Consistent tangent operators for implicit non-local models of integral type

• Consistent linearisation of non-local implicit models of the integral type is discussed.
• Closed-form analytical expressions are derived for a J2 plasticity and a Lemaitre-based non-local damage models.
• The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described.
• Numerical examples demonstrate that the quadratic rate of convergence of the Newton-Raphson method is successfully achieved.

This work is concerned with the consistent linearisation of non-local models of the integral type whenever the non-local variable is an implicit function of the other constitutive variables. The general framework for the derivation of consistent non-local tangent operators is initially presented for elasto-plastic materials. Then, closed-form analytical expressions are established for a J2J2 hybrid local/non-local plasticity model and the Lemaitre-based non-local model. The structure of the consistent tangent operators is discussed and the corresponding assembly procedure is described. The numerical results show the efficiency of the approach and demonstrate that quadratic rates of convergence are successfully achieved.