An alternative implementation of the incremental energy/dissipation based arc-length control method

Abstract

A robust solution algorithm is essential to trace the arduous equilibrium paths typically confronted with in cohesive fracture and continuum damage mechanics of quasi-brittle materials. Although robust arc-length type solvers exist suitable for such problems, the use of these methods is hindered by their non-standard implementation requirements. Departing from this fact, in this paper, the recently proposed arc-length solver presented in reference May et al. (2016) is reconsidered within the limitations/capabilities of the commercial software packages and recast in a form which is suitable for implementation through user element formalism. The constraint equation is re-expressed and appended to the system of equations through the internal force column and tangent stiffness matrix of a user element. The effectiveness of the proposed alternative implementation is illustrated by means of two cohesive fracture problems.