rbatra's blog

Nearly 50 years ago, Eringen developed a nonlocal theory of elasic solids according to which the Causchy stress tensor "sigma" at a point x depends upon the strain tensor "epsilon" not only at the point x but also at all other points in the body.  For homogeneous solids, and a few additional assumptions, he showed that the constitutive relation can be reduced to a differential form that has become popular among people studying deformations of functionally graded materials (FGMs).  However, an FGM is inhomogene

We address the challenging issue of simultaneously finding transverse shear and normal stresses at all points in a plate from a priori known values of the in-plane stresses at plate’s interior points. The principle of virtual work is employed to equate the work done by the transverse stresses to the difference between the work done by the external forces (applied surface tractions and body forces) and that by the in-plane stresses.

Job Title: Assistant/Associate Professor

Location of Position: Blacksburg, Virginia

Employing Institution: Virginia Tech

Myfeeling is that what we're trying to find are elastic constants of a continuum structure whose response in several (ideally all) deformations is the same as that of the carbon nanotube subjected to the same boundary conditions as the continuum structure.  We (A. Sears and R. C. Batra, Macroscopic Properties of Carbon Nanotubes from Molecular-Mechanics Simulations, Physical Reviews B, 69, 235406, 2004) have simulated simple tension and torsional deformations of a SWNT and its equivalent continuum structure defined as the one whose strain energy density is the same as that of the SWNT.  For an isotropic structure, the thickness of the equivalent structure was found to be~0.21 and it depends upon the MM potential used.  This has been validated by performing bending, buckling and combined loading tests on the SWNT and the equivalent continuum structure.