Convergence and Stability Analysis of Diametrical Compression in a Linear Elastic Disk Using Smoothed Particle Hydrodynamics

This work evaluates total Lagrangian Smoothed Particle Hydrodynamics (SPH) in DualSPHysics on a polycarbonate disk under diametrical compression against the Hondros analytical solution and two photoelastic experiments, with the stresses measured once the disk comes to rest. Stability tests reveal a broad optimal range of artificial viscosity above a stability threshold, within which the choice rests mainly on computational cost. A two-decade variation in piston velocity changes the error by at most 1.1%, and hourglass control reduces it by a factor of 7.3–8.5. A Convergence map of 6438 simulations across varying smoothing-length ratios, particle spacings and three kernels indicates that the von Mises error converges to first order in the smoothing length, down to 0.0026–0.0030 at the finest resolution. There, the contact zones account for 51–78% of the total error. Away from contacts, SPH interpolation of the exact field converges to second order, whereas the full simulation remains near first order. Finally, a single staged simulation reproduces the fringe patterns of four experimental photographs, matching dark fringes within 0.07–0.96 mm on average. Thus, concentrated contact loads govern both the error magnitude and, for interpolation, its convergence order. These findings guide SPH simulations of contact-loaded engineering structures.