Determination of material properties of a linearly elastic peridynamic material

We investigate the properties of an isotropic linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which considers both length and relative angle changes, and is based on a free energy function proposed in previous work that contains four material constants. To this end, we consider a class of equilibrium problems in mechanics to show that, in interior points of the body where deformations are smooth, the corresponding solutions in classical linear elasticity are also equilibrium solutions in peridynamics. More generally, we show that the equations of equilibrium are satisfied even when two of the four peridynamic constants are arbitrary. Pure torsion of a cylindrical shaft and pure bending of a cylindrical beam are particular cases of this class of problems and are used together with a correspondence argument proposed elsewhere to determine these two constants in terms of the elasticity constants of an isotropic material from the classical linear elasticity. One of the constants has a singularity in the Poisson ratio, which needs further investigation. Two additional experiments concerning bending of cylindrical beam by terminal load and anti-plane shear of a hollow cylinder, which do not belong to the previous class of problems, are used to validate these results.

Some Applications of Integrated Elasticity

This paper examines the effects of relaxing the assumption of classical linear elasticity that the loads act in their entirety on the undeformed shape. Instead, loads here are applied incrementally as deformation proceeds, and resulting fields are integrated. A formal statement of the attendant integrated elasticity theory is provided. A class of problems is identified for which this formulation is amenable to solution in closed form. Some results from these configurations are compared with linear elasticity and experimentally measured data. The comparisons indicate that, as deformation increases, integrated elasticity is capable of tracking the physical response better than linear elasticity.

Scattered wave functions and electronic states of dislocations

This article outlines a model for calculating the localized electronic states of a [Formula: see text] edge dislocation in α-Fe and in Mo. A method is presented using a Wannier function approach for calculating the scattered wave function of a dislocated lattice. The model used for the calculations of the electronic structure is based on the multiple scattering model. In addition the computer simulation procedure for calculating the atomic configuration of dislocations is combined with classical linear elasticity theory and the self-consistent scattered wave model.

Axisymmetric Stress Field Around Spheroidal Inclusions and Cavities in a Transversely Isotropic Material

A spheroidal inclusion is embedded in an elastic matrix composed of a different material. Both materials are transversely isotropic with the material property axes parallel to the geometric axis of the spheroid. At the interface, the two materials are bonded. The matrix is subjected to a uniform axisymmetric stress field at infinity. Explicit expressions for the stress and displacement fields in the inclusion and the matrix will be presented. The analysis is within the realm of classical linear elasticity.