Elastic field near the tip of an anticrack in a decagonal quasicrystalline material

We investigate the elastic field near the tip of an anticrack in a homogeneous decagonal quasicrystalline material subject to plane strain deformations. The phonon and phason stresses exhibit a square root singularity at the anticrack tip. Two realvalued phonon stress intensity factors and two real-valued phason stress intensity factors are introduced to scale four separate modes of deformation. We obtain four analytic functions which completely characterize the induced phonon and phason stresses as well as the displacement field. In particular, we derive a concise yet elegant representation of the anticrack contraction force.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux.A conformal mapping function for the coating and matrix is introduced,which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane.Using analytic continuation,we derive a general solution in terms of two auxiliary functions.The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface.Once the two auxiliary functions have been obtained in the elementary-form,the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined.The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition.Finally,the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.

Interaction effects on heat conduction and thermal stress in an infinite elastic plane with two circular holes

Numerous researches have focused on the physical behavior of an elastic material in the vicinity of a single hole under the assumption that the interaction effects arising from the introduction of multiple holes remain negligible if the holes are placed sufficiently far from each other.In an effort to understand hole interaction effects on heat conduction and thermal stress,we consider the case when two circular holes are embedded in an infinite elastic material and use complex variable methods together with numerical analysis to obtain solutions describing temperature and elastic fields in the vicinity of the two circular holes.The results indicate that the interaction effects on temperature distribution and stress strongly depend on the relative size of the two holes and the distance placed between them but not on the actual size of the holes.

A screw dislocation near one open inhomogeneity and another closed inhomogeneity both permitting constant interior stresses

We prove that the interior stresses within both a non-parabolic open inhomogeneity and another interacting non-elliptical closed inhomogeneity can still remain constant when the matrix is simultaneously under the action of a screw dislocation and uniform remote anti-plane stresses.The constancy of interior stresses is realized through the construction of a conformal mapping function for the doubly connected domain occupied by the surrounding matrix.The mapping function is endowed with the information describing the screw dislocation via the incorporation of two specifically defined logarithmic terms.The constant interior stress fields are observed to be independent of the specific open and closed shapes of the two inhomogeneities and the existence of the screw dislocation.In contrast,the existence of the neighboring screw dislocation significantly affects the open and closed shapes of the two inhomogeneities.

The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane

The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials.In anti-plane shear and plane deformations,certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading.Correspondingly,sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of(uniform)remote loading have also been established.In this paper,we demonstrate rigorously that,in all cases,these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.