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ABSTRACT. A ONE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM OF ISOTHERMAL ELASTODYNAMICS FOR A MICRO-PERIODIC LAYERED SEMI-SPACE IN WHICH A MICROSTRUCTURAL LENGTH IS TAKEN INTO ACCOUNT, IS STUDIED. IN SUCH A THEORY, CALLED REFINED AVERAGED THEORY (RAT), THE LAYERED SEMI-SPACE IS COMPOSED OF IDENTICAL TWO-LAYER HOMOGENEOUS ISOTROPIC ELASTIC SUBUNITS THAT ARE MECHANICALLY BONDED TO FORM A SPATIALLY PERIODIC PATTERN.THE FIELD EQUATIONS CONSIST OF: (I) THE H-APPROXIMATION OF A DISPLACEMENT FIELD WHICH MEANS THAT THE DISPLACEMENT IS A LINEAR FUNCTION OF A MICRO-PERIODIC SHAPE FUNCTION H, (II) TWO EQUATIONS OF MOTION INVOLVING A STRESS S, A BODY FORCE H, AND TWO COEFFICIENTS OF THE H-APPROXIMATION: A MACRO-DISPLACEMENT U AND A DISPLACEMENT CORRECTOR V, AND (III) TWO CONSTITUTIVE RELATIONS CONNECTING (S,H) TO (U,V). BY ELIMINATING U,V, AND H FROM (II) AND (III), ONE OBTAINS THE STRESS EQUATION OF MOTION FOR S INVOLVING A HIGH FREQUENCY PARAMETER. IN THE PAPER A PURE STRESS INITIAL-BOUNDARY VALUE PROBLEM FOR THE MICRO-PERIODIC LAYERED SEMI-SPACE IS FORMULATED, AND A UNIQUENESS THEOREM FOR THE PROBLEM IS PROVED. THE PROOF IS BASED ON OBSERVATION THAT THE STRESS PROBLEM DESRIBED BY THE PARTIAL DIFFERENTIAL EQUATION SUBJECT TO SUITABLE INITIAL AND BOUNDARY CONDITIONS CAN BE REPLACED BY THE PROBLEM INVOLVING AN INTEGRO-DIFFERENTIAL EQUATION FOR WHICH AN ENERGY INTEGRAL VANISHES. ALSO, A CLOSED-FORM GREEN S FUNCTION FOR THE PURE STRESS PROBLEM IS OBTAINED, AND A NUMBER OF PROPERTIES OF THE FUNCTION ARE REVEALED.
KEYWORDS: SOLID MECHANICS, WAVE PROPAGATION, COMPOSITES, MICROPERIODIC LAYERING
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