Constitutive matrices for 32 typical classes of crystalline solids with couple stress, quadrupole, and curvature-based flexoelectric effects

The constitutive matrices for 32 typical classes of crystalline solids are determined for elastic dielectrics considering couple stress, quadrupole, curvature-based flexoelectric, and other higher-order effects. According to the Neumann’s principle, a simple but general method based on the transformation laws of tensor components is presented to derive the constitutive matrices of different classes of crystals. Derivations of constitutive matrices for curvature-based flexoelectricity of crystals of classes O_h (m3m) and C _6v (6mm) are explicitly shown as examples. Based on our program, we have: (i) the classical elastic stiffness matrix, piezoelectric matrix, and dielectric matrix obtained in the current work are consistent with those existing results; (ii) the non-classical (higher-order) constitutive matrices in 32 typical classes of crystals, such as couple stress stiffness, coupling between Cauchy stress and couple stress, higher-order dielectrics for quadrupole, curvature-based flexoelectricity, and the converse of flexoelectricity are obtained. The number of independent material constants in constitutive matrices for 32 classes of crystals is also summarized. The present paper provides a reference for solid mechanics researchers facing higher-order multiple physics problems in different categories of crystals and guidance for relevant material experiments.