research

In this paper we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space.

The paper presents a novel analysis of localisation and transmission properties of randomly-perturbed flexural systems. Attention is given to the study of propagation regimes and the connection with localised resonance modes in the context of Anderson's localisation. The analytical study is complemented with numerical simulations relevant to the design of efficient vibration isolation systems.

Eigenvalues, reflected and transmitted energy, localisation factors for the examined bi-coupled random system:

Large-eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) simulation of wind and wave forced oceanic turbulence in unstratified shallow water are performed in order to investigate the influence of wall modeling on results. The LES is also used to investigate the dependence of results on downwind and crosswind lengths of the computational domain, representative of a shallow shelf coastal ocean (10-to-30 m deep) unaffected by lateral boundaries.

Amit Acharya, Gui-Qiang Chen, Siran Li, Marshall Slemrod, and Dehua Wang

(To appear in Archive for Rational Mechanics and Analysis)

We are concerned with underlying connections between fluids,
elasticity, isometric embedding of Riemannian manifolds, and the existence of
wrinkled solutions of the associated nonlinear partial differential equations. In
this paper, we develop such connections for the case of two spatial dimensions,
and demonstrate that the continuum mechanical equations can be mapped into
a corresponding geometric framework and the inherent direct application of
the theory of isometric embeddings and the Gauss-Codazzi equations through
examples for the Euler equations for fluids and the Euler-Lagrange equations
for elastic solids. These results show that the geometric theory provides an
avenue for addressing the admissibility criteria for nonlinear conservation laws
in continuum mechanics.

This work introduces a new microscopically-motivated model for the electromechanical response of elastomers:

http://ac.els-cdn.com/S0022509615303525/1-s2.0-S0022509615303525-main.pdf?_tid=1db1e302-202a-11e6-8a60-00000aacb361&acdnat=1463927774_d9ad1fa74b5b42fafcb28a8b6b2c9b60

The merit of this novel model is demonstrated in the following paper

A research paper published in Vol. 83 of Journal of Applied Mechanics

http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?art…

Abstract

P. I. Galich and S. Rudykh, Manipulating pressure and shear waves in dielectric elastomers via external electric stimuli. International Journal of Solids and Structures, 91, 18 – 25 (2016)

• This work formulates an elasto-viscoplastic model at finite strains.
• A particularly efficient numerical integration algorithm is presented.
• A closed-form analytical expression is derived for the consistent tangent operator.
• The non-linear behaviour of polymers is captured in the numerical examples.
• Quadratic rate of convergence is successfully achieved.

doi:10.1016/j.compstruc.2016.01.002