Solutions of contact problems by the assumed stress hybrid model

A method was developed for contact problems which may be either frictional or frictionless and may involve extensive sliding between deformable bodies. It was based on an assumed stress hybrid approach and on an incremental variational principle for which the Euler's equations of the functional include the equilibrium and compatibility conditions at the contact surface. The tractions at an assumed contact surface were introduced as Lagrangian multipliers in the formulation. It was concluded from the results of several example solutions that the extensive sliding contact between deformable bodies can be solved by the present method

Energy Distribution for SH-Waves in Slightly Anisotropic Materials

Many polycrystalline metal aggregates display a slight amount of anisotropy due to texture that develops during fabrication procedures such as rolling. This macroscopic anisotropy produces a birefringence of SH-waves propagating normal to the plate, i.e., the velocity of SH-waves polarized parallel to the rolling direction is usually faster than that of SH-waves polarized perpendicular to the rolling direction. For polarization angles not in or perpendicular to the rolling direction the wave is assumed to split into two waves, one polarized parallel and one polarized perpendicular to the rolling (similar to what is observed for particular propagation directions in single crystals). However slightly anisotropic materials have only a small percentage of preferential grain alignment, the bulk of the grains being of random orientation. In consideration of these materials being nearly isotropic, having slight anisotropy superimposed, and the possibility of multiple textures, we address the energy distribution of SH-waves as a function of polarization angle with respect to the material symmetry axes and the transducer orientation. The importance of considering attenuation in this work is also addressed