Strain softening with creep and exponential algorithm

A constitutive relation that can describe tensile strain softening with or without simultaneous creep and shrinkage is presented, and an efficient timestep numerical integration algorithm, called the exponential algorithm, is developed. Microcracking that causes strain softening is permitted to take place only within three orthogonal planes. This allows the description of strain softening by independent algebraic relations for each of three orthogonal directions, including independent unloading and reloading behavior. The strain due to strain softening is considered as additive to the strain due to creep, shrinkage and elastic deformation. The time-step formulas for numerical integration of strain softening are obtained by an exact solution of a first-order linear differential equation for stress, whose coefficients are assumed to be spnstant duriijg the time step but may vary discontinuously between the steps.This algorithm is unconditionally stable and accurate even for very large time steps, and guarantees that the stress is always reduced exactly to zero as the normal tensile strain becomes very large. This algorithm, called exponential because its formulas involve exponential functions, may be combined with the well-known exponential algorithm for linear aging rate-type creep. The strain-softening model can satisfactorily represent the test data available in the literature.