Accompanying dataset for the paper: "One-dimensional elastoplastic models with isotropic hardening as differential inclusions in primal form"

Contributions Author 1 carried out most of the study, structured and wrote the manuscript, implemented the algorithms, and performed the simulations. Author 2 contributed substantially to the development of the methodology, assisted throughout the study, and revised and improved several versions of the draft. Author 3 provided valuable mathematical insights and participated in proofreading. Author 4 contributed substantially to the construction and mathematical formulation of the model and participated in proofreading. All authors read and approved the final manuscript. Licensing CC BY 4.0 — attribution required Funding sources This work was supported by the WSL Institute for Snow and Avalanche Research SLF, Switzerland. This work was supported by the Geobrugg AG, Switzerland data: folder containing results for case 1 bouncing_ball - folder containing the data for the bouncing ball example + README.md - Description + hardening_II_primal_kinematics.csv - t, positions x1,y1,y2 and velocities of ball and table, formulation II primal form; y1,y2,x1 used in figure 18 + hardening_II_primal_kinetics.csv - t, percussions PN,PF,PP, forces laN,laF,laP, plastic variables p1,p2,gamma1,gamma2, formulation II primal form; PN,PF,PP used in figure 18 minimal_example - folder containing the data for the minimal example + README.md - Description + HardeningIIPrimal_force_linear.csv - linear isotropic hardening, box excitation; figures 11, 12 and 15 + HardeningUnilateralCompressionIIPrimal.csv - unilateral hardening element, compressive only; figure 15 + HardeningUnilateralTensionIIPrimal.csv - unilateral hardening element, tensile only; figure 15 + IdealPlasticIIPrimal.csv - ideal plasticity, i.e. no hardening; figure 15 + NonlinearHardeningBothIIPrimal.csv - nonlinear hardening, exponential and polynomial combined; figure 16 + NonlinearHardeningExpIIPrimal.csv - nonlinear hardening, exponential law; figure 16 + NonlinearHardeningPolyIIPrimal.csv - nonlinear hardening, polynomial law; figure 16 + analytical_sol.csv - t,q,u of the analytical reference solution of the minimal example; figure 12 + convergence_study_hardening_II_primal_global.csv - global errors of q,u,la_P,q_P,u_P for six time steps dt from 3e-2 to 1e-4, plus the reference slopes dt2…dt6 (only dt is plotted); figure 13 + convergence_study_hardening_II_primal_iterations_global.csv - fixed point tolerance (1e-3 … 1e-12) versus max and avg number of iterations; figure 14 + force_box.csv - t,f of the prescribed box excitation force f(t); figures 15 and 16 + force_box_negative.csv - t,f of the mirrored excitation force -f(t); figure 15 + solution_diff_abs.csv - absolute difference numerical minus analytical solution in q,u; figure 12 (bottom right) rockfall - folder containing the data for the rockfall example + README.md - Description + net_energy.csv - t, total E, kinetic T and potential V energy [kJ] and rate of dissipation D [kJ/s] of the net; figure 20(b) and (c) + rock_energy.csv - t, total E, kinetic T and potential V energy [kJ] of the test block; figure 20(a) cdr_files.zip: archive containing CorelDraw files of the figures Software used Corel Draw 2024 Python 3.14 matlab 2023 Paper Description To improve the numerical simulation of rockfall protection barriers, this work addresses an extension of a one-dimensional model for elastoplasticity using a friction element and a spring in series, to include isotropic hardening and unilateral behavior. We reformulate the resulting system of differential inclusions in primal form and develop a timestepping scheme via an extended version of Moreau's midpoint rule. The scheme handles nonsmooth dynamics consistently, allowing to include frictional contact and impacts. The results provide a rigorous and implementable framework for simulating coupled elastoplastic frictional contact systems, contributing to the analysis and computation of nonsmooth rate-independent processes.