Strain Softening with Creep and Exponential Algorithm

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Abstract
A constitutive relation that can describe tensile strain softening with or without simultaneous creep and shrinkage is presented, and an efficient time‐step 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 soft‐ening 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 constant during the time step but may vary discontinuously between the steps. This algorithm is unconditionally stable and accurate even for very large tifhesteps, and guar...

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