Elastic-plastic contact law for simulation of tablet crushing using the biharmonic equation

This work presents a technique for shape modelling of cylindrical and spherical tablets subject to compression. This technique is based on the use of partial differential equations (PDEs), the biharmonic equation in particular. The deformation of the compressed elastic-plastic tablet of both shapes was obtained using the existing contact models found in literature. The mathematical properties of the biharmonic equation have been exploited to achieve simple mathematical expressions characterising the shape of the distorted tablet. Thus, the height, radius and contact area of both configurations due to uniaxial compression are represented by analytic expressions relating the coefficients associated with the solution of the biharmonic equation. The results obtained from the PDE-based simulation are compared with the theoretical ones. It is found that the analytic solution of the elliptic PDE can be utilised to represent the physical changes of the deformed object.