Microplane model for cyclic triaxial behavior of concrete

A recently proposed microplane model, which describes not only cracking but also general nonlinear triaxial response, is extended to cyclic loading and the rate effect, and is implemented in a three-dimensional finite element code. The material properties are characterized separately on planes of various orientations within the material, called the microplanes, on which no tensorial invariance requirements need to be observed. The state of each microplane is described by normal deviatoric and volumetric strains, and by shear strain. To avoid spurious localization instabilities due to strain softening and the consequent mesh-sensitivity problems, the concept of nonlocal continuum with local strain is adopted. The rate effect is introduced by combining the damage model on each microplane with the Maxwell rheologic model. The results of finite element analysis of some basic cases on the material level, as well as of plain concrete specimens loaded in bending and compression, are demonstrated. The calculated responses yield hysteretic loops of an approximately correct area and correct initial unloading slope. For shear, the calculated loops exhibit the well-known pinched form.