COMPARATIVE ANALYSIS OF CK- AND C0-GFEM APPLIED TO TWO-DIMENSIONAL PROBLEMS OF CONFINED PLASTICITY

Abstract

FOR MANY PRACTICAL APPLICATIONS IN ENGINEERING, A COMPLEX STRUC-TURE SHOWS LINEAR ELASTIC BEHAVIOR OVER ALMOST ALL ITS EXTENSION, BUT EXHIBITS CONFINED PLASTICITY CONTAINED IN SOME SMALL CRITICAL REGIONS, E.G. STRESS CONCENTRATIONS IN FILLETS AND SHARP INTERNAL CORNERS. THE BEHAVIOR OF C0- AND CK-GFEM IS INVESTIGATED IN THIS CLASS OF PROBLEMS. THE FIRST GOAL OF THIS STUDY IS TO VERIFY THE ACTUAL FORMULATION OF THE CK-GFEM FOR TWO-DIMENSIONAL ELASTOPLASTICITY, AS A MODIFICATION OF THE C0-GFEM FORMULATION. THE CK-GFEM IS BASED ON A SET OF BASIS FUNCTIONS WITH CK CONTINUITY OVER THE DOMAIN. THE APPROXIMATION FUNCTIONS ARE CONSTRUCTED FROM A CK CONTINUOUS PARTITION OF UNITY, OVER WHICH POLYNOMIAL ENRICHMENT FUNCTIONS (OR ANY SPECIAL FUNCTION) CAN BE APPLIED, IN THE SAME FASHION AS IN THE USUAL C0-GFEM. IN THIS WAY, THE FINITE ELEMENT APPROXIMATIONS SHOW CONTINUOUS RESPONSES FOR BOTH DISPLACEMENTS AND STRESSES ACROSS INTER-ELEMENT INTERFACES. AN INVESTIGATION IS PERFORMED TO ASSESS THE BEHAVIOR OF HIGH-ER-REGULARITY PARTITIONS OF UNITY AGAINST CONVENTIONAL C0 COUNTER-PARTS. THE IRREVERSIBLE RESPONSE AND HARDENING EFFECTS OF THE MA-TERIAL IS REPRESENTED BY THE RATE INDEPENDENT J2 PLASTICITY THEORY WITH LINEAR ISOTROPIC HARDENING OF MATERIAL AND VON MISES YIELD CRITERIA, BEING CONSIDERED ONLY MONOTONIC LOADING AND THE KINEMATICS OF SMALL DISPLACEMENTS AND SMALL DEFORMATIONS. THE FOCUS HEREIN IS TO ENLIGHTEN ANY POSSIBLE ADVANTAGE OF SMOOTHNESS IN THE PRESENCE OF PLASTIFICATION PHENOMENA, SEEKING FOR IMPROVEMENTS IN CAPTURING THE EVOLUTION OF THE PROCESS ZONE.