| Multi-field materials refer to materials with multi-field coupling characteristics.Due to the mutual conversion between non-mechanical energy(thermal,electrical,magnetical,chemical,etc.)and mechanical energy,they have attracted widespread attentions in the scientific and engineering fields.In the framework of linear theory,considering thermal effect,this dissertation carries out systematically theoretical and numerical investigations on three-dimensional(3D)planar crack problems for several typical Multi-field materials such as thermopiezoelectric materials,thermopiezoelectric semiconductors,thermo-magneto-electro-elastic materials,and quasicrystals.The main work is listed as follows:1)Investigations on 3D crack problems under the coupling frame of thermal,electrical,magnetical,and mechanical fields for thermopiezoelectric(TPE)and thermo-magneto-electro-elastic(TMEE)media are performed.Firstly,the temperature discontinuity is introduced to characterize the effect of cracks in the media on the temperature field disturbance,and the framework of extended displacement discontinuity(EDD)is developed for crack problems in TPE and TMEE materials.Then,fundamental solutions for point EDDs are derived with integral transformation technology and the 3D general solution of the relevant medium.Furthermore,by virtue of the obtained solutions and superposition principle,the EDD boundary integral equations are established for 3D crack problems of TPE and TMEE materials.The relationship among the temperature discontinuity and other EDDs are analyzed.Using the hypersingular integral equation method,the singularities of near-crack border fields are obtained and the extended stress field intensity factors are expressed in terms of the EDDs.Finally,based on the constant triangular element,a EDD boundary element method for 3D crack problems of TPE and TMEE materials is proposed and the elliptical crack problems are studied.2)Considering the thermal and electrical properties of the medium in the crack cavity for TPE materials,five types of crack models based on thermal and electrical crack boundary conditions are established for 3D crack problems.Theoretical analysis of the influence of different models on relevant fracture parameters is conducted,and the corresponding EDD boundary element method is proposed.3)The hypersingular integral equation method is used to study 3D crack problems of thermopiezoelectric semiconductor(TPSC).Based on the fundamental solutions for piezoelectricity and Laplace equation,through the Somigliana identity of TPE materials and Green’s formula,the EDD boundary integral equations for 3D crack problems of TPSC are derived.The obtained boundary integral equations consist of the hypersingular integral term related to the unknown variables(EDDs)over the crack domain,the bounded surface integral related the given outer boundary conditions,and the bounded volume term related to the space charge caused by carriers and the temperature change.By virtue of the hypersingular integral term,the singular behavior of the EDD and the extended stress fields are analyzed,and the relationships for both are established.Based on the "piezoelectric-conductor" iterative approach of piezoelectric semiconductors,the finite element method is used to solve the penny-shaped crack problem,and the correctness of the theoretical derivation is verified numerically.4)The EDD boundary integral equation-boundary element method is developed to analyze 3D crack problems in quasicrystal(QC)media.The 3D fundamental solutions for the EDDs,including the phonon/phason displacement discontinuity and temperature discontinuity,are derived for two-dimensional(2D)hexagonal QCs with thermal effect.The EDD boundary integral equations of 3D crack problems are obtained.The asymptotic behavior along the crack front is studied and the extended stress intensity factors are expressed in terms of the EDDs across crack surfaces.Finally,the energy release rate is obtained in term of the stress intensity factors.5)The EDDs over the crack surface serve as the unknown variables in Fabrikant’s potential function method which are used to study 3D crack problems of 2D hexagonal QCs and one-dimensional(1D)hexagonal piezoelectric QCs with thermal effect.The EDD boundary governing equations for 3D crack problems of the corresponding medium are expressed in differential-integral form and hypersingular integral form,respectively.The equivalence of these two forms is proved,and the equivalent relationship of the correlation coefficients are given.Based on the boundary differential-integral equation,closed-form solutions of the elliptical crack and penny-shaped crack problems are derived.These solutions include not only solutions on the crack plane,but also full-field solutions in the space.The hypersingular integral equation is used to analyze asymptotic singularities of coupled fields near the crack edge.Expressions are then presented for extended stress intensity factors in terms of EDDs,and the basic relationships between the energy release rate and the extended stress intensity factors are established.6)Based on the theoretical formulations via the revised Fabrikant’s potential function method with EDDs as basic variables,a direct and effective method is proposed to derive the fundamental solution for EDDs.The 3D EDD fundamental solutions for the point source and element are obtained for 1D hexagonal piezoelectric QCs with thermal effect.A numerical approach,known as EDD boundary element method,is proposed to solve 3D crack problems of 1D hexagonal piezoelectric QCs with thermal effect. |
