research
Universal Deformations in Inhomogeneous Isotropic Nonlinear Elastic Solids
Universal (controllable) deformations of an elastic solid are those deformations that can be maintained for all possible strain-energy density functions and suitable boundary tractions. Universal deformations have played a central role in nonlinear elasticity and anelasticity. However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen. In this paper, we extend Ericksen's analysis of universal deformations to inhomogeneous compressible and incompressible isotropic solids.
Journal Club for September 2021: Phononic materials: controlling elastic waves in solids
Phononic materials: controlling elastic waves in solids
Ignacio Arretche (ia6 [at] illinois.edu), Ganesh Patil (gupatil2 [at] illinois.edu), Kathryn Matlack (kmatlack [at] illinois.edu)
On the Interaction of Viscoelasticity and Waviness in Enhancing the Pull-Off Force in Sphere/Flat Contacts
Motivated by roughness-induced adhesion enhancement (toughening and strengthening) in low modulus materials, we study the detachment of a sphere from a substrate in the presence of both viscoelastic dissipation at the contact edge, and roughness in the form of a single axisymmetric waviness. We show that the roughness-induced enhancement found by Guduru and coworkers for the elastic case (i.e. at very small detachment speeds) tends to disappear with increasing speeds, where the viscoelastic effect dominates and the problem approaches that of a smooth sphere.
Precipitation during creep in magnesium-aluminum alloys
Dear Colleagues,
I am writing to share with you my article titled, "Precipitation during creep in magnesium-aluminum alloys" , which has been published in the journal Continuum Mechanics and Thermodynamics.
Lightweight magnesium-aluminum alloys show significant tension-compression asymmetry under creep loading. This work offers an explanation of this phenomenon.
Link to the article: https://rdcu.be/ct4zi
Elastocapillary cleaning of twisted bilayer graphene interfaces
Dear iMechanicians, I would like to share our recent work on a drop confined by two adhesive graphene sheets (as illustrated below).
Variational principles for nonlinear pde systems via duality
Amit Acharya
A formal methodology for developing variational principles corresponding to a given nonlinear
pde system is discussed. The scheme is demonstrated in the context of the incompressible
Navier-Stokes equations, systems of first-order conservation laws, and systems of Hamilton-
Jacobi equations.
An action for nonlinear dislocation dynamics
Amit Acharya
To appear in J. Mech. Phys Solids
Amit Acharya
An action functional is developed for nonlinear dislocation dynamics. This serves as a fi rst step
towards the application of eff ective field theory in physics to evaluate its potential in obtaining
a macroscopic description of dislocation dynamics describing the plasticity of crystalline solids.
Connections arise between the continuum mechanics and material science of defects in solids,
eff ective field theory techniques in physics, and fracton tensor gauge theories.
The scheme that emerges from this work for generating a variational principle for a nonlinear
pde system is general, as is demonstrated by doing so for nonlinear elastostatics involving a stress
response function that is not necessarily hyperelastic.