On the thermodynamics of pseudo-elastic material models which reproduce the M ullins effect

Abstract

a b s t r a c tThis work focuses on the thermodynamics of pseudo-elastic material models which represent the MULLINS effect. Two established models are analyzed theoretically, their thermomechanical properties are derived, and certain disadvantageous points are identified. These findings are used to deduce an alternative approach to deviate pseudo-elasticity. This is achieved by defining a suitable free energy which imposes conditions on the stress tensor and the dissipation using the CLAUSIUS-DUHEM inequality. The concept of pseudo-elasticity is then generalized to extend arbitrary thermomechanical, even inelastic, material models to allow for softening effects. Under weak assumptions on the softening function the thermomechanical consistency is shown.

Comparison of discontinuous damage models of Mullins-type

“…< 0 is sufficient to fulfill inequality (24), see [32]. A discrepancy between these demands for monotonicity and experimental findings are discussed by [22].…”

“…[33] coined the name pseudoelasticity for this model type. The idea was first described by [11] and generalised by [32]. Furthermore, the latter authors proved that the only feasible choice for the scalar measure of maximum load is the basic strain…”

Hyperviscoelastic Constitutive Modelling of Solid Propellants with Damage and Compressibility

“…A new theory (Pseudoelastic approach) for stress softening is proposed by Ogden and Roxburgh [44] and Nueman and Ihlemann [45] through a single continuous parameter termed as damage parameter. This parameter controls the material behavior under unloading and subsequent reloading through the strain energy function and hence the asso-ciated phenomenon is referred as Pseudoelastic phenomenon.…”

“…are determined through curve fitting of uniaxial cyclic loading test. The sufficient condition for the thermomechanical consistency of the damage model is given by [45] @g i ðy; y m Þ @y m 0 ð22Þ…”

Predictive Continuum Constitutive Modeling of Unfilled and Filled Rubbers

“…The network decomposition model has been developed and extended by Dargazany and Itskov [21,22], by Dargazany, Khiêm, and Itskov [23], and by Khiêm and Itskov [24,25]. The pseudo-elastic model was developed by Ogden and Roxburgh [26], Dorfmann and Ogden [27,2], Rickaby and Scott [28], and Naumann and Ihlemannthe [29]. Many models developed include the network alteration theory by Septanika and Ernst [30], extensively applied by Marckmann et al [31], Diani, Brieu, and Vacherand [32], Zhao [33], Wang and Gao [34], and Zhu and Zhong [35,36], the internal sliding and friction thermodynamics model by Cantournet, Desmorat, and Besson [37], and so forth.…”