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Disordered network materials abound in both nature and synthetic situationswhile rigorous analysis of their nonlinear mechanical behaviors still is verychallenging. The purpose of this paper is to connect the mathematical frameworkof sweeping process originally proposed by Moreau to a generic class of LatticeSpring Models with plasticity phenomenon. We explicitly construct a sweepingprocess and provide numerical schemes to find the evolution of stresses in aLattice Spring Model with infinitesimal strains and perfect plasticity. Inparticular, we develop a highly efficient "leapfrog" computational frameworkthat allow ones to rigorously track the progression of plastic events in thesystem based on the sweeping process theory. The utility of our framework isdemonstrated by analyzing the elastoplastic stresses in a novel class ofdisordered network materials exhibiting the property of hyperuniformity, inwhich the infinite wave-length density fluctuations associated with thedistribution of network nodes are completely suppressed. We find enhancedmechanical properties such as increasing stiffness, yield strength and tensilestrength as the degree of hyperuniformity of the material system increases. Ourresults have implications for optimal network material design and ourevent-based framework can be readily generalized for nonlinear stress analysisof other heterogeneous material systems. We also include some insights to themodel from the viewpoint of the rigidity theory.

Sweeping process approach to stress analysis in elastoplastic Lattice Springs Models with applications to Hyperuniform Network Materials