Chang-Chun Wu

Numerical solutions on fracture of piezoelectric materials by hybrid element

Abstract The cracked piezoelectric problem is observed numerically. To simulate the characteristic singularity at the crack tip, a plane piezoelectric hybrid element is derived. The new model involves displacement u, stress σ, electric displacement D and electric potential ϕ as independent variables. The electromechanical coupling behavior of the cracked piezoelectric ceramics PZT-4 and PZT-5 is investigated. Under impermeable crack condition, the 1/ r -singularity at the crack-tip zone is exactly represented for σ and D. The efficiency of implementing the permeable crack condition is also inspected. To examine current energy release rate formulas, the path-independent integral is computed, and then a fitting formula for the energy release rate is obtained. In this paper, all the numerical results are compared with the previously reported theoretical solutions.

Micromechanics of composite materials using multivariable finite element method and homogenization theory

Abstract A new method for evaluation of the micro-mechanical properties of composite materials via incompatible multivariable FEM and homogenization theory is proposed in this paper. An incompatible displacement element and a hybrid stress element are developed and extended to predict the effective mechanical properties of composite materials. The mechanical performances obtained by these elements are compared with the experimental data as well as the results by Mori–Tanaka theory and traditional rule-of-mixtures. It turns out that the proposed new method provides with the best results comparing to the experimental results.

Dual analysis for path integrals and bounds for crack parameter

A dual analysis for the path integrals is carried out theoretically and numerically. As a dual form of Rices J-integral, an alternative path-independent I∗-integral is suggested in the paper, which can be formulated as the complementary energy release rate for the linear/nonlinear elasticity fracture system with a blunting crack model. As an energy functional of the stress and displacement, I∗ is equivalent to J in value since the effect of the stress distributions on the front of crack is included in its formulation. Dealing with bound estimation problems for crack parameters, the upper and lower bound theorems are described, respectively. I∗ is useful by the fact that its approximate solution is able to provide an upper bound for the exact one, and that it will enable the hybrid finite element to be a power role in fracture calculations. A series of numerical results is offered to verify the points mentioned in the paper.

Deviatoric hybrid model and multivariable elimination at element level for incompressible medium

A deviatoric hybrid element approach, in which the deviatoric stress σ′, the pressure p and the displacement u are independently dealt with as the element variables, is suggested. The present approach is naturally universal for compressible and fully incompressible mediums. Moreover, it can be extended to the simulation of Stokes flow directly. The resulting hybrid model is able to meet the zero volumetric strain constraint in terms of the incompatible displacement mode only. Therefore an incompressible elimination can be carried out within an individual element, and the complex system elimination for nodal displacements is then avoided. The present 3-field hybrid model maintains the important features of current hybrid stress elements—finally resulting in a set of displacement-type discrete equations which can be easily solved, while not a set of u-p mixed-type equations resulted. Regarding the numerical stability of the element, an effective strategy is offered to suppress all the zero energy modes hidden in the model. Copyright