In this paper, a new local arc-length method has been introduced to follow the snap-back at the microscale
as well as in the macroscale for a multiscale problem. First order multiscale computational
homogenization (FE2) approach has been employed to study the behaviour of a one dimensional (1D)
bar with cohesive cracks in the both scale. The macroscale material properties and constitutive equations
are unknown. The local macroscopic constitutive response is determined by solving the related
microscale Representative Volume Element (RVE). Each RVE has cohesive cracks whose damage parameters
are a function of the displacement jump. The non-damaged part of RVEs are assumed to be
linear elastic. In FE2 multiscale methods, the arc-length method is used in the macroscale and the displacement
control method is used in the microscale, however, the displacement control cannot follow
the snap back. The comparison of the new local arc-length method and conventional local arc-length is
presented
