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In this paper 8-node traction singular boundary clcments are employed to represent displacement and traction variations in the vicinity of the crack front in thrce-dimensional geometries. The numerical procedure suggested for evaluating the singular integrals extending over these special elements is described. The efficiency and accuracy of the special elements and integration procedure are demonstrated by the results obtained in a simple test problem whose analytical solution is known. Theinteraction of two circular coplanar cracks embedded in an infinite medium under uniform tension loading is also analysed. Finally, the stress intensity factor variation computed for a semi-circular inner surface crack in a pressurized cylinder is presented.

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The use of Mixed Reality in the product development process is emerging as a promising solution that combines the advantages of virtual and rapid prototyping. A mixed prototype is usually based on a physical mock-up on which the visual appearance of the product is superimposed thanks to the augmented reality technologies. An open issue in mixed prototyping is the reduction of time and efforts required to generate and update the behaviour model of the product. This paper presents a Mixed Reality environment in which the product behaviour is simulated using the same models and the same software employed by the engineers in the design phase. This approach guarantees the reliability of the simulation and allows a strong reduction of the time needed to develop the digital prototype. Moreover the paper presents an innovative technique, specifically studied for the simulation of electrical appliances, that aims to make the user able to naturally interact with the mixed prototype. This technique is able to manage the occlusion between real and virtual objects and the interpretation of the user’s gestures while he/she is interacting with the elements of the product interface. The novelty of the technique is that it does not require any specific device like data-gloves or tracking systems.

The paper discusses two physically based weakest-link approaches, commonly adopted to evaluate the reliability of ceramic components in multiaxial states of stress (namely, Evans’ multiaxial elemental strength method and Batdorf’s flaw density approach) whose equivalence has been recently proven. It is shown here how the two formulations can be simultaneously derived from the basic assumptions and simply regarded as two different ways to evaluate the same integral. Differences in computational efficiency yielded by the two different integration schemes are also illustrated.