Kp. Walker et al., THERMOVISCOPLASTIC ANALYSIS OF FIBROUS PERIODIC COMPOSITES BY THE USEOF TRIANGULAR SUBVOLUMES, Composites science and technology, 50(1), 1994, pp. 71-84
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.