The paper "Consistent Tangent Operators for Rate-Independent Elasto-Plasticity" by Juan C. Simo and Robert L. Taylor discusses the importance of consistent tangent operators in preserving the quadratic rate of asymptotic convergence of iterative solution schemes for rate-independent elastoplasticity. The authors present a methodology to develop consistent tangent operators within the framework of closest-point-projection algorithms, which are commonly used for numerical integration of rate constitutive equations. They consider associative $J_2$ flow rules with general nonlinear kinematic and isotropic hardening rules, as well as a simple class of non-associative flow rules. The resulting iterative solution scheme maintains the asymptotic quadratic convergence characteristic of Newton's method, unlike the use of the so-called elasto-plastic tangent with radial return integration algorithms, which can lead to suboptimal convergence rates. The paper includes numerical examples to illustrate the practical importance of consistent tangent operators, demonstrating significant improvements in convergence rates when compared to the use of the "continuum" elastoplastic tangent.The paper "Consistent Tangent Operators for Rate-Independent Elasto-Plasticity" by Juan C. Simo and Robert L. Taylor discusses the importance of consistent tangent operators in preserving the quadratic rate of asymptotic convergence of iterative solution schemes for rate-independent elastoplasticity. The authors present a methodology to develop consistent tangent operators within the framework of closest-point-projection algorithms, which are commonly used for numerical integration of rate constitutive equations. They consider associative $J_2$ flow rules with general nonlinear kinematic and isotropic hardening rules, as well as a simple class of non-associative flow rules. The resulting iterative solution scheme maintains the asymptotic quadratic convergence characteristic of Newton's method, unlike the use of the so-called elasto-plastic tangent with radial return integration algorithms, which can lead to suboptimal convergence rates. The paper includes numerical examples to illustrate the practical importance of consistent tangent operators, demonstrating significant improvements in convergence rates when compared to the use of the "continuum" elastoplastic tangent.