  Dissipated energy, representing a monotonically increasing state variable in
nonlinear fracture mechanics, can be used as a restraint for tracing the
dissipation instead of the elastic unloading path of the structure response. In
this work, in contrast to other energy-based approaches that use internal
energy and the work done by the external loads, a novel arc-length approach is
proposed. It directly extracts the dissipated energy based on crack openings
and tractions (displacement jumps and cohesive forces between two surfaces of
one crack), taking advantage of the global/extended method of cracking
elements. Its linearized form is developed, and the stiffness factor of the
arc-length restraint is naturally obtained by means of the Sherman-Morrison
formula. Once cohesive cracks appear, the proposed approach can be applied
until most of the fracture energy is dissipated. Results from several numerical
tests, in which arc-length control and self-propagating cracks are jointly
used, are presented. They demonstrate the robustness of the proposed method,
which captures both global and local peak loads and all snap-back parts of the
force-displacement responses of loaded structures with multiple cracks.
