The other answer is great and comes from a viewpoint of macroscopic plasticity. I'd just like to note that another perspective on plasticity exists, a multiscale view based on following atomistic mechanisms up through the length scales to aim for an understanding of plasticity that is increasingly based on physical mechanisms. The enormous range of length scales makes this a daunting task, and it's therefore still an area of active research.
Much of the research focuses on the evolution of dislocation populations, as the motion of these defects controls the plasticity of metals in many cases. At the very smallest scales, molecular dynamics simulations have been used to study the motion of individual dislocation mechanisms and even some dislocation populations . These are limited to a very high strain rate due to the small time steps required during the numerical integration of Newton's laws to describe the motion of atoms.
At a higher length scale, dislocations can be represented as discrete objects  or as part of a continuum . The behaviors of dislocation populations determined through these methods can give an idea of the stress-strain response for a single crystal. Often these rules of strength evolution at the slip system scale are then incorporated into the crystal plasticity finite element method, in which multiple grains of difference orientations and morphologies can be considered in a representative volume element to give a final, overall stress-strain curve . (More commonly, crystal plasticity models are fit to an existing stress-strain curve, to be used only on the same material system.)
Unfortunately, a multiscale approach does not give you a unified mathematical model to describe plasticity. There are important physics to consider at multiple length scales, and you'd have to incorporate an even wider variety of mechanisms if you want to predict failure. Most researchers recognize that all computational methods are compromises and choose the best tool to investigate their specific question. Cited are some recent papers on each topic, not necessarily the best review articles to start out with.
 Zepeda-Ruiz, L. A.; Stukowski, A.; Oppelstrup, T.; Bertin, N.; Barton, N. R.; Freitas, R.; Bulatov, V. V. Atomistic Insights into Metal Hardening. Nat. Mater. 2020. https://doi.org/10.1038/s41563-020-00815-1.
 Akhondzadeh, Sh.; Sills, R. B.; Bertin, N.; Cai, W. Dislocation Density-Based Plasticity Model from Massive Discrete Dislocation Dynamics Database. Journal of the Mechanics and Physics of Solids 2020, 145, 104152. https://doi.org/10.1016/j.jmps.2020.104152.
 Xu, S.; Smith, L.; Mianroodi, J. R.; Hunter, A.; Svendsen, B.; Beyerlein, I. J. A Comparison of Different Continuum Approaches in Modeling Mixed-Type Dislocations in Al. Modelling Simul. Mater. Sci. Eng. 2019, 27 (7), 074004. https://doi.org/10.1088/1361-651X/ab2d16.
 Nguyen, K.; Zhang, M.; Amores, V. J.; Sanz, M. A.; Montáns, F. J. Computational Modeling of Dislocation Slip Mechanisms in Crystal Plasticity: A Short Review. Crystals 2021, 11 (1), 42. https://doi.org/10.3390/cryst11010042.