Mathematical Theories of Elasticity

Reduced Theories in Nonlinear Elasticity

The purpose of this note is to report on the recent development concerning the analysis and the rigorous derivation of thin film models for structures with nontrivial geometry. This includes: (i) shells with mid-surface of arbitrary curvature, and (ii) plates exhibiting residual stress at free equilibria. In the former setting, we derive a full range of models, some of them previously absent fr...

Structures in Mathematical Theories

Axiomatizing Mathematical Theories: Multiplication

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some mathematical structures are now classical theorems in Logic, Algebra and Geometry. In this paper we will study the axiomatizability of the theories of multiplication i...

Investigation of Linear and Nonlinear Buckling of Orthotropic Graphene Sheets with Nonlocal Elasticity Theories

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of  nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the me...

Mathematical Representations of Development Theories

In this paper we explore the consequences of particular stage linkage structures for the evolution of a population. We first argue the importance of constructing "dynamic" models of developmental theories and show through a series of examples the implications of various stage connections for population movements. In discussing dynamic models, one thrust of our comments is to identify the sorts ...