Research Interests
Over the past few years my research has narrowed to two areas. One involves the development of the material point method for the numerical analysis of problems involving large motions and deformations. The second is a unified approach for incorporating material failure with constitutive equations through the discontinuous bifurcation criterion. When combined, these two areas provide the potential for the simulation of certain manufacturing processes involving large deformation and material failure that have not generally been amenable to analysis.
The material point method has evolved from the particle-in-cell method developed at Los Alamos National Laboratory to a new method with reduced numerical dissipation and the capability to include history-dependent materials. The result is that deformable or rigid bodies can be followed through motions including large translations, rotations and deformations. The algorithm automatically precludes interpenetration so impact is handled with no need for a special slide-line or impact algorithm. So far the procedure has been used to analyse the motion of elastic bodies in a fluid, the impact of elastic and inelastic bodies, the penetration of an inelastic halfspace, the Taylor problem of a cylindrical rod impacting a rigid surface, and metal rolling. The procedure is a natural one to apply to material processing areas such as metal cutting, the filling of molds, the effect of fibers in the flow of molten metals or polymers, metal forming and plasma sprays. Some of these areas of application are currently being investigated.
There are a wide variety of failure criteria for materials such as maximum stress, maximum strain, fatigue cycles, and fracture energy. Constitutive equations which are normally interpreted to describe the stress-strain behavior of materials should automatically provide an indication of failure. The need for a systematic failure criterion is necessary because many manufacturing processes inherently include the generation of new surfaces as exhibited for example, by metal cutting and penetration. It is proposed that the existence of a discontinuous bifurcation is a good indicator of the initiation of material failure and that the evolution of failure can be simulated as the decohesion between two material surfaces. Furthermore, the combination of continuum damage and plasticity in a constitutive equation used for the analysis of cyclic loading can also provide a method for predicting failure due to fatigue.
The combination of advanced numerical methods and constitutive equations provides great promise for simulating those aspects of manufacturing involving material processing. The prediction of limiting conditions for metal forming, metal rolling, plasma sprays, casting, and imbedded particles are examples where the potential is great for elimination of many of the current steps associated with trial and error.