Microplane model M4 for concrete. I: Formulation with work-conjugate deviatoric stress

The first part of this two-part study presents a new improved microplane co nstitutive model for concrete, representing the fourth Version in the Line of microplane models developed at Northwestern University. The constitutive law is characterized as a relation between the normal, volumetric, deviato ric, and shear stresses and strains on planes of various orientations, call ed the microplanes. The strain components on the microplanes are the projec tions of the continuum strain tensor, and the continuum stresses are obtain ed from the microplane stress components according to the principle of virt ual work. The improvements include (I) a work-conjugate volumetric deviator ic split-the main improvement, facilitating physical interpretation of stre ss components; (2) additional horizontal boundaries (yield limits) for the normal and deviatoric microplane stress components, making it possible to c ontrol the curvature at the peaks of stress-strain curves; (3) an improved nonlinear frictional yield surface with plasticity asymptote; (4) a simpler and more effective fitting procedure with sequential identification of mat erial parameters; (5) a method to control the steepness and tail length of postpeak softening: and (6) damage modeling with a reduction of unloading s tiffness and crack-closing boundary. The second part of this study, by Cane r and Bazant, will present an algorithm for implementing the model in struc tural analysis programs and provide experimental verification and calibrati on by test data.