Consistent tangent matrices for substepping schemes ?
A very simple and general expression of the consistent tangent matrix for substepping time-integration schemes is presented. If needed, the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation. These two strategies (substepping and numerical differentiation) lead to quadratic convergence in complex nonlinear inelasticity problems.
substepping numerical differentiation quadratic convergence finite element method computational plasticity nonlinear problems