This short note addresses a misconception that seems to be prevalent with regard to the use of compatibility conditions for the strains in both the linearized and non-linear theories of elasticity, when one uses a “stress-based” approach.
RajagopalKR. On implicit constitutive theories. Appl Math2003; 48: 279–319
2.
RajagopalKR. The elasticity of elasticity. Zeitschrift für angewandte Mathematik und Physik2007; 58: 309–317.
3.
RajagopalKRSrinivasaAR. On a class of non-dissipative solids that are not hyperelastic. Proc Roy Soc A2009; 465: 493–500.
4.
MaxwellJC. On the dynamical theory of gases. Phil Trans Roy Soc Lond1967; A157: 49–88.
5.
BurgersJM. Mechanical considerations model systems phenomenological theories of relaxation and viscosity. In: First report on viscosity and plasticity, Chapter 1. New York: Nordemann Publishing, 1939, 5–67.
6.
OldroydJG. On the formulation of rheological equations of state. Proc Roy Soc Lond1950; A200: 523–591.
RajagopalKRSrinivasaAR. On the thermodynamics of fluids defined by implicit constitutive relations. Zeitschrift für angewandte Mathematik und Physik2008; 59: 715–729.
9.
PrusaVMalekJRajagopalKR. Generalizations of the Navier-Stokes fluid from a new perspective. Int J Eng Sci2012; 48: 1907–1924.