Constitutive laws, intrinsic

The intrinsic constitutive laws (equations of state) are those of each phase. The external constitutive laws are four transfer laws at the walls (friction and mass transfer for each phase) and three interfacial transfer laws (mass, momentum, energy). The set of six conservation equations in the complete model can be written in equivalent form ... 

One must note that the balance equations are not dependent on either the type of material or the type of action the material undergoes. In fact, the balance equations are consequences of the laws of conservation of both linear and angular momenta and, eventually, of the first law of thermodynamics. In contrast, the constitutive equations are intrinsic to the material. As will be shown later, the incorporation of memory effects into constitutive equations either through the superposition principle of Boltzmann, in differential form, or by means of viscoelastic models based on the Kelvin-Voigt or Maxwell models, causes solution of viscoelastic problems to be more complex than the solution of problems in the purely elastic case. Nevertheless, in many situations it is possible to convert the viscoelastic problem into an elastic one through the employment of Laplace transforms. This type of strategy is accomplished by means of the correspondence principle. 

The viscoelastic nature of polymers generally determines rate and temperature dependence of their mechanical properties. At low strain levels, i.e. in a linear regime, this dependence is well described by intrinsic material properties defined within constitutive viscoelastic laws [1]. At high strains, in presence of failure processes, such as yielding or fracture, it is more difficult to establish a constitutive behaviour as well as to define material properties able to intrinsically characterise the failure process and its possible viscoelastic features. 

As expected, the energy release rate J and lump-sum cohesive law can be experimentally determined if the crack tip separation 8, the loadhne rotation Op of the adherends, and the global peel load P are simultaneously recorded during the fracture test. It is noted that this interface constitutive relationship is the equivalent interface cohesive law, not necessarily the intrinsic cohesive law. This is because, in addition to the intrinsic cohesive separation, possible plastic deformation in the adhesive layer contributes to the entire normal separation between the two adherends during the fracture test. Of course, with the decrease of the adhesive thickness, it is expected that this equivalent interface cohesive law will finally approach the intrinsic cohesive law [66]. 

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