MULTI-SCALE REPRESENTATION OF PLASTIC DEFORMATION IN FIBER-REINFORCED MATERIALS: APPLICATION TO REINFORCED CONCRETE

Abstract

HERE WE PRESENT A MULTI-SCALE MODEL TO CARRY OUT THE COMPUTATION OF BRITTLE COMPOSITE MATERIALS REINFORCED WITH FIBERS, AND WE SHOW ITS APPLICATION TO STANDARD REINFORCED CONCRETE. THE COMPUTATION IS PERFORMED WITHIN AN OPERATOR-SPLIT FRAMEWORK ON THE MACRO-SCALE, WHICH ALLOWS FOR DIFFERENT FAILURE MECHANISMS TO DEVELOP IN SEPARATE PHASES, AS BOTH THE CONCRETE AND THE BOND-SLIP EXHIBIT NON-LINEAR BEHAVIOR. THE COMPUTATIONS ON THE MICRO-SCALE ARE PERFORMED FOR EACH CONSTITUENT SEPARATELY. THE REINFORCEMENT IS TAKEN TO BE LINEAR ELASTIC, AND THE BOND-SLIP IS HANDLED AS A PLASTIC DEFORMATION. THE STANDARD ELASTOPLASTIC PROCEDURE IS USED TO COMPUTE THE BOND STRESSES, COMBINED WITH THE X-FEM METHODOLOGY TO GIVE THE GLOBAL REPRESENTATION OF SLIP. THE CRACK DEVELOPMENT IN CONCRETE, ON THE OTHER HAND, IS DESCRIBED WITH A DAMAGE MODEL WITH EXPONENTIAL SOFTENING, WHERE ED-FEM IS USED TO REPRESENT LOCALIZED FAILURE. A NUMERICAL EXAMPLE IS SHOWN TO TEST THE DEVELOPED METHODOLOGY.