irreversible rate formulation are obtained using a mathematical programming procedure in the form of a linear complementary problem. Other work is aimed at incorporating fibre reinforcement in the model. Fibre particles are modelled by introducing additional linear elements interconnecting distant interface nodes in the matrix media after the generation of matrix-aggregate structure.

Among all existing fuel cell technologies, the planar solid oxide fuel cell (SOFC) is the most promising one for high power density applications. A planar SOFC consists of two porous ceramic layers (the anode and cathode) through which flows the fuel and oxidant. These ceramic layers are bonded to a solid electrolyte layer to form a tri-layer structure called PEN (positive-electrolyte-negative) across which the electrochemical reactions take place to generate electricity. Because SOFCs operate at high temperatures, the cell components (e.g., PEN and seals) are subjected to harsh environments and severe thermomechanical residual stresses. It has been reported repeatedly that, under combined thermomechanical, electrical and chemical driving forces, catastrophic failure often occurs suddenly due to material fracture or loss of adhesion at the material interfaces. Unfortunately, there have been very few thermomechanical modeling techniques that can be used for assessing the reliability and durability of SOFCs. Therefore, modeling techniques and simulation tools applicable to SOFC will need to be developed. Such techniques and tools enable us to analyze new cell designs, evaluate the performance of new materials, virtually simulate new stack configurations, as well as to assess the reliability and durability of stacks in operation. This research focuses on developing computational techniques for modeling fracture failure in SOFCs. The objectives are to investigate the failure modes and failure mechanisms due to fracture, and to develop a finite element based computational method to analyze and simulate fracture and crack growth in SOFCs. By using the commercial finite element software, ANSYS, as the basic computational tool, a MatLab based program has been developed. This MatLab program takes the displacement solutions from ANSYS as input to compute fracture parameters. The individual stress intensity factors are obtained by using the volume integrals in conjunction with the interaction integral technique. The software code developed here is the first of its kind capable of calculating stress intensity factors for three-dimensional cracks of curved front experiencing both mechanical and non-uniform temperature loading conditions. These results provide new scientific and engineering knowledge on SOFC failure, and enable us to analyze the performance, operations, and life characteristics of SOFCs.