On large deformation generalized plasticity

Abstract

Dedicated to the memory of Juan C. Simo for his seminal contributions to solid and computational mechanics Large deformation generalized plasticity is presented in a covariant setting. For this purpose, the tensor analysis on manifolds is utilized and the manifold structure of the body as well of the ambient and the state space is postulated. On the basis of the multiplicative decomposition of the deformation gradient into elastic and plastic parts and the use of hyperelastic stress-strain relations, a large deformation elastoplasticity model is proposed. Computational aspects and the predictions of the model under uniaxial and biaxial straining are also presented.

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.…”

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).…”

Erratum to: Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration

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At the time of publication of this paper, the authors were unaware of the small deformation models in [1,2] and the large deformation model in [3]. Lubliner et al [2] generalized previous work by the first author and developed a rateindependent overstress model with a smooth elastic-inelastic transition for which the inelastic deformation rate depends linearly on the stress rate.

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“…Their model included both kinematic and isotropic hardening and the comparison with the present model can only be made for the isotropic hardening case. The model in [2] was generalized for large deformations in [3] but the function h used in this generalization limited attention to sharp elastic-inelastic transitions. Einav [1] generalized previous hypo-plastic and hyper-plastic models which produce rate-independent smooth stress-strain curves with no elastic range and for which the inelastic deformation rate depends linearly on the total strain rate.…”

“…Einav [1] generalized previous hypo-plastic and hyper-plastic models which produce rate-independent smooth stress-strain curves with no elastic range and for which the inelastic deformation rate depends linearly on the total strain rate. The model in this paper can be considered as a unifying generalization to large deformations of the models in [1][2][3] …”