  The total Lagrangian smoothed particle hydrodynamics (TL-SPH) for elastic
solid dynamics suffers from hourglass modes which can grow and lead to the
failure of simulation for problems with large deformation. To address this
long-standing issue, we present an hourglass-free formulation based on
volumetric-devioatric stress decomposition. Inspired by the fact that the
artifact of nonphysical zigzag particle distribution induced by the hourglass
modes is mainly characterized by shear deformation and the standard SPH
discretization for the viscous term in the Navier-Stokes (NS) equation, the
present formulation computes the action of shear stress directly through the
Laplacian of displacement other than from the divergence of shear stress. A
comprehensive set of challenging benchmark cases are simulated to demonstrate
that, while improving accuracy and computational efficiency, the present
formulation is able to eliminate the hourglass modes and achieves very good
numerical stability with a single general effective parameter. In addition, the
deformation of a practically relevant stent structure is simulated to
demonstrate the potential of the present method in the field of biomechanics.
