Fundamentals of linear viscoelasticity

Despite complexities such as aging due to cement hydration or strong moisture sensitivity, the creep of concrete at service stress levels belongs to the broad realm of linear viscoelasticity, a theory that has been extensively studied beginning with the works of Maxwell, Kelvin, and Boltzmann in the late nineteenth century. Thanks to linearity, we introduce the compliance function as the basic material characteristic for constant sustained stress. Then we use the principle of superposition to characterize the creep at variable stress, calculate the relaxation function for constant imposed strain, and generalize the creep model to multiaxial stress. Finally we introduce an operator notation, which simplifies the mathematical exposition and illuminates the main concepts.