Explicit harmonic structure of bidimensional linear strain-gradient elasticity

In the perspective of homogenization theory, strain-gradient elasticity is a strategy to describe overall behavior materials with coarse mesostructure. this approach, effect mesostructure described by use three tensors whose orders vary from 4 6. Higher-order constitutive make it possible rich physical phenomena. However, these objects have intricate algebraic structures that prevent us having clear picture their modeling capabilities. The harmonic decomposition fundamental tool investigate anisotropic properties tensor spaces. For higher-order (i.e. order n≥3), determination generally difficult task. paper, novel procedure obtain introduced. This method, which we called Clebsch–Gordan Harmonic Algorithm, allows one explicit decompositions satisfying good such as orthogonality and uniqueness. elements also precise geometrical meaning simplifying interpretation. new algorithm here developed in specific case 2D space applied Mindlin’s Strain-Gradient Elasticity. We provide, for first time, fifth- sixth-order involved law. Algorithm not restricted may find interesting applications different fields mechanics involve tensors.