In this paper, we formulate a theory for the coupling of accretion mechanics and thermoelasticity. We present an analytical formulation of the thermoelastic accretion of an infinite cylinder and of a two-dimensional block.
In nonlinear elasticity, universal deformations are the deformations that exist for arbitrary strain-energy density functions and suitable tractions at the boundaries. Here, we discuss the equivalent problem for linear elasticity. We characterize the universal displacements of linear elasticity: those displacement fields that can be maintained by applying boundary tractions in the absence of body forces for any linear elastic solid in a given anisotropy class.
In this paper we discuss the mechanics of anelastic bodies with respect to a Riemannian and a Euclidean geometric structure on the material manifold. These two structures provide two equivalent sets of governing equations that correspond to the geometrical and classical approaches to nonlinear anelasticity. This paper provides a parallelism between the two approaches and explains how to go from one to the other. We work in the setting of the multiplicative decomposition of deformation gradient seen as a non-holonomic change of frame in the material manifold.
In this book chapter we discuss some applications of algebraic topology in elasticity. This includes the necessary and sufficient compatibility equations of nonlinear elasticity for non-simply-connected bodies when the ambient space is Euclidean. Algebraic topology is the natural tool to understand the topological obstructions to compatibility for both the deformation gradient F and the right Cauchy-Green strain C. We will investigate the relevance of homology, cohomology, and homotopy groups in elasticity.
A new family of mixed finite element methods --- compatible-strain mixed finite element methods (CSFEMs) --- are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu-Washizu-type functional is extremized in order to obtain a mixed formulation for nonlinear elasticity. The independent fields of the mixed formulations are the displacement, the displacement gradient, and the first Piola-Kirchhoff stress. A pressure-like field is also introduced in the case of incompressible elasticity.
The 55th Meeting of the Society for Natural Philosophy: Microstructure, defects, and growth in mechanics will be from September 13-15, 2019 at Loyola University Chicago.
http://webpages.math.luc.edu/55SNP.html
A very limited number of openings to give Roundtable (25 min) talks are available. Special consideration will be given to young researchers. Two nights of lodging will be funded for these speakers. If you are interested in giving a Roundtable talk, you must submit an abstract.
The 55th Meeting of the Society for Natural Philosophy: Microstructure, defects, and growth in mechanics
September 13-15, 2019, Loyola University Chicago
In this paper we formulate the problems of nonlinear and linear elastodynamic transformation cloaking in a geometric framework. In particular, it is noted that a cloaking transformation is neither a spatial nor a referential change of frame (coordinates); a cloaking transformation maps the boundary-value problem of an isotropic and homogeneous elastic body (virtual problem) to that of an anisotropic and inhomogeneous elastic body with a hole surrounded by a cloak that is to be designed (physical problem).
We formulate a geometric nonlinear theory of the mechanics of accretion. In this theory the reference configuration of an accreting body is represented by a time-dependent Riemannian manifold with a time-independent metric that at each point depends on the state of deformation at that point at its time of attachment to the body, and on the way the new material is added to the body. We study the incompatibilities induced by accretion through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body.
The Daniel Guggenheim School of Aerospace Engineering and the School of Civil and Environmental Engineering at the Georgia Institute of Technology are seeking applications for a tenure-track faculty position in the area of space habitat systems. The position is expected to be a joint appointment between both schools. Multidisciplinary collaboration with related research groups and colleges at Georgia Tech is highly encouraged.
