Research Projects

Hysteresis is a history-dependent, high-dimensional phenomenon seen in many engineering systems. The current research proposal is motivated by the classical work by Mindlin and Deresiewicz (1953) on elastic spheres in contact under varying oblique forces. Due to the presence of slip, the energy of the system dissipates and that result in hysteresis in the load vs. displacement. The work of Mindlin and Deresiewicz has several practical applications in the field of contact mechanics. In this proposal we will study detailed finite element model of elastic bodies in frictional contact under various oblique forces. The resulting hysteresis will be captured by a high-dimensional hysteresis model with two layers of springs and frictional sliders. The system governing equation is not a system of ordinary differential equations (ODEs) in usual sense. The system can be cast into an LCP. Finally, a reduced order hysteresis model will be developed that will capture a wide variety of hysteretic behaviors.