Most micro-mechanical analyses for composites are based on repeated unit cell models (RUCs) by assuming a periodical distribution of the reinforcing phase. In this paper, the uniqueness of solution by applying unified displacementdifference periodic boundary conditions on the RUCs has been proved. Further it is deduced that (1) selection of the RUCs for a fixed periodic array may not be unique, however, the solution is independent on the choice of the different RUCs; (2) boundary traction continuity conditions can be guaranteed by the application of the proposed unified displacement-difference periodic boundary conditions. Illustrative examples are presented and advantages of applying this type of unified periodic boundary conditions are discussed.
The present study examined the production of European Portuguese (EP) lateral consonants by 14 Chinese learners, through a picture naming task eliciting the target segments in all possible syllable and word-level positions. Our results illustrate that /l/ is stable in singletons (100% target-like) due to the positive transfer from Mandarin Chinese. However, it is very often vocalized in codas (only 16.7% target-like production, [ɫ]), which might be attributed to a phonetically based tendency (Graham, 2017; Johnson & Britain, 2007). The high accuracy (97% target-like) of /l/ in onset clusters, an absent structure in the L1, can be the result of the heterosyllabic nature of EP obstruent-liquid sequences (Veloso, 2006) or of the association of two segments to a single skeletal position, which was also argued as an intermediate stage in EP L1 acquisition (Freitas, 2003). /ʎ/ is still in acquisition (52.4% target-like), and is often produced as an L1 category [lj], due to acoustic and articulatory similarity.
Meso-fracture process for metal matrix composites (MMC) reinforced by particles of large volume fraction is pursued in this paper. Particle reinforced Al 2 O 3 /Al MMC is made under a pressure-less filtration technique. Samples are tested in uniaxial tension, compression and three-point bending, and their fracture patterns and fractography are recorded. The micromechanics model of the composite is composed of identical elastic spheres linked by columns of elastic perfectly plastic matrix. The metallic matrix is treated in two categories: the elastic perfectly plastic von Mises columns linking various particles are actively engaged in forming the skeleton of the MMC; while the rest of the matrix is inactive and only serves to constrain the radial deformation of linking columns. The failure of the interface is governed by the interfacial energy release rate, the matrix damage by the Rice-Tracey void evolution law, and the particle breaking by the largest principal stress. The macroscopic stress-strain relation is derived from the normal and tangential moduli of the two-particle linkages by averaging over a statistical assembly of three packing patterns.Two random variables are adopted for the fluctuations of local stresses in particles and along particle/matrix interfaces. The simulated overall constitutive responses agree with the experiments for the uniaxial tensile, uniaxial compression and three-point bending specimens. The simulated meso-fracture patterns under three testing configurations reproduce the experimental results. Simulated proportions of failure by interface debonding, matrix voiding and particle breaking also agree with the experiments.
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