The cross-section of an injection-molded plate of foamed long glass fiber reinforced polypropylene was analyzed using scanning electron microscopy. The distribution of the glass fiber orientations and the microcellular structure in the thickness direction were also studied. A multilayer representative volume element was constructed based on the fiber orientation tensors and the cell distribution. Nested and two-step homogenization methods based on the Mori–Tanaka and Voigt models were used to homogenize each layer of the representative volume element. Finally, classic laminate theory was used to obtain the effective elastic modulus of the material. The computed elastic moduli of the single-layer and multilayer representative volume element models with different loading directions predicted by the homogenization and finite element methods were compared with the experimental results. We found that the constructed multilayer representative volume element model can predict the elastic moduli of the foamed glass fiber reinforced polypropylene effectively and that the predicted results were accurate and stable.

The influences of non-mentallic inclusions on the quality and properties of the steel are depended not only on the quantity of inclusions, but also on the type、shape、size、deformation behavior and distribution condition. The effects of lanthanide rare earth(RE) on the shape、size and distribution condition of inclusions in large rudder arm steel casting is investigated. It was proved that the shape and distribution of inclusions could be improved in the large rudder arm steel casting, and the plastic and toughness of the steel can be increased obviously by the rare earth modification. By means of ANSYS finite element analysis software, the stress field distribution around matrix was simulated, and the reaction mechanism of inclusions by modification was clarified.