THERMOVISCOPLASTIC ANALYSIS OF FIBROUS PERIODIC COMPOSITES BY THE USEOF TRIANGULAR SUBVOLUMES

The non-linear viscoplastic behavior of fibrous periodic composites is analyzed by discretizing the unit cell into triangular subvolumes. A set of these subvolumes can be configured by the analyst to construct a representation for the unit cell of a periodic composite. In each st ep of the loading history the total strain increment at any point is g overned by an integral equation which applies to the entire composite. A Fourier series approximation allows the incremental stresses and st rains to be determined within a unit cell of the periodic lattice. The non-linearity arising from the viscoplastic behavior of the constitue nt materials comprising the composite is treated as a fictitious body force in the governing integral equation. Specific numerical examples showing the stress distributions in the unit cell of a fibrous tungste n/copper metal-matrix composite under viscoplastic loading conditions are given. The stress distribution resulting in the unit cell when the composite material is subjected to an overall transverse stress loadi ng history perpendicular to the fibers is found to be highly heterogen eous, and typical homogenization techniques based on treating the stre ss and strain distributions within the constituent phases as homogeneo us result in large errors under inelastic loading conditions.