LAUSR

Abstract The prediction of equilibrium paths in the presence of brittle fractures remains a challenge, despite the advances in the fracture modelling techniques. Difficulties arise in the solution of the equilibrium equations in the presence of material and structural instabilities. This work proposes a continuation method with multiple restrictions to solve the nonlinear system of equilibrium equations and overcome global convergence problems owing to the sudden energy release in fracture propagation analyses. The method combines simultaneously the cylindrical arc-length and the dissipation-energy control methods. In addition, this method allows the use of algorithms for the solution of linear systems of equations, which do not require the assembly of the global stiffness matrix. Numerical examples of tensile-mode and mixed-mode fracture propagation are presented and compared with experimental results. A zero-thickness interface element with linear softening damage model simulates mixed-mode fracture. The results show the accuracy, robustness, and effectiveness of the proposed continuation method even for challenging fracture problems.