Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.
Poly （N-isopropylacrylamide） （PNIPAM） microgels are widely used in drug delivery due to their fast response to temperature. In order to get a better biocompatibility, PNIPAM mi- crogels are typically coated with a layer of biocompatible material, resulting in composite microgels with core-shell structure. In a composite microgel prepared recently, for example, a microsphere of PNIPAM gel is enclosed by a phospholipid membrane, and the composite microgel exhibits a substantial volume transition in response to temperature changes. Here we develop a theoretical model to describe the thermal-responsive behavior of this composite microgel. In particular, we treat the phospholipid membrane as an elastic layer behaving like rubber-like elastomers and adopt the form of the free-energy function for nematic gels （which refer to anther species of thermal- sensitive gels whose behavior has been intensively studied） as that for PNIPAM gels. We show that the thermal-responsive behavior of the composite microgel can be markedly influenced by the membrane. By investigating the state of stress on the interface, we further predict that when the coating membrane is stiff and thin, wrinkles are expected to occur on the outer surface of the composite microgel after the volume transition.
Both nematic elastomers and nematic hydrogels are known to display striped patterns.In contrast to a large body of proposed models for nematic elastomers,few studies exist to interpret striping in nematic hydrogels.In this paper,a theoretical model based on free energyminimization is developed to simulate the drying-induced striping in a layer of nematic hydrogel bonded to a rigid substrate.The liquid crystalline polymers in the nematic hydrogel rotate by certain angles to form the striping in response to a drying environment.Moreover,the striping occurs only for a finite range of humidity,and the boundaries of this range can be tuned.
Three-dimensional thermoelastic analysis is presented for an orthotropic functionally graded rectangular plate, which is simply supported and isothermal on its four lateral edges. With the assumption that material properties have arbitrary dependence on the thickness-coordinate a Peano-Baker series solution is obtained for the thermoelastic fields of the functionally graded plate subjected to mechanical[ and thermal loads on its upper and lower surfaces by means of state space method. The correctness of the obtained series solution is validated through numerical examples. The influence of different material properties distributions on the structural response of the plate is also studied.
The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials.The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic medium.The electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields.A closed-form solution can be obtained for the disturbance fields,which is convenient for the manipulation of the energy functional.As an application,a two-phase piezoelectric composite with nonpiezoelectric matrix is considered.Expressions of upper and lower bounds for the overall electromechanical moduli of the composite can be developed.These bounds are shown better than the Voigt-Reuss type ones.
Cellular space-charge polymer film, also called cellular piezoelectret, has very large piezoelectric effect due to their unique microvoid structure. In this article, the cellular piezoelectret film is considered to be a periodic composite material with closed-cell microvoids aligned periodically. Three dimensional finite element modeling is carried out to obtain the effective elastic modulus and piezoelectric coefficients. Sensitivity analysis was presented by modeling the effec- tive electromechanical properties with different individual variable, including material constants and void shape parameters. By assuming a relation between void shape and void volume fraction, the finite element model can simulate quite well the inflation experiments of the voided charged Polypropylene film published in literature. Finally, the finite element model is used to explore the voided charge polymer film with non-uniform distribution of the trapped charges on the internal surface of voids. It was found that the resultant overall piezoelectric coefficients will be more significant if charges are closely gathered in the central area, and sparse in the around area of the internal surface of voids.
Due to the large quasi-piezoelectric d33 coefficient in the film thickness direction, cellular piezoelectret has emerged as a new kind of compliant electromechanical transducer materials. The macroscopic piezoelectric effect of cellular piezoelectret is closely related to the void microstructures as well as the material constants of host polymer. Complex void microstmctures are usually encountered in the optimum design of cellular piezoelectret polymer film with ad- vanced piezoelectric properties. Analysis of the effective electromechanical properties is generally needed. This article presents an overview of the recent progress on theoretical models and numerical simulation for the effective electromechanical properties of cellular piezoelectret. Emphasis is placed on our own works of cellular piezoelectret published in past several years.
