A consistency-check based algorithm for element condensation in augmented finite element methods for fracture analysis

• A consistency-check based condensation algorithm with mathematical exactness.
• A local instability treatment that improves numerical stability and robustness.
• Demonstration of 100–1000x improvement in numerical efficiency over other methods.

This paper reports a new algorithm that provides analytic solution to the equilibrium equation in A-FEM. It utilizes a consistency check between trial cohesive stiffness and resulting displacements to differentiate crack displacements from nodal displacements. Benchmark numerical tests demonstrate that the algorithm yields superior numerical accuracy, efficiency, and robustness to other methods. The overall improvement in numerical efficiency is ∼50 times that of the phantom-node based A-FEM in modeling a 4-point shear beam test. For mixed-mode composite delamination problems, the A-FEM with the algorithm is 20–30% faster than standard CZM despite that in the CZM delamination paths are pre-defined.