This paper deals with the magnetoelastic interactions for a structure consisting of two elastic current carrying superconducting substrates, separated by a gap (vacuum). The two elastic substrates, which have no acoustic contacts, are coupled by a magnetic field generated by the deformations of the substrates. The surface magnetoelastic waves of Rayleigh type, decaying exponentially with distance from substrates surfaces, are studied. For a plane harmonic wave the dispersion equation is derived and solved to obtain the coupled wave frequencies. The magnetomechanical coupling effects are investigated in detail and simulations show that the magnetoelastic coupling effect is quite significant when the gap relative thickness is rather small. The existence of two surface gap waves with two different velocities is shown. In superconducting media the constitutive relations of magnetic field and electrical current of primary nondeformed state are given by means of London’s equations.

Elastic-plastic indentation of a single-crystal half-space by a rigid cylinder was analyzed by discrete dislocation plasticity. Short-range dislocation interactions were modeled by a set of constitutive rules of dislocation emission, glide, pinning (by obstacles), and annihilation. The occurrence of the first dislocation dipole, multiplication of dislocations, and evolution of subsurface stress field were examined in terms of contact load, dislocation source density, slip-plane distance and orientation angle, and indenter radius. In the presence of defects (dislocation sources), the critical load for dislocation initiation is less than that of a defect-free medium and depends on dislocation source density, slip-plane distance, and indenter radius. The critical indenter radius resulting in deformation under the theoretical material strength is determined from numerical results, and the role of dislocation obstacles is interpreted in terms of their spatial density. Simulations provide insight into yielding and plastic deformation of indented single-crystal materials, and establish a basis for developing coarse-grained plasticity models of localized contact deformation in polycrystalline solids.

In this paper, we study the deformation of a thin elastic rod constrained inside a cylindrical tube and under the action of an end twisting moment. The ends of the rod are clamped in the lateral direction. Unlike the previous works of others, in which only the fully developed line-contact spiral was considered, we present a complete analysis on the deformation when the dimensionless twisting moment M x is increased from zero. It is found that the straight rod buckles into a spiral shape and touches the inner wall of the tube at the midpoint when M x reaches 8.987. As M x increases to 11.472, the contact point in the middle splits into two, leaving the midpoint floating in the air. As M x increases to 13.022, the midpoint returns to touch the tube wall and the two-point-contact deformation evolves to a three-point-contact deformation. Starting from M x = 13.098 , the point contact in the middle evolves to a line contact, and the deformation becomes a point-line-point contact configuration and remains so thereafter. In the case when the line-contact pattern is fully developed, it is possible to predict the spiral shape analytically. The numerical results are found to agree very well with those predicted analytically. Finally, an experimental setup is constructed to observe the deformation evolution of the constrained rod under end twist.

We investigate the problem of an N -phase elliptical inhomogeneity in plane elasticity. The elliptical inhomogeneity is bonded to the unbounded matrix through the intermediate ( N − 2 ) interphases, and the matrix is subjected to remote uniform stresses. We observe that the stress field inside the elliptical inhomogeneity is still uniform when the following two conditions are satisfied: (i) The formed interfaces are ( N − 1 ) confocal ellipses, and (ii) the interphases and the matrix possess the same shear modulus but different Poisson’s ratios. In Appendixes A xB , we also discuss an arbitrary number of interacting arbitrary shaped inhomogeneities embedded in an infinite matrix, and an N -phase inhomogeneity with ( N − 1 ) interfaces of arbitrary shape. Here all the phases comprising the composite possess the same shear modulus but different Poisson’s ratios. The results in the main body and in Appendixes A xB are further extended in Appendix C to finite plane strain deformations of compressible hyperelastic harmonic materials.

Elastoplastic deformation occurs widely in engineering impact. Although many empirical solutions of elastoplastic impact between two spheres have been obtained, the analytical solution, verified by means of other methods, to the impact model has not been put forward. This paper proposes a dynamic pattern of elastoplastic impact for two spheres with low relative velocity, in which three stages are introduced and elastic and plastic regions are both considered. Finite element analyses with various parameters are carried out to validate the above model. The numerical results prove to agree with the theoretical predictions very well. Based on this model, the dissipation nature of elastoplastic impact are then analyzed, and the conclusion can be drawn that materials with lower yield strength, higher elastic modulus, and higher mass density have better attenuation and dissipation effects. The study provides a basis to predict the particle impact damping containing plastic deformation and to model the impact damped vibration system enrolling microparticles as a damping agent.

Cohesive zone models are being increasingly used to simulate fracture and debonding processes in metallic, polymeric, and ceramic materials and their composites. The crack initiation process as well as its actual stress and damage distribution beyond crack tip are important for understanding fracture of materials and debonding of adhesively bonded joints. In the current model, a natural boundary condition based method is proposed, and thus the concept of extended crack length (characteristic length l ) is no longer required and more realistic and natural local deformation beyond crack tip can be obtained. The new analytical approach, which can consider both crack initiation and propagation as well as local deformation and interfacial stress distribution, can be explicitly obtained as a function of the remote peel load P with the given bilinear cohesive laws. An intrinsic geometric constraint condition is then used to solve the remote peel load P . The nonlinear response in both the ascending and descending stages of loading is accurately predicted by the current model, as evidenced by a comparison with both experimental results and finite element analysis results. It is found that the local deformation and interfacial stress beyond crack tip are relatively stable during crack propagation. It is also found that, when the cohesive strength is low, it has a significant effect on the critical peel load and loadline deflection. In principle, the approach developed in the current study can be extended to multilinear cohesive laws, although only bilinear cohesive law is presented in this work as an example.

In this paper, we discuss the motion of a vesicle in a linear shear flow. It is known that deformable vesicles such as liposomes show the so-called tank-treading and tumbling motions depending on the viscosity ratio between the inside and outside of the vesicle, the swelling ratio, and so on. First, we have conducted numerical simulations on the tank-treading motion of a liposome in a linear shear flow and compared the results with other numerical and experimental results. It is confirmed that the inclination angle of the vesicle becomes smaller when the viscosity ratio becomes larger or the swelling ratio becomes smaller and that the present results show quantitatively good agreement with other results. Then, the effects of membrane modeling are discussed from the mechanics point of view. There are two types of modeling for the lipid bilayer biomembrane. One is a two-dimensional fluid membrane, which reflects the fluidity of the lipid molecules. The other is a hyperelastic membrane, which reflects the stiffness of cytoskeleton structure. Liposome is usually modeled as a fluid membrane and red blood cell (RBC) is modeled as a hyperelastic one. We discuss how these differences of membrane models affect the behaviors of vesicles under the presence of shear flow. It is shown that the hyperelastic membrane model for RBC shows a less inclination angle of tank-treading motion and early transition from tank-treading to tumbling.

We consider an elliptical inhomogeneity embedded in an infinite isotropic elastic matrix subjected to in-plane deformations under the assumption of remote uniform loading. The inhomogeneity-matrix interface is assumed to be imperfect, which is simulated by the spring-layer model with vanishing thickness. Its behavior is based on the assumption that tractions are continuous but displacements are discontinuous across the interface. We further assume that the same degree of imperfection on the interface is realized in both the normal and tangential directions. We find a form of interface function, which leads to uniform stress field within the elliptical inhomogeneity. The explicit expressions for the uniform stress field within the elliptical inhomogeneity are derived. The obtained results are verified by comparison with existing solutions. The condition under which the internal stress field is not only uniform but also hydrostatic is also presented.

In 1970, F. Y. M. Wan derived a single, complex-valued ordinary differential equation for an elastically isotropic right circular conical shell ( “On the Equations of the Linear Theory of Elastic Conical Shells,” Studies Appl. Math., 49, pp. 69–83 ). The unknown was the n th Fourier component of a complex combination of the midsurface normal displacement and its static-geometric dual, a stress function. However, an attempt to formally replace the Fourier index n by a partial derivative in the circumferential angle θ results in a partial differential equation, which is eighth order in θ . The present paper takes as unknowns the traces of the bending strain and stress resultant tensors, respectively, and derives static-geometric dual partial differential equations of fourth order in both the axial and circumferential variables. Because of the explicit appearance of Poisson ratios of bending and stretching, these two equations cannot be combined into a single complex-valued equation. Reduced equations for beamlike (axisymmetric and lateral) deformations are also derived.

The phenomenon of elastic boundary layers under quasistatic loading is investigated using the Floquet–Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localized elastic deformation, confined to the free edge of a lattice. Boundary layer phenomena in three isotropic lattice topologies are investigated: the semiregular Kagome lattice, the regular hexagonal lattice, and the regular fully triangulated lattice. The boundary layer depth is on the order of the strut length for the hexagonal and the fully triangulated lattices. For the Kagome lattice, the depth of boundary layer scales inversely with the relative density. Thus, the boundary layer in a Kagome lattice of low relative density spans many cells.

We consider the contact problem for a particular class of compressible hyperelastic materials of harmonic type undergoing finite plane deformations. Using complex variable techniques, we derive subsidiary results concerning a half-plane problem corresponding to this class of materials. Using these results, we solve the contact problem for a harmonic material in the case of a uniform load acting on a finite area. Finally, we show how we can then deduce the corresponding results for the case of a point load.

A fracture parameter M c is proposed for evaluation of the surface energy associated with the creation of multiple curved cracks in 2D rubbery solids under the action of large deformation. Based on the concept of the M -integral, the parameter is developed by performing the integration along a closed contour enclosing all the cracks and with respect to a reference coordinate system originated at the geometric center of all the crack tips. The integration is shown to be path-independent so that the complicated singular stress field in the near-tip areas need not be involved in the calculation. It is thus suggested that M c be possibly used as a fracture parameter for describing the degradation of material and∕or structural integrity caused by irreversible evolution of multiple curved cracks in a rubbery media.

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

The behavior of a nano-scale cylindrical body (e.g., a fiber), lying on a substrate and acted upon by a combination of normal and tangential forces, is the subject of this investigation. As the scale decreases to the nano level, adhesion becomes an important issue in this contact problem. Thus, this investigation treats the two-dimensional plane strain elastic deformation of both the cylinder and the substrate during a rolling/sliding motion, including the effect of adhesion using the Maugis model. For the initiation of sliding, the Mindlin approach is used, whereas for rolling, the Carter approach is utilized. Each case is modified for nano-scale effects by including the effect of adhesion on the contact area and by using the adhesion theory of friction for the friction stress. Analytical results are given for the normal and tangential loading problems, including the initiation of sliding and rolling in terms of dimensionless quantities representing adhesion, cylinder size, and applied forces.

The fractal parameters (fractal dimension and topothesy), describing the contact behavior of rough surface, were considered as constant in the earlier models. However, their results are often significantly different from the experimental results. In the present study, these two roughness parameters have been derived analytically as a function of the mean separation first, then they are found with the aid of the experimental results. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variation of topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained from the experimental results of the number of contact spots and the power spectrum function at different mean separations. The probability density function of asperity heights, achieved at a different mean separation, was obtained from experimental results as a non-Gaussian distribution; it is expressed as a function of the skewness and the kurtosis. The relationship between skewness and mean separation can be established through the fitting of experimental results by this non-Gaussian distribution. For a sufficiently small mean separation, either the total load or the real contact area predicted by variable fractal parameters, as well as non-Gaussian distribution, is greater than that predicted by constant fractal parameters, as well as Gaussian distribution. The difference between these two models is significantly enhanced as the mean separation becomes small.

A statically admissible solution for a perfectly plastic material in plane stress is presented for the mode I crack problem. The yield condition employed is an alternative type first proposed by von Mises in order to approximate his original yield condition for plane stress while eliminating most of the elliptic region as pertaining to partial differential equations. This yield condition is composed of two intersecting parabolas rather than a single ellipse in the principal stress space. The attributes of this particular solution of the mode I problem over that previously obtained are that it contains neither stress discontinuities nor compressive stresses anywhere in the field.

A simple micromechanical model is presented for predicting the onset of tearing at slitlike damage sites in biaxially stressed coated plain weave fabrics. The stress concentration in the first intact yarn at the slit tip is determined as a function of increasing loading, and predictions for the onset of tearing are made under the assumption that tearing initiates through the rupture of the first intact yarn at a characteristic yarn breaking load. Extensive onset of tearing experiments on various coated nylon and polyester fabrics are presented, and the model is shown to capture the onset of tearing in these fabrics quite well over a range of slit lengths.

A three-dimensional solution for the problem of transversely loaded, all-round clamped rectangular plates of arbitrary thickness is presented within the linear, small deformation theory of elasticity. The Ritz minimum energy principle is employed to derive the governing equation of the plate made of functionally graded materials. In theory, if we employ an infinite number of terms in the displacement series, the exact solution can be determined. However, a practical limit always exists due to numerical implementation. The solution has a validity comparable to some higher order theories. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent are investigated.

This work considers the effect of external forces during finite duration collisions using an incremental model of impact. The deformation of the “rigid” body is modeled through an elastic element and the time interval over which contact occurs is of finite duration. Moreover, the work done by the external forces is nonzero during the collision. This model allows for an equivalent coefficient of restitution e to be identified. In the presence of a constant external force the coefficient of restitution depends not only on the system parameters, but the initial relative velocity at the point of impact. For external forces which tend to bring the colliding bodies together, the colliding bodies remain in contact for sufficiently small impact velocities ( e = 0 ) while for larger incoming speeds, the coefficient of restitution is positive. This state dependent restitution arises from the coupling of external forces to the collision model, and is not seen in more familiar models of impact. Finally, based on the results of the experimental system and the incremental model, the standard algebraic model of restitution is modified to include these finite duration effects.