The corotational stability postulate: Positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity

In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that < D-degrees/Dt[sigma],D >>0 for all D is an element of Sym(3)\{0}, (0.1) where D degrees Dt is any corotational stress rate, sigma is the Cauchy stress and D=symL is the Eulerian rate of deformation tensor where L=FF-1=D xi v is the spatial velocity gradient. For <sigma(logV)>sigma(V) it is equivalent almost everywhere to the monotonicity (TSTS-M+) (0.2) <sigma(logV1)-sigma(logV(2)),logV(1)-logV(2)>>0 for all V-1,V-2 is an element of Sym++(3),V-1 not equal V-2. For hyperelasticity, (CSP) is in general independent of convexity of the mapping For hyperelasticity, (CSP) is in general independent of convexity of the mapping Fbar right arrowW(F) or Ubar right arrowW(U). Considering a family of diagonal, homogeneous deformations tbar right arrowF(t) one can, nevertheless, show that (CSP) implies positive incremental Cauchy stress moduli for this deformation family, including the incremental Young's modulus, the incremental equibiaxial modulus, the incremental planar tension modulus and the incremental bulk modulus. Aside, (CSP) is sufficient for the Baker-Ericksen and tension-extension inequality. Moreover, it implies local invertibility of the Cauchy stress-stretch relation. Together, this shows that (CSP) is a reasonable constitutive stability postulate in nonlinear elasticity, complementing local material stability viz. LH-ellipticity.