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A numerical method is presented in this paper for determining the load-bearing capacities of ductile composites such as metal matrix composites based on homogenization theory and the kinematic limit theorem. A representative volume element is chosen to re®ect the microstructure of a periodic composite. By directly introducing the von Mises yield criterion into the kinematic limit theorem, a nonlinear optimization formulation can be obtained to calculate the ultimate strength of a ductile composite. The nite-element modelling of the kinematic limit analysis is formulated as a nonlinear mathematical programming problem with equality-constraint conditions, which can be solved by a direct iterative algorithm. An interface failure model based on the microscopic ®uctuation displacements is proposed to account for the e¬ects of interfaces on the failure of composites. The present method can e¬ectively reveal the e¬ects of the microstructure on the macroscopic properties and micromechanical failure mechanisms of composites. Finally, some numerical examples illustrate the validity of the present method.

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Antrodia cinnamomea is a medicinal mushroom producing potent bioactive triterpenoids. However, triterpenoids of A. cinnamomea in submerged culture are much less than those in fruiting bodies. Here we evaluated effects of different extracts from a host-related species, Cinnamomum camphora, on the mycelial growth and triterpenoid production of A. cinnamomea in submerged culture. The hot water extract of the stem showed the strongest promotion of the mycelial growth. The petroleum ether extract of the stem (PES) (0.05 g L(-1)) showed the greatest stimulatory effect on content and production of triterpenoids. A total of 39 compounds including terpenoids, phenolic and aromatic compounds were identified in the PES by GC-MS analysis. Furthermore, the effects of seven compounds contained in the PES on the mycelial growth and triterpenoid production of A. cinnamomea were evaluated. Among them, α-terpineol (0.5 mg L(-1)) showed the greatest stimulatory effect on the triterpenoid content (23.31 mg g(-1)) and triterpenoid production (91.33 mg L(-1)) of A. cinnamomea. Results of LC-MS analysis showed that α-terpineol (0.5 mg L(-1)) stimulated the syntheses of six triterpenoids in the mycelia of A. cinnamomea. This indicates that α-terpineol can act as an elicitor for triterpenoid biosynthesis in A. cinnamomea.

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