Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

In this paper, an analytical solution is developed for the problem of an infinite 1D hexagonal piezoelectric quasi-crystal medium weakened by an elliptical crack and subjected to mixed loads on the crack surfaces. The mixed loads comprise the phonon pressure, phason pressure, electric displacement, and temperature increment, and the crack surfaces can be electrically permeable or impermeable. Based on a general solution, combined with the generalized potential theory, the steady-state 3D thermo-electro-elastic field variables in the quasi-crystal are obtained in terms of elliptic integral functions and elementary functions. Several important physical quantities on the cracked plane, such as the generalized crack surface displacements, normal stresses, and stress intensity factors, are derived in closed forms. An illustrative numerical calculation verifies the presented analytical solution and shows the distribution of the 3D thermo-electro-elastic field. It is indicated that the influence of the phason field on the result is pronounced, especially for the electric field variables, and the electric permeability of crack surfaces has a significant effect on the electric displacement intensity factor at the crack tip.

A Constitutive Model Incorporating Mixed Soil Slurry for Interface

In projects, mixed soil slurry between cut-off wall and coarse-grained soil always exists. It may influence on or change mechanical properties of interface between coarse-grained soil and structure. The mechanical behaviors of the interface between coarse-grained soil and concrete were investigated by simple shear tests under mixed soil slurry. The significant dilatancy and stress-strain softening can be achieved through the results, which also indicate that the cement content play an important role in the shear strength of the interface. The peak strength and the position when the dilatancy occurs are related to both normal stress and cement content. An elasto-plastic constitutive model for interface considering mixed soil slurry was formulated in the framework of generalized potential theory. The entire model parameters can be identified by experimental tests. Finally, the predictions of the model have been compared with experimental results, and results show the model is reasonable and practical.

A Tensor Boundary Value Problem of Mixed Type

The boundary value problems of generalized potential theory on finite Riemannian manifolds may be regarded as extensions of the Dirichlet and Neumann problems for harmonic functions. In the tensor theory there is, in fact, a greater variety of such problems; that is to say, these generalizations from classical potential theory can be made in various ways. We here introduce yet another pair of boundary value problems for the tensor equation of Laplace.