... periodicity multiscale analysis Column structures with various reinforcements as shown in Fig. 1 are widely used in structural engineering. The reinforcements in the columns quite often exhibit periodic distribution along the column axial direction although they themselves may have three...

...) inclusions micromechanics cohesive zone model crack polycrystalline solid fracture multiscale analysis Due to the exponential growth in microelectronic devices and extensive application of ceramics and ceramic composites, the reliability of polycrystalline materials has become a major...