TWO-DIMENSIONAL NUMERICAL MODEL OF THE FRACTURE PROCESS IN STEEL FIBRE REINFORCED CONCRETE WITH THE CONTINUUM STRONG DISCONTINUITY APPROACH AND FUNCTIONAL DATA ANALYSIS

Abstract

THIS PAPER PRESENTS THE FORMULATION OF A TWO-DIMENSIONAL NUMERICAL MODEL ABLE TO DESCRIBE THE FRACTURE PROCESS IN STRUCTURAL MEMBERS OF STEEL FIBRE REINFORCED CONCRETE (SFRC) FROM THE VOLUME RATIO OF THE FIBRES AND THE MECHANICAL PROPERTIES OF THE COMPONENTS: A CONCRETE MATRIX AND A SET OF STEEL FIBRES WITH A RANDOM ORIENTATION. THE RELATIONSHIP BETWEEN THE STRESS AND THE STRAIN FIELDS OF THE COMPOSITE MATERIAL IS OBTAINED USING THE MIXTURE THEORY WITH A COMPATIBILITY STRAIN OF ITS COMPONENT MATERIALS. THE CONCRETE MATRIX IS REPRESENTED WITH A SCALAR DAMAGE CONSTITUTIVE MODEL WITH A SOFTENING STRAIN AND A DIFFERENT STRENGTH IN TENSION AND COMPRESSION. THE MECHANICAL STRAIN OF AN INSULATED FIBRE AND THE SLIP BETWEEN THE FIBRE AND THE MATRIX ARE SIMULTANEOUSLY DESCRIBED WITH A ONE-DIMENSIONAL PLASTICITY CONSTITUTIVE MODEL. THE CRACKING OF THE COMPOSITE MATERIAL INDICATES A JUMP IN THE DISPLACEMENT FIELD AND NON-BOUNDED VALUES OF THE STRAIN FIELD, WHICH ARE REPRESENTED BY THE CONTINUUM STRONG DISCONTINUITY APPROACH. THE MODEL HAS BEEN IMPLEMENTED IN THE FRAMEWORK OF THE NONLINEAR ANALYSIS WITH THE FINITE ELEMENT METHOD, USING CONSTANT STRAIN TRIANGULAR ELEMENTS. MOREOVER, THE FIBRES DISTRIBUTION AND ORIENTATION CHANGE RANDOMLY IN EACH FINITE ELEMENT AND EACH SIMULATION OR OBSERVATION. THE STRUCTURAL RESPONSES OF THE SIMULATIONS ARE TREATED AS CURVES AND ANALYSED BY TOOLS FROM THE FUNCTIONAL DATA ANALYSIS. CONFIDENCE INTERVALS FOR THE STRUCTURAL RESPONSE ARE BUILT USING BOOTSTRAP METHODOLOGY. FINALLY, EXPERIMENTAL TESTS OF SFRC MEMBERS SUBJECTED TO TENSION AND BENDING ARE SIMULATED. THE STRUCTURAL RESPONSE AND THE CRACKING PATTERNS OBTAINED FROM THE NUMERICAL SIMULATION ARE SATISFACTORY.