Contribution of nonlocal integral elasticity to modified strain gradient theory

The nonlocal integral elasticity and the modified strain gradient theory are consistently integrated in the framework of the nonlocal modified gradient theory of elasticity. The equivalent differential formulation of the constitutive law, equipped with appropriate nonstandard boundary conditions, is introduced. The size-dependent effects of the dilatation gradient, deviatoric stretch gradient, and symmetric rotation gradient in addition to the nonlocality are beneficially captured in the flexure problem of nano-beams. The well posedness of the proposed nonlocal modified gradient problem is demonstrated via analytical examination of the elastostatic flexure and the wave dispersion phenomenon in nano-beams. The dispersive behavior of flexural waves is verified in comparison with the molecular dynamics simulation. The dominant stiffening effect of the gradient characteristic parameters associated with the nonlocal modified gradient elasticity is confirmed. Both the stiffening and softening responses of nano-structured materials are effectively realized in the framework of the introduced augmented elasticity theory. The conceived nonlocal modified gradient elasticity theory can accordingly provide a practical approach for nanoscopic study of the field quantities.

Automated summary

The nonlocal integral elasticity and the modified strain gradient theory are integrated in the framework of the nonlocal modified gradient theory of elasticity, capturing size-dependent effects in nano-beams. The proposed nonlocal modified gradient problem is well-posed, demonstrated through analytical examination and comparison with molecular dynamics simulation. The stiffening effect of the gradient characteristic parameters is confirmed, providing an effective approach for nanoscopic study of field quantities.