Nonlocal microplane concrete model with rate effect and load cycles. I: General formulation

The nonlocal microplane model for concrete is improved to describe unloading, reloading, cyclic loading, and the rate effect. The differences compared to the previous formulation are: (1) Normal strain component on the microplane is not split into its volumetric and deviatoric parts—rather the normal component is made dependent on the lateral normal strains on the microplane; and (2) instead of considering on each microplane only one shear strain vector parallel to the shear stress vector, the shear strain is represented by two independent components on the microplane. To introduce rate effect, the stress-strain law for each microplane component is described by a generalized Maxwell model—a series coupling of a linear viscous element and an elastoplastic-fracturing element. Nonlinear unloading-reloading hysteresis rules with back- and objective-stresses are developed to introduce hysteresis. The model is then combined with nonlocal theory to enable describing localization phenomena and avoid spurious mesh sensitivity due to strain softening. The numerical implementation in finite-element programs is described. The study consists of two parts; part I deals with the general formulation (part II deals with experimental verification).