S.-T. Gu

Characterization of surface and nonlinear elasticity in wurtzite ZnO nanowires

Surface elasticity and nonlinear effects are reported in ZnO nanowires and characterized by ab initio calculations. Fully anisotropic elastic and stress coefficients related to (101¯0) surfaces are provided and used to construct a continuum model of nanowires based on the Gurtin-Murdoch surface elasticity theory, able to capture mechanical size effects. Nonlinear elasticity is observed through non-zero third order energy derivative terms with respect to axial strain in the direction of the nanowire. The associated material parameters are found to be themselves size-dependent.

Penny-shaped Dugdale crack in a transversely isotropic medium and under axisymmetric loading

The present work is concerned with a penny-shaped crack embedded in a transversely isotropic medium and oriented in parallel with the isotropic plane of the latter. Three axisymmetric crack problems are investigated. In the first one, the upper and lower lips of the crack are subjected to a pair of annular opposite pressures. In the second and third problems, two opposite concentrated forces of the same magnitude are applied successively at the upper and lower crack lip centres and at any two points outside the crack and on the axis perpendicular to the crack. Using the basic idea underlying Dugdales crack model, the extent of the plastic zone is analytically estimated in each of the three cases. In addition, the corresponding crack surface displacement is determined explicitly. Numerical examples are provided to discuss the effects of some geometrical and material parameters involved. Apart from their own usefulness in carrying out some simplified crack analyses, the results obtained in this work can in particular serve as benchmarks for computational fracture mechanics.

Compact closed-form micromechanical expressions for the effective uncoupled and coupled linear properties of layered composites

This work aims mainly to derive closed-form expressions for the effective properties of layered composites when linear uncoupled and coupled phenomena, such as conduction, elasticity, thermoelectricity and piezomagnetoelectricity, are concerned. In addition, properties may be graded in the direction normal to the layer plane. The remarkable feature of the obtained results is that they are expressed in a unified and very compact way for all uncoupled and coupled linear mechanical and physical phenomena. Our results include as special ones all the relevant results reported up to now in the literature. The key to obtaining our general compact coordinate-free results resides in extending Hill’s interfacial relations for a perfect elastic interface to the setting of an arbitrary finite number of uncoupled and coupled linear phenomena. The effects of the presence of stiffeners and softeners on the effective properties of layered composites are also investigated. In particular, four limiting cases for piezoelectricity are studied in detail. As illustrations, the general results are applied to several coupled phenomena and to functionally graded layered composites.

Variational principles and size-dependent bounds for piezoelectric inhomogeneous materials with piezoelectric spring–layer imperfect interfaces

The piezoelectric spring–layer interface model is widely used in describing some imperfect interfaces frequently involved in piezoelectric inhomogeneous materials. Typically, it is appropriate for modeling a thin, soft and low conducting interface between two bulk phases. This model stipulates that, across an interface, the displacement and electric potential are discontinuous while the traction and normal electric displacement are continuous and proportional to the displacement and electric potential jumps, respectively. In this work, the classical minimum potential principles of linear piezoelectricity are extended to piezoelectric inhomogeneous materials with piezoelectric spring–layer imperfect interfaces, and to investigating the interface effects on their effective properties. By choosing simple admissible displacement–electric displacement and stress–electric potential coupling fields, the extended Voigt and Reuss bounds can explicitly be derived for the corresponding effective properties of a transversely isotropic fiber reinforced composite which is subjected to remotely uniform in-plane electric loading and anti-plane mechanical loading. Numerical results are provided to illustrate the size-dependent features of the obtained Voigt and Reuss bounds.

Asymptotic derivation of a curved piezoelectric interface model and homogenization of piezoelectric composites

In this work, we derive a general piezoelectric interface model by using a coordinate-free asymptotic approach. Next, this interface model is applied to the homogenization of fibrous piezoelectric composites. The overall piezoelectric properties are calculated and compared to the ones obtained by using the three-phase model.