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An energy criterion is introduced to define the effective stress of the ductile matrix, and with which Tandon and Weng’s (1988) theory of particle-reinforced plasticity is capable of predicting the desired plastic volume expansion under a pure hydrostatic tension. This modification also makes the theory suitable for application to porous materials at high triaxiality. Despite its simplicity, it offers a reasonable range of accuracy in the fully plastic state and is also versatile enough to account for the influence of pore shape. The theory is especially accurate when the work-hardening modulus of the ductile matrix is high, consistent with the concept of a linear comparison material adopted. If the matrix is also elastically incompressible, the theory with spherical voids is found to coincide with Ponte Castaneda’s (1991) lower bound for the strain potential (or upper bound in the sense of flow stress) of the Hashin-Shtrikman (1963) type, and with any other randomly oriented spheroidal voids, it provides an overall stress-strain relation which lies below this upper-bound curve. This energy approach is finally generalized to a particle-reinforced composite where the inclusions can be elastically stiffer or softer than the matrix, and it is also demonstrated that the prediction by the new theory is always softer than Tandon and Weng’s original one.

This article explores the relationship between informal and formal institutions and how their interactions shape the outcome of locational choices for foreign direct investment (FDI) in China's interior. This is an important but neglected aspect of China's economic development. The focus is on why FDI exists in host locations where the investment environment is poor and less competitive. Evidence from Shaanxi province suggests that the intertwined role played by personal networks and institutional involvement is a crucial part of the explanation. Networks are the key: at the individual/personal level, they are in the form of personal networks, and at the institutional/organization level, they take the form of institutional involvement. Moreover, the relationships among FDI, personal networks, and institutional involvement have a hierarchical structure: the larger the foreign parent firms, the more institutional involvement, while the smaller the foreign parent firms, the more personal networks are involved.

Based on the models of Hashin (1962) and Hashin and Rosen (1964), the effective elastic moduli of thickly coated particle and fiber-reinforced composites are derived. The microgeometry of the composite is that of a progressively filled composite sphere or cylinder element model. The exact solutions of the effective bulk modulus κ of the particle-reinforced composite and those of the plain-strain bulk modulus κ23, axial shear modulus μ12, longitudinal Young’s modulus E11, major Poisson ratio ν12, of the fiber-reinforced one are derived by the replacement method. The bounds for the effective shear modulus μ and the effective transverse shear modulus μ23 of these two kinds of composite, respectively, are solved with the aid of Christensen and Lo’s (1979) formulations. By considering the six possible geometrical arrangements of the three constituent phases, the values of κ, and of κ23, μ12, E11, and ν12 are found to always lie within the Hashin-Shtrikman (1963) bounds, and the Hashin (1965), Hill (1964), and Walpole (1969) bounds, respectively, but unlike the two-phase composites, none coincides with their bounds. The bounds of μ and μ23 derived here are consistently tighter than their bounds but, as for the two-phase composites, one of the bounds sometimes may fall slightly below or above theirs and therefore it is suggested that these two sets of bounds be used in combination, always choosing the higher for the lower bound and the lower for the upper one.

Silicon is regarded as one of the most promising next generation lithium-ion battery anodes due to its exceptional theoretical capacity, appropriate voltage profile and vast abundance. Nevertheless, huge volume expansion and drastic stress generated upon lithiation cause poor cyclic stability. It has been one of the central issues to improve cyclic performance of silicon based lithium-ion battery anodes.Constructing hierarchical macro-/mesoporous silicon with tunable pore size and wall thickness is developed to tackle this issue. Rational structure design, controllable synthesis and theoretical mechanical simulation are combined together to reveal fundamental mechanisms responsible for an improved cyclic performance.A self-templating strategy is applied using Stöber silica particles as templating agent and precursor, coupled with a magnesiothermic reduction process. Systematic variation of the magnesiothermic reduction time allows a good control over the structures of the porous silicon. Finite element mechanical simulations on the porous silicon show that an increased pore size and a reduced wall thickness generate less mechanical stress in average along with an extended lithiation state. Besides the mechanical stress, the evolution of strain and displacement of the porous silicon is also elaborated with the finite element simulation.