Research Interests include :

Continuum Mechanics and Applications

Nonlinear Elasticity Theory

Mathematical Modeling of Functionally Graded Materials

Smart Materials

Current Research Projects ( C. O. Horgan )

Recent research efforts in nonlinear elasticity have been concerned with large deformations of rubber-like solid materials. The mathematical and mechanical modeling used involves the theory of nonlinear elasticity for both compressible and incompressible materials.

Recent work has considered the effects of limiting chain extensibility at the molecular level and its implications in constitutive modeling. Such materials exhibit hardening at large deformations. Fundamental boundary-value problems have been solved analytically for a number of recently proposed strain-energy densities. These problems include those of torsion, axial shear, circular shear and the deformations induced in rotating cylinders. The results have implications for the design of experiments to measure the mechanical properties of rubber, polymers and biological materials. Mathematical methods for the analysis of nonlinear ordinary and partial differential equations were employed. This work was funded by NSF and AFOSR.

Mathematical modeling of functionally-graded materials (FGMs) is another area of active contemporary interest. FGMs are being used, for example, as interfacial zones to improve the bonding strength of layered composites, to reduce the residual and thermal stresses in bonded dissimilar materials and as wear resistant layers in machine and engine components. One of the advantages of FGMs over laminates is that, due to continuous material property variation, there is no stress build-up at sharp material boundaries thus eliminating potential structural integrity issues such as delamination. When a continuum mechanics approach is appropriate, models involving nonhomogeneous materials with continuously varying properties have attracted considerable recent attention. Using this viewpoint within the theory of linear isotropic elasticity, we have investigated several problems including end effects in FGMs, torsion, pressurized tubes and disks and rotating disks. The stress distribution is shown to be significantly different from that in the homogeneous material. In particular, the location of the maximum stresses depend critically on the degree of inhomogeneity of the material. Extension to smart materials (e.g. piezoelectric solids) is currently under investigation. This work was funded by NSF, NASA and AFOSR.