Non-classical continuum theories for solid and fluent continua and some applications

Abstract

This paper presents two specific thermodynamically consistent non-classical continuum theories for solid and fluent continua. The first non-classical continuum theory for solid continua incorporates Jacobian of deformation in its entirety in the conservation and the balance laws and the derivation of the constitutive theories. The second non-classical continuum theory for solid continua considers Jacobian of deformation in its entirety as well as the Cosserat rotations in the conservation and balance laws as well as the constitutive theories. The first non-classical continuum theory for fluent continua presented here considers velocity gradient tensor in its entirety. The second non-classical continuum theory for fluent continua considers velocity gradient tensor in its entirety as well as Cosserat rotation rates in the derivation of the conservation and balance laws and the constitutive theories. Since the non-classical continuum theories for solid and fluent continua considered here incorporate additional physics of deformation due to rotations and rotation rates compared to classical continuum mechanics, the conservation and balance laws of classical continuum mechanics are shown to require modification as well as a new balance law balance of moment of moments is required to accommodate the new physics due to rotations and rotation rates. Eringen’s micropolar, micromorphic and microstretch theories, couple stress theories and nonlocal theories are also discussed within the context of the non-classical theories presented here for solid and fluent continua. Some applications of these theories are also discussed.

Keywords

• Non-classical
• continuum theories
• micropolar
• Jacobian of deformation
• internal rotations
• Cosserat rotations
• Cosserat rotation rates