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This study focuses on analyzing a slanted lip-shaped crack within a thermoelectric plate that experiences both a temperature gradient and an electric potential gradient. Based on the electrically insulated and thermally permeable crack model, we derive analytical solutions for the thermoelectric field and the associated thermal stress field in the cracked thermoelectric material by employing the complex variable method. Subsequently, we evaluate the stress intensity factors at the tips of the lip-shaped crack. Under the impact of thermoelectric loading, both mode-I and mode-II stress intensity factors occur at the tips of a slanted lip-shaped crack. Numerical examples are provided to demonstrate the influence of crack width, crack angle and thermal conductivity of the filling medium on the stress intensity factors at the crack tip. [ABSTRACT FROM AUTHOR]

An interface crack between dissimilar elastic thin-films with surface effect has been investigated. By using integral transform technique the mixed boundary value problem of an interface crack is reduced to singular integral equations, which can be further reduced to a Riemann–Hilbert problem with analytical solution. The crack-tip singularities of the interface crack have been studied for possible combination of the dissimilar isotropic elastic materials with surface effect, and it is shown that there can be either oscillatory or non-oscillatory singularity for the interface crack. Analytical solution of the normal and shear stresses on the bonded interface is obtained, the relative crack opening displacement (COD) and relative crack sliding displacement (CSD) were given, and energy release rates (ERRs) for the interface crack are obtained for both oscillatory and non-oscillatory singularity cases. The oscillatory and non-oscillatory singularity parameters for interface cracks between dissimilar isotropic elastic materials with surface effect have been obtained. [ABSTRACT FROM AUTHOR]

An investigation is made on the Gurtin–Murdoch (GM) model for soft spherical elastic solids with surface tension-induced bulk residual stress. Unlike the original GM model which treats the surface tension as a finite value but the surface tension-induced bulk residual stress as infinitesimal, the present model treats both consistently as finite values. Detailed comparisons between the present model and the GM model show that for a solid sphere (for which the surface tension-induced bulk residual stress remains uniform in the entire body), the GM model deviates considerably from the present model. Conversely, for a small cavity in an infinite body (for which the surface tension-induced bulk residual stress is significant only nearby the cavity's surface but quickly diminishes with radial distance), the deviation between the present model and the original GM model is negligible. It is concluded that the surface tension-induced bulk residual stress, which is addressed in the present paper but ignored in the GM model, can have a significant effect on deformation and vibration of soft elastic solids when its magnitude does not vanishingly diminish within the body. [ABSTRACT FROM AUTHOR]

We consider the thermoelastic problem of an interface crack between two dissimilar semi-infinite isotropic materials under a uniform remote heat flux in plane deformation. The crack face is assumed to be partially thermopermeable (defined by a partial insulation coefficient of the crack), while the interface is assumed to be perfectly bonded except that a constant thermal resistance is introduced into the interfacial region near the tips of the crack. By using the integral transform method, we obtain the analytic solution for the thermoelastic field in the entire bi-material system. Numerical examples are presented to study the influence of interfacial thermal resistance on the thermal stress intensity factors and the crack opening/sliding displacements. It is shown that the magnitudes of the mode I and mode II TSIFs, as well as the crack opening displacements, increase with the increasing interfacial thermal resistance, while the crack sliding displacement is insensitive to the change of interfacial thermal resistance. [ABSTRACT FROM AUTHOR]

Investigated in this paper is the surface tension-induced stress field around a nanoscale inclusion of arbitrary shape embedded in an infinite elastic plane, with an emphasis on the combined effects of surface tension and arbitrary inclusion shape. Muskhelishvili's complex variable method is employed to formulate the basic equations that are solved with the aid of conformal mapping and series expansion methods. Accuracy of the present solution is verified by comparing its predictions with known results of an arbitrarily shaped hole. The surface tension-induced stress field is demonstrated for four shapes of inclusions (ellipse, approximately regular triangle, square and regular pentagon with round corners). The numerical results show that as the inclusion changes from a 'soft' to a 'hard' one (compared to the matrix), hoop and normal stresses along the inclusion-matrix interface on the inclusion side will increase, while those on the matrix side will decrease. However, shear stress along the inclusion-matrix interface does not considerably change as the inclusion changes from a 'soft' to a 'hard' one. It is also found that the maximum hoop stress on the matrix side of a 'soft' inclusion and the maximum shear stress always occur nearby, but not exactly at the round corners where all other stresses for all four discussed inclusion shapes attain their maximums. Besides, for the four inclusion shapes discussed, shear stress along the inclusion-matrix interface vanishes at all corners as a consequence of the symmetry. [ABSTRACT FROM AUTHOR]

We re-examine the conclusion established earlier in the literature that in the presence of a homogeneously imperfect interface, the circular inhomogeneity is the only shape of inhomogeneity which can achieve a uniform internal strain field in an isotropic or anisotropic material subjected to anti-plane shear. We show that under certain conditions, it is indeed possible to design such non-circular inhomogeneities despite the limitation of a homogeneously imperfect interface. Our method proceeds by prescribing a uniform strain field inside a non-circular inhomogeneity via perturbations of the uniform strain field inside the analogous circular inhomogeneity and then subsequently identifying the corresponding (non-circular) shape via the use of a conformal mapping whose unknown coefficients are determined from a system of nonlinear equations. We illustrate our results with several examples. We note also that, for a given size of inhomogeneity, the minimum value of the interface parameter required to guarantee the desired uniform internal strain increases as the elastic constants of the inclusion approach those of the matrix. Finally, we discuss in detail the relationship between the curvature of the interface and the displacement jump across the interface in the design of such inhomogeneities. [ABSTRACT FROM AUTHOR]

A simple method is proposed to analyze asymmetric indentation of a supported elastic beam by a rigid cylinder placed at an arbitrary position on the beam. A key advantage of our method over existing methods is that a single governing Kerr-type differential equation, which gives the relation between contact pressure and the normal deflection of the pressured surface of the beam, is applied both inside and outside the contact zone. With the present method, the two ends of contact zone will be determined as part of the solution, in contrast to the existing related studies which were all based on a simplifying assumption that the contact zone is geometrically symmetric about the tip of the indenter. Indeed, our results confirm that the contact zone is generally geometrically non-symmetric about the indenter tip, and even the whole contact zone can locate on one side of the indenter tip in some cases. Asymmetric indentation behaviors are demonstrated with numerical examples, with an emphasis on asymmetric contact pressure distribution inside the contact zone. Explicit formulas for the contact-zone width-displacement, force-displacement and moment-displacement relations are derived and illustrated with numerical examples. In particular, the present model predicts that as the indentation displacement exceeds a critical value, the indenter will lose contact with the beam inside the contact zone, which implies that the actual contact zone becomes two separate contact strips. Validity and accuracy of the present method are demonstrated by comparing its predictions with known results for some special cases. New features of asymmetric indentation as compared to symmetric indentation are summarized at the end of the paper. [ABSTRACT FROM AUTHOR]