Journal of Elasticity

This study uncovers the stress distributions on or adjacent to the bonded interface connecting two sections in a circular shaft subjected to torsional shear loads on the surfaces of both ends. The material in each section is considered to be cylindrically orthotropic with radial inhomogeneity. The derived results in explicit expressions enable us to investigate the trends of variations in stress near the connecting interface due to the varying degree of material anisotropy, forms of end loads, and material inhomogeneity. According to the numerical results of the examples, when both end surfaces are subjected to radially power-distributed torsional shear loads, the interfacial influences on stress distributions will be strongly dependent on the degree of material anisotropy, and the maximum magnitudes of the torsional stresses near the interface can be effectively alleviated by properly introducing a radial inhomogeneity into the material and adjusting the forms of the end torsional loads, even though the end surfaces are sufficiently far from the interface. When one designs the structure of a tube-to-tube connected shaft subjected to torsional loads, besides paying attention to the maximum magnitude of the interfacial longitudinal shear stress, the transverse shear stress adjacent to the interface has to be considered, especially when one section possesses strong anisotropy.

This paper contains an analysis of the interaction of longitudinal waves with a penny-shaped crack located in an infinitely long elastic cyclinder. The problem is reduced to a Fredholm integral equation of the second kind which is solved numerically for a range of values of the frequency of the incident waves and the radius of the cylinder. Numerical values of the dynamic stress intensity factor at the rim of the crack have been calculated.

The conventional formulation used in the past for problems involving interface cracks leads to a physical contradiction: The two sides of the crack are assumed to be free of tractions in the formulation, but the crack faces are seen to overlap after the solution is constructed. This unsatisfactory feature can be eliminated by introducing contact zones at the tips of an interface crack. The present article investigates the effect of friction in the contact zones for loads that start from zero and are increased monotonically. As an application, shear loading is considered, and the problem is reduced to a singular integral equation with a Cauchy-type kernel which is solved numerically. The results show that one of the contact zones is large and that friction affects the global nature of the stress fields. The results worked out include also the stress intensity factors, crack opening displacement, and the pressure distribution in the larger contact zone.

Elementary vector methods and the path-independent definition of a conservative force are used to show that a position dependent pressure p on a closed surface is conservative and has the potential ∫R dV, where R is the region bounded by the surface. A useful definition of tensor cross product is introduced.

Previous studies introduced a constitutive theory for fiber reinforced hyperelastic materials that allows the fibers to undergo microstructural changes. In this theory, increasing deformation of the matrix leads to increasing stretch of the fibers that causes their gradual dissolution. The dissolving fibers reassemble in the direction of maximum principal stretch of the matrix. The implications of the constitutive theory were first studied for two homogeneous deformations: uniaxial extension along the fibers and simple shear in the direction normal to the fibers. The constitutive theory was then used in treatment of the non-homogeneous deformation of combined axial stretch and twisting. The emphasis was on the determination of the influence of increasing axial stretch and twist on the spatial distribution of fiber dissolution and reassembly within the cylinder and also on the axial force and torque applied to the end faces of the cylinder. The present work is concerned with another aspect of combined axial stretch and twisting of the cylinder, namely unloading following dissolution and reassembly of some of the fibers. In this case, the cylinder is given an initial twist until there is an inner core of original fiber/matrix material and an outer sheath of remodeled fiber/matrix material. A condition is established that determines the combinations of axial stretch and twist that cause no additional dissolution and reassembly of fibers during unloading. It is also shown that there is a residual axial stretch and twist if the axial force and torque become zero. A numerical example illustrates this for a particular choice of matrix and fiber properties.

In this paper, we discuss the field equations of a rod with three deformable directors. We then deal with the rod subjected to internal constraints. Finally, we compare the theory of the constrained directed rod with that of an unconstrained rod with two deformable directors and with that of Cosserat rods.

Walter Noll’s trailblazing constitutive theory of material defects in smoothly uniform bodies is recast in the language of Lie groupoids and their associated Lie algebroids. From this vantage point the theory is extended to non-uniform bodies by introducing the notion of singular material distributions and the physically cognate idea of graded uniformity and homogeneity.

An equivalent indentation method is developed for the external crack problem with a Dugdale cohesive zone in the both axisymmetric and two-dimensional (2D) cases. This is achieved based on the principle of superposition by decomposing the original problem into two simple boundary value problems, with one considering action of a constant traction within the cohesive zone, and the other corresponding to indentation by a rigid concave punch. Closed-form expressions are derived for the distributions of displacement and traction on the crack interface, which are consistent with the classical results in fracture mechanics. Results show that the interfacial traction distributions in the axisymmetric and 2D cases share the similar mathematical forms except for different coordinate parameters. Finite element analysis is performed to validate the obtained analytical solutions. The proposed method relies solely on a few contact solutions on the surface irrespective of a general elasticity solution in the whole body, and it may find applications in the external crack analysis and adhesive contact model involving functionally graded elastic solids or piezoelectric materials.