Some properties of media defined by constitutive equations in implicit form
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Large deformation axial element for implicit constitutive relations
2019, International Journal of Non-Linear MechanicsCitation Excerpt :In Cauchy or Green elasticity, the Cauchy stress is explicitly related to the deformation gradient. However, as pointed out by Morgan [15] the stress and deformation gradient could be related through an implicit function. Restrictions on these implicit relations due to second law of thermodynamics has been studied [16–20].
Tensorial implicit constitutive relations in mechanics of incompressible non-Newtonian fluids
2015, Journal of Non-Newtonian Fluid MechanicsCitation Excerpt :The theoretical phenomenological approach based on the notion of a simple fluid has not been fully followed in various works, see for example Seely [4], Blatter [5], Matsuhisa and Bird [6], where the generalised viscosity has been considered to be a function of the first invariant of the Cauchy stress. ( See also Morgan [7] for an early discussion of implicit constitutive relations for the solids.) Despite this fact the concept of the simple fluid has played a dominant role in the phenomenological theory of constitutive relations.
On the gradient approach - Relation to Eringen's nonlocal theory
2011, International Journal of Engineering ScienceGradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results
2011, International Journal of Solids and StructuresImplicit constitutive relations in thermoelasticity
2011, International Journal of Non-Linear Mechanics