Finite deformation elasticity theory

This chapter provides the framework for the development of constitutive theories of solids by focusing on constitutive laws for nonlinearly elastic solids. These exemplify the general principles of constitutive theory that should be applied to all types of material behaviour, in particular, the notions of objectivity and material symmetry, including the important symmetries of isotropy, transverse isotropy and orthotropy based in part on deformation invariants. Details are given for the various general stress–deformation relations for each case of symmetry in respect of hyperelastic materials (which are characterized by a strain-energy function), with or without an internal constraint such as incompressibility, and these are illustrated by particular prototype models. The notion of residual stress (in an unloaded configuration) is discussed and the form of strain-energy function required to accommodate residual stress in the material response is developed

On dynamic boundary conditions within the linear Steigmann-Ogden model of surface elasticity and strain gradient elasticity

Within the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity is considered. As a result, we derived the motion equations and the natural boundary conditions which include inertia terms

Large single crystal growth, transport property and spectroscopic characterizations of three-dimensional Dirac semimetal Cd3As2

The three dimensional (3D) Dirac semimetal is a new quantum state of matter that has attracted much attention recently in physics and material science. Here, we report on the growth of large plate-like single crystals of Cd(3)As(2) in two major orientations by a self-selecting vapor growth (SSVG) method, and the optimum growth conditions have been experimentally determined. The crystalline imperfections and electrical properties of the crystals were examined with transmission electron microscopy (TEM), scanning tunneling microscopy (STM), and transport property measurements. This SSVG method makes it possible to control the as-grown crystal compositions with excess Cd or As leading to mobilities near 5–10(5) cm(2)V(−1)s(−1). Zn-doping can effectively reduce the carrier density to reach the maximum residual resistivity ratio (RRR[Image: see text]ρ(300K)/ρ(5K)) of 7.6. A vacuum-cleaved single crystal has been investigated using angle-resolved photoemission spectroscopy (ARPES) to reveal a single Dirac cone near the center of the surface Brillouin zone with a binding energy of approximately 200 meV