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IN THIS PAPER, A MICROMECHANICAL EXTENSION OF THE FINITE-VOLUME DIRECT AVERAGING MICROMECHANICS THEORY (FVDAM) IS PRESENTED FOR EVALUATION OF THE HOMOGENIZED RELAXATION MODULI OF LINEAR VISCOELASTIC UNIDIRECTIONAL FIBER REINFORCED COMPOSITES WITH PERIODIC MICROSTRUCTURES. SUCH MATERIALS ARE ASSUMED AS COMPOSED OF REPEATING UNIT CELL WITH ARBITRARY INTERNAL ARCHITECTURAL ARRANGEMENTS OF FIBERS COATED BY THIN FLEXIBLE INTERPHASES. THESE INTERPHASES ARE REPLACED BY EQUIVALENT IMPERFECT INTERFACE ELEMENTS WITH IMPOSED CONTINUITY IN TRACTIONS AND DISCONTINUITY IN DISPLACEMENTS. INDEED, THE PROPOSED COMPUTATIONAL PROCEDURE ALLOWS AN EASY AND EFFICIENT TREATMENT OF THE DISPLACEMENT DISCONTINUITY CONDITION ACROSS THE INTERFACES. THE VISCOELASTIC BEHAVIOR OF THE CONSTITUENT PHASES IS MODELED USING THE GENERALIZED MAXWELL MODEL. THE FORMULATION OPERATES DIRECTLY IN THE TIME DOMAIN USING A NUMERICAL INCREMENTAL TIME-STEPPING PROCEDURE BASED ON THE CONCEPT OF INTERNAL STRESS VARIABLES. THE PERFORMANCE OF THE PROPOSED APPROACH IS DEMONSTRATED THROUGH HOMOGENIZATION OF VISCOELASTIC FIBER REINFORCED COMPOSITES AND PERIODIC MULTILAYER MATERIALS WITH FLAT AND WAVY ARCHITECTURES.

A Model for Homogenization of Linear Viscoelastic Periodic Composite Materials with Imperfect Interface