  This paper presents a stabilization scheme which addresses the
rank-deficiency problem in meshless collocation methods for solid mechanics.
Specifically, Smooth-Particle Hydrodynamics (SPH) in the Total Lagrangian
formalism is considered. This method is rank-deficient in the sense that the
SPH approximation of the deformation gradient is not unique with respect to the
positions of the integration points. The non-uniqueness can result in the
formation of zero-energy modes. If undetected, these modes can grow and
completely dominate the solution. Here, an algorithm is introduced, which
effectively suppresses these modes in a fashion similar to hour-glass control
mechanisms in Finite-Element methods. Simulations utilizing this control
algorithm result exhibit much improved stability, accuracy, and error
convergence properties. In contrast to an alternative method which eliminates
zero-energy modes, namely the use of additional integration points, the here
presented algorithm is easy to implement and computationally very efficient.
