Related papers: Optimal orientation of anisotropic solids
Stretching in continuum mechanics is naturally described using the Cauchy-Green strain tensors. These tensors quantify the Lagrangian stretching experienced by a material element, and provide a powerful way to study processes in turbulent…
We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness…
Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while…
In \cite{Lei}, the author derived an exact rotation-strain model in two dimensions for the motion of incompressible viscoelastic materials via the polar decomposition of the deformation tensor. Based on the rotation-strain model, the author…
Term "asymmetrical pseudoelasticity" refers to the theory, in which a symmetrical stress tensor and a symmetrical strain tensor are connected by means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix of elasticity…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
Aims: To investigate the stability and angular momentum transport by the strato-rotational instability in the nonlinear regime. Methods: The hydrodynamic compressible equations are solved in a cartesian box in which the outer cylinder is…
Superfluid 3He-A in a fully characterized stretched aerogel, used in previous work [1], has been studied for parallel and perpendicular orientations of the magnetic field relative to the anisotropy axis of the aerogel. Consistently, we find…
A quantitative mathematical model for the critical thickness of strained epitaxial metal films is presented, at which the magnetic moment experiences a reorientation from in-plane to perpendicular magnetic anisotropy. The model is based on…
In this paper we study universal deformations in anisotropic Cauchy elasticity. We show that the universality constraints of hyperelasticity and Cauchy elasticity for transversely isotropic, orthotropic, and monoclinic solids are…
A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is…
Efficient optimization of topology and raster angle has shown unprecedented enhancements in the mechanical properties of 3D printed materials. Topology optimization helps reduce the waste of raw material in the fabrication of 3D printed…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
Suspensions of anisotropic particles are commonly encountered in a wide spectrum of applications, including industrial and architectural coatings, targeted drug delivery and manufacturing of fiber-reinforced composites. A grand challenge in…
The lower bound usually cited for Poisson's ratio {\nu} is -1, derived from the relationship between {\nu} and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound…
A new variational principle - extremizing the fixed frame kinetic energy under constant relative enstrophy - for a coupled barotropic flow - rotating solid sphere system is introduced with the following consequences. In particular, angular…
We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…
A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…