research

Amit Acharya         Marta Lewicka         Mohammad Reza Pakzad

In Nonlinearity, 29, 1769-1797

We study a class of design problems in solid mechanics, leading to a variation on the
classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new
context, we derive a necessary and sufficient existence condition, given through a system of total
differential equations, and discuss its integrability. In the classical context, the same approach
yields conditions of immersibility of a given metric in terms of the Riemann curvature tensor.
In the present situation, the equations do not close in a straightforward manner, and successive
differentiation of the compatibility conditions leads to a more sophisticated algebraic description
of integrability. We also recast the problem in a variational setting and analyze the infimum value
of the appropriate incompatibility energy, resembling "non-Euclidean elasticity".  We then derive a
Γ-convergence result for the dimension reduction from 3d to 2d in the Kirchhoff energy scaling
regime. A practical implementation of the algebraic conditions of integrability is also discussed.

Dear colleagues,

There have been two changes at NSF that do affect the imechanica community. I would like to bring these to your attention.

Abstract: We present a model for the rheological behaviour of non-dilute suspensions of initially spherical viscoelastic particles in viscous fluids under uniform Stokes flow conditions. The particles are assumed to be neutrally buoyant Kelvin–Voigt solids undergoing time-dependent finite deformations and exhibiting generalized neo-Hookean behaviour in their purely elastic limit.

Size-affected dislocation-mediated plasticity is important in a wide range of materials and technologies. The question of how to explain and predict the effect of size on the properties and response of materials has been at the forefront of mechanics and materials research.

The two-phase solid–liquid coexisting structures of Ni, Cu, and Al are studied by molecular dynamics (MD) simulations using the second nearest-neighbor (2NN) modified-embedded atom method (MEAM) potential. For this purpose, the existing 2NN-MEAM parameters for Ni and Cu were modified to make them suitable for the MD simulations of the problems related to the two-phase solid–liquid coexistence of these elements.

F. Xu, M. Potier-Ferry, S. Belouettar, H. Hu

International Journal of Non-Linear Mechanics (2014), http://dx.doi.org/10.1016/j.ijnonlinmec.2014.12.006

Abstract:

Phase-field crystal (PFC) is a model with atomistic-scale details acting on diffusive time scales. PFC uses the density field as its order parameter, which takes a constant value in the liquid phase and a periodic function in the solid phase. PFC naturally takes into account elasticity, solid–liquid interface free energy, surface anisotropy, and grain boundary free energy by using this single-order parameter in modeling of coexisting solid–liquid structures.

Composites reinforced by thinner fibers are intensively studied in recent years and expected to have better
mechanical properties. With development of nanotechnology, the diameter of fiber can be as thin as
several nanometers, such as nanofibers and nanotubes. Then, do these thinner fibers definitely result in
composites with better mechanical properties? In this paper, the toughening effect of reinforcing fibers in
composites is investigated based on the three-level failure analysis model. It is found that thinner