  Disordered network materials abound in both nature and synthetic situations
while rigorous analysis of their nonlinear mechanical behaviors still is very
challenging. The purpose of this paper is to connect the mathematical framework
of sweeping process originally proposed by Moreau to a generic class of Lattice
Spring Models with plasticity phenomenon. We explicitly construct a sweeping
process and provide numerical schemes to find the evolution of stresses in a
Lattice Spring Model with infinitesimal strains and perfect plasticity. In
particular, we develop a highly efficient "leapfrog" computational framework
that allow ones to rigorously track the progression of plastic events in the
system based on the sweeping process theory. The utility of our framework is
demonstrated by analyzing the elastoplastic stresses in a novel class of
disordered network materials exhibiting the property of hyperuniformity, in
which the infinite wave-length density fluctuations associated with the
distribution of network nodes are completely suppressed. We find enhanced
mechanical properties such as increasing stiffness, yield strength and tensile
strength as the degree of hyperuniformity of the material system increases. Our
results have implications for optimal network material design and our
event-based framework can be readily generalized for nonlinear stress analysis
of other heterogeneous material systems. We also include some insights to the
model from the viewpoint of the rigidity theory.
