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Dissipated energy, representing a monotonically increasing state variable innonlinear fracture mechanics, can be used as a restraint for tracing thedissipation instead of the elastic unloading path of the structure response. Inthis work, in contrast to other energy-based approaches that use internalenergy and the work done by the external loads, a novel arc-length approach isproposed. It directly extracts the dissipated energy based on crack openingsand tractions (displacement jumps and cohesive forces between two surfaces ofone crack), taking advantage of the global/extended method of crackingelements. Its linearized form is developed, and the stiffness factor of thearc-length restraint is naturally obtained by means of the Sherman-Morrisonformula. Once cohesive cracks appear, the proposed approach can be applieduntil most of the fracture energy is dissipated. Results from several numericaltests, in which arc-length control and self-propagating cracks are jointlyused, are presented. They demonstrate the robustness of the proposed method,which captures both global and local peak loads and all snap-back parts of theforce-displacement responses of loaded structures with multiple cracks.

Direct dissipation-based arc-length approach for the cracking elements method