Theeffectsoftwogeometricrefinementstrategieswidespreadinnaturalstructures,chiralityandself-similarhierarchy,onthein-planeelasticresponseoftwo-dimensionalhoneycombswerestudiedsystematically.Simpleclosed-formexpressionswerederivedfortheelasticmoduliofseveralchiral,antichiral,andhierarchicalhoneycombswithhexagonandsquarebasednetworks.Finiteelementanalysiswasemployedtovalidatetheanalyticalestimatesoftheelasticmoduli.Theresultswerealsocomparedwiththenumericalandexperimentaldataavailableintheliterature.WefoundthatintroducingahierarchicalrefinementincreasestheYoung'smodulusofhexagonbasedhoneycombswhiledecreasestheirshearmodulus.Forsquarebasedhoneycombs,hierarchyincreasestheshearmoduluswhiledecreasingtheirYoung'smodulus.IntroducingchiralitywasshowntoalwaysdecreasetheYoung'smodulusandPoisson'sratioofthestructure.However,chiralityremainstheonlyroutetoauxeticity.Inparticular,wefoundthatanti-tetra-chiralstructureswerecapableofsimultaneouslyexhibitinganisotropy,auxeticity,andremarkablylowshearmodulusasthemagnitudeofthechiralityoftheunitcellincreases.
