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.
The known realization of transformation acoustic devices requires exotic material parameters and has been hampered by limited available materials. By merging the conformal mapping and the embedded coordinate transformation method, we demonstrate that transformation-based acoustic devices can be made from isotropic materials, which greatly facilitates their implementation. The acoustic directional antenna based on such approach is presented and validated by full-wave simulations using the finite element method.
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