Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path

Abbasi, Behrooz; Parsa, Mohammad Habibi

doi:10.1002/nme.1747

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…In addition, in (2), s ¼ R _ SR T is a corotational rate. Several discussions are available in the literature, for example Abbasi and Parsa [1] have compared several spins including Lehmann's [30] logarithmic spin. An important work on spins is the one of Reinhard and Dubey [35] where a rationale for the aforementioned equivalence is described.…”

Section: Objective Ratesmentioning

confidence: 99%

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

Areias

Rabczuk

Sá

et al. 2016

Engineering Structures

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A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelasticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green-Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complementarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.

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Section: Objective Ratesmentioning

confidence: 99%

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

Areias

Rabczuk

Sá

et al. 2016

Engineering Structures

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“…9 The reader interested in the numerical treatment of constitutive equations for a variety of different spin tensors is referred to Abbasi and Parsa (2006).…”

Section: Zaremba-jaumann and Green-naghdi Ratesmentioning

confidence: 99%

“…The reader interested in the numerical treatment of constitutive equations for a variety of different spin tensors is referred toAbbasi and Parsa (2006).10 It is also known as Green-Naghdi-Dienes rate, Green-McInnis rate or polar rate.…”

mentioning

confidence: 99%

Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change

Shutov

Ihlemann

2014

International Journal of Plasticity

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There is a large variety of concepts used to generalize the classical Prandtl-Reuss relations of infinitesimal elasto-plasticity to finite strains. In this work, some basic approaches are compared in a qualitative way with respect to a certain invariance property. These basic approaches include the additive hypoelasto-plasticity with corotational stress rates, additive plasticity in the logarithmic strain space, and multiplicative hyperelasto-plasticity.The notion of weak invariance is introduced in this study. Roughly speaking, a material model is weakly invariant under a certain transformation of the local reference configuration if this reference change can be neutralized by a suitable transformation of initial conditions, leaving the remaining constitutive relations intact. We analyse the basic models in order to find out if they are weakly invariant under arbitrary volume-preserving transformations of the reference configuration.It is shown that the weak invariance property corresponds to a generalized symmetry which provides insights into underlying constitutive assumptions. This property can be used for a systematic study of different frameworks of finite strain elasto-plasticity. In particular, it can be used as a classification criterion.Keywords: finite strain elasto-plasticity, reference change, weak invariance, hypoelasto-plasticity, logarithmic elasto-plasticity, multiplicative plasticity 2000 MSC: 74D10, 74C15 determinant of a second-rank tensor X unimodular part of a second-rank tensor X T transposition of a second-rank tensor sym(X) symmetric part of a second-rank tensor skew(X) skew-symmetric part of a second-rank tensor tr(X) trace of a second-rank tensor X Frobenius norm of a second-rank tensor X : Y scalar product of two second-rank tensors t, t ′ , t 0 time instances (typically t 0 ≤ t ′ ≤ t) Z 0 initial state

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Is an additive decomposition of a rate of deformation and objective stress rates passé?

Jiao

Fish

2017

Computer Methods in Applied Mechanics and Engineering

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Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path

Cited by 3 publications

References 24 publications

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change

Is an additive decomposition of a rate of deformation and objective stress rates passé?

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