frameindifference

Frame indifference, also called objectivity in continuum mechanics, is the principle that constitutive laws describing material response are invariant under superposed rigid body motions of the observer. In practice this means that if the reference frame undergoes a time-dependent rotation and translation, the material’s constitutive relation retains its form and yields the same physical predictions.

Mathematically, objects such as the Cauchy stress tensor and internal state variables must transform consistently under a change of frame. If F is the deformation gradient and R(t) is a rotation, then the constitutive relation must satisfy T'(F', …) = R T(F, …) R^T with F' = R F. To maintain frame indifference when taking time derivatives, researchers use objective rates of stress such as the Jaumann derivative, Green-Naghdi rates, or Oldroyd rates, which remove spurious rotation-induced artifacts.

Frame indifference is a foundational assumption in many areas of continuum mechanics, including elasticity, plasticity, and viscoelasticity. It ensures that constitutive models reflect material behavior rather than observer artifacts, and avoids unphysical predictions when a body undergoes rigid motions. The concept is associated with the broader principle of objectivity and was formalized in the rational mechanics literature by Truesdell and Noll, among others, in the mid-20th century.

Some models with external fields or microstructural effects may require relaxations of strict objectivity, and debates exist about the scope of frame indifference in non-equilibrium or relativistic contexts.