In this study we use the material elastic properties as a base. A tow dimensional cracked plate under traction is modelled by finite element method (FEM) then a reduced model is built using the proper orthogonal decomposition method (POD) with help of radial basis functions (RBF) method of interpolation. The crack length is estimated as an inverse identification problem, basing on the deformati...

The current status o f the problem of small cracks in fatigue is presented. Several classes o f small cracks are distinguished, and their individual characteristics described. Specifically, for cracks small compared with microstructural size scales, for cracks small compared with the ex tent o f local plasticity or for cracks which are either chemically or physically small (e.g. about 1 mm or l...

A two-dimensional, time-harmonic eddy-current problem is examined in which a uniform field is perturbed by a long, surface-breaking crack in a non-magnetic, conducting half-space. The crack is assumed to be ideal in the sense that it has infinitesimal opening and yet forms a perfect barrier to the passage of electric current. A solution is sought which is accurate both at high frequencies, at w...

Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinen...

the cracked brazilian disc (cbd) specimen is widely used in order to determine mode-i/ii and mixed-mode fracture toughness of a rock medium. in this study, the stress intensity factor (sif) on the crack-tip in this specimen is calculated for various geometrical crack conditions using the extended-finite element method (x-fem). this method is based upon the finite element method (fem). in this m...

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...