TWO-SCALE TOPOLOGY OPTIMIZATION OF MACROSTRUCTURE AND POROUS MICROSTRUCTURE COMPOSED OF MULTIPHASE MATERIALS WITH DISTINCT POISSON’S RATIOS

Abstract

NEGATIVE POISSON’S RATIO (NPR) MATERIAL ATTRACTS A LOT OF ATTENTIONS FOR ITS UNIQUE MECHANICAL PROPERTIES. HOWEVER, ACHIEVING NPR IS AT THE EXPENSE OF REDUCING YOUNG’S MODULUS. IT HAS BEEN OBSERVED THAT THE COMPOSITE STIFFNESS CAN BE ENHANCED WHEN BLENDING POSITIVE POISSON’S RATIO (PPR) MATERIAL INTO NPR MATERIAL. BASED ON THE RESPECTIVE INTERPOLATION OF YOUNG’S MODULUS AND POISSON’S RATIO, A TWO-SCALE TOPOLOGY OPTIMIZATION NUMERICAL FRAMEWORK IS ESTABLISHED TO EXPLORE THE POISSON’S RATIO EFFECT IN POROUS MICROSTRUCTURE. IN THIS ARTICLE, TWO CONSTRAINT MODELS ARE DISCUSSED, ONE IS CALLED AS INDEPENDENT-CONSTRAINT MODEL, AND THE OTHER IS CALLED AS COUPLED-CONSTRAINT MODEL. IN THE INDEPENDENT-CONSTRAINT MODEL, THE VOLUME CONSTRAINTS ARE RESPECTIVELY IMPOSED ON THE MACRO AND MICRO STRUCTURES; IN THE COUPLED-CONSTRAINT MODEL, BESIDES SETTING AN UPPER BOUND ON THE TOTAL AVAILABLE BASE MATERIALS ON MACRO AND MICRO STRUCTURES, THE MICRO THERMAL INSULATION CAPABILITY IS CONSIDERED AS WELL. BESIDES CONSIDERING THE INFLUENCE OF MICRO THERMAL INSULATION CAPABILITY ON THE OPTIMIZED RESULTS, THE SIMILAR AND DISSIMILAR INFLUENCES OF POISSON’S RATIOS, VOLUME FRACTIONS UNDER TWO TYPES OF CONSTRAINTS ARE ALSO INVESTIGATED THROUGH SEVERAL 2D AND 3D NUMERICAL EXAMPLES. IT IS OBSERVED THAT THE CONCURRENT STRUCTURAL STIFFNESS RESULTING FROM THE MIXTURE OF PPR AND NPR MATERIALS CAN EXCEED THE CONCURRENT STRUCTURAL STIFFNESS COMPOSED OF ANY INDIVIDUAL BASE MATERIAL.