A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displac...A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.展开更多
The problem of a piezoelectric ellipsoidal inclusion in an infinite non- piezoelectric matris is very important in engineering. In this paper, it is solved via Green's function technique. The closed-form solutions...The problem of a piezoelectric ellipsoidal inclusion in an infinite non- piezoelectric matris is very important in engineering. In this paper, it is solved via Green's function technique. The closed-form solutions of the electroelastic Eshelby's tensors for this kind of problem are obtained. The electroelastic Eshelby's tensors can be expressed by the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem. Since the closed-form solutions of the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem can be given by theory of elasticity and electrodynamics, respectively, the electroelastic Eshelby's tensors can be obtained conveniently. Using these results, the closed-form solutions of the constraint elastic fields and the constraint electric fields inside the piezoelectric ellipsoidal inclusion are also obtained. These expressions can be readily utilized in solutions of numerous problems in the micromechanics of piezoelectric solids, such as the deformation and energy analysis, damage evolution and fracture of the piezoelectric materials.展开更多
基金supported by the National Natural Science Foundation of China (11072068 and 11002041)
文摘A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.
基金The project supported by the National Natural Science Foundation of China
文摘The problem of a piezoelectric ellipsoidal inclusion in an infinite non- piezoelectric matris is very important in engineering. In this paper, it is solved via Green's function technique. The closed-form solutions of the electroelastic Eshelby's tensors for this kind of problem are obtained. The electroelastic Eshelby's tensors can be expressed by the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem. Since the closed-form solutions of the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem can be given by theory of elasticity and electrodynamics, respectively, the electroelastic Eshelby's tensors can be obtained conveniently. Using these results, the closed-form solutions of the constraint elastic fields and the constraint electric fields inside the piezoelectric ellipsoidal inclusion are also obtained. These expressions can be readily utilized in solutions of numerous problems in the micromechanics of piezoelectric solids, such as the deformation and energy analysis, damage evolution and fracture of the piezoelectric materials.
