Related papers: A multilayered plate theory with transverse shear …
Mode coupling theory (MCT) appears to explain several, though not all, aspects of the glass transition in colloids (particularly when short-range attractions are present). Developments of MCT, from rational foundations in statistical…
In this note, we address several issues, including some raised in recent works and commentary, related to bending measures and energies for plates and shells, and certain of their invariance properties. We discuss overlaps and distinctions…
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their…
In this paper, we examine the pure bending of plates within the framework of modified couple stress theory (M-CST) and consistent couple stress theory (C-CST). In this development, it is demonstrated that M-CST does not describe pure…
Deformation twinning and martensitic transformations are displacive transformations; they are defined by high speed collective displacements of the atoms, the existence of a parent/daughter orientation relationship, and plate or lath…
We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…
While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…
Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out…
This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the…
Folding paper along curves leads to spatial structures that have curved surfaces meeting at spatial creases, defined as curve-fold origami. In this work, we provide an Eulerian framework focusing on the mechanics of arbitrary curve-fold…
Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be…
In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
Three general modes are distinguished in the deformation of a thin shell; these are stretching, drilling, and bending. Of these, the drilling mode is the one more likely to emerge in a soft matter shell (as compared to a hard, structural…
Flexible structures in an incoming perpendicular flow typically undergo elastic reconfiguration that reduces drag; however, at higher velocities, they are prone to dynamical instabilities that entail complex wake dynamics and fluctuating…
Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk…
The aim of this paper is to offer an analytic theory of the shear banding instability in amorphous solids that are subjected to athermal quasi-static shear. To this aim we derive nonlinear equations for the displacement field, including the…
We explore the diversity of warped metric function in five-dimensional gravity including a scalar field and a 3-brane. We point out that the form of the function is determined by a parameter introduced here. For a particular value of the…
A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…
Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations…