Consistent tangent operator for cutting-plane algorithm of elasto-plasticity

•The paper deals with the integration of elasto-plastic constitutive equations with the cutting-plane algorithm (CPA).•The consistent tangent operator (CTO) for the CPA is derived analytically; thus, quadratic convergence rate is ensured.•The convergence rate of the CPA in the global finite element equilibrium is drastically improved.•For complex models a very interesting alternative for the CTO computation is also the proposed semi-analytical approach.•The approach used in the CTO derivation is appropriate also for other numerical integration schemes.

The paper presents a derivation of the consistent tangent operator (CTO) for the cutting-plane algorithm (CPA). For a class of plasticity models that are suitable to be integrated using CPA, an explicit recursive expression is analytically derived and is updated in each iteration of the CPA integration procedure to yield the final value of the CTO when the CPA is converged.