The concept of physical metric in rate-independent generalized plasticity

Mechanics of Shape Memory Alloy Materials – Constitutive Modeling and Numerical Implications

“…In general, the elastic domain at Q is a subset of the elastic range (Lubliner, 1987). The particular case in which the two sets coincide corresponds to classical plasticity and the boundary of the elastic domain, that is the initial loading surface, constitutes the yield surface (see Eisenberg and Phillips, 1971;Lubliner, 1987;Panoskaltsis et al, 2008aPanoskaltsis et al, , 2008bPanoskaltsis et al, , 2011c.…”

“…In turn, the rate equations for the evolution of the plastic variables within the generalized plasticity context -which includes classical plasticity as a special case (see Lubliner, 1987;Panoskaltsis et al, 2008aPanoskaltsis et al, , 2011c) -may be stated as…”

“…In particular, within the context of continuum mechanics the invariance properties of the balance of energy equation, under some groups of transformations, may be systematically used in order to derive the conservation laws, the balance laws and/or to determine some restrictions imposed on the equations describing the material constitutive response (e.g., Ericksen, 1961;Green and Rivlin, 1964;Marsden and Hughes, 1994, pp. 163 -167, 200 -203;Yavari et al, 2006;Panoskaltsis et al, 2011c). For instance, Marsden and Hughes (1994, pp.…”

Logarithmic Spin, Logarithmic Rate and Material Frame-Indifferent Generalized Plasticity

“…Since the time of its initial introduction as "a simple theory of plasticity" [Lubliner, 1974], generalized plasticity has been further elaborated in order to deal with the yield surface concept [Lubliner, 1975], an axiomatic structure [Lubliner, 1980], the maximum plastic dissipation postulate [Lubliner, 1984], non-isothermal behavior [Lubliner, 1987], spatial covariance [Panoskaltsis et al, 2008b] and invariance principles [Panoskaltsis et al, 2011]. The theory has been also used as a practical way of describing the elastic-plastic behavior of metallic materials in both the infinitesimal, (see, e.g., Lubliner [1991]; Lubliner et al [1993]; Auricchio and Taylor [1995]) and the finite regimes, (see, e.g., Panoskaltsis et al [2008bPanoskaltsis et al [ ,a, 2011).…”

“…The theory has been also used as a practical way of describing the elastic-plastic behavior of metallic materials in both the infinitesimal, (see, e.g., Lubliner [1991]; Lubliner et al [1993]; Auricchio and Taylor [1995]) and the finite regimes, (see, e.g., Panoskaltsis et al [2008bPanoskaltsis et al [ ,a, 2011). …”