A strain-gradient elastic theory for special Cosserat rods

Micro -and nano -rods have been identified for various applications in actuators, sensors, and energy harvesters. This paper develops a general framework for micro -and nano -rods based on the one-dimensional straingradient theory for special Cosserat rods that considers large displacement and rotation of the cross section, chirality, and size effects. Initially, we obtain the linear momentum balance and angular momentum balance equations for rods utilizing the three-dimensional strain -gradient elasticity theory. Subsequently, we derive the constitutive relations for the strain -gradient elastic rods while considering material objectivity. We further identify the strain -gradient measures and their corresponding higher -order forces and higher -order moment terms. Using these constitutive relations, we show the applicability of our theory by deriving several closedform solutions for geometrically nonlinear thin rods undergoing extension, shear, torsion, and bending deformation. Finally, we rigorously examine the effect of the length scale parameter on all these deformations of the strain -gradient elastic special Cosserat rod under classical and higher -order boundary conditions. Our analysis through these interesting examples can help in developing next -generation architected metamaterials using micro -and nano -rods.