On a new integration scheme for von‐Mises plasticity with linear hardening

Auricchio, Ferdinando; Veiga, L. Beirão da

doi:10.1002/nme.612

Cited by 49 publications

(36 citation statements)

References 11 publications

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“…In this study the material is assumed to follow an associative von Mises plasticity model with linear kinematic and isotropic hardening [38]. Introducing a linear isotropic elastic relation, the volumetric plastic strain is zero, leading to a deviatoric-volumetric decoupling.…”

Section: Theoretical Model Of the Materialsmentioning

confidence: 99%

Morphological characterization of shocked porous material

Xu¹,

Zhang²,

Pan³

et al. 2009

J. Phys. D: Appl. Phys.

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Abstract. Morphological measures are introduced to probe the complex procedure of shock wave reaction on porous material. They characterize the geometry and topology of the pixelized map of a state variable like the temperature. Relevance of them to thermodynamical properties of material is revealed and various experimental conditions are simulated. Numerical results indicate that, the shock wave reaction results in a complicated sequence of compressions and rarefactions in porous material. The increasing rate of the total fractional white area A roughly gives the velocity D of a compressive-wave-series. When a velocity D is mentioned, the corresponding threshold contour-level of the state variable, like the temperature, should also be stated. When the threshold contour-level increases, D becomes smaller. The area A increases parabolically with time t during the initial period. The A(t) curve goes back to be linear in the following three cases: (i) when the porosity δ approaches 1, (ii) when the initial shock becomes stronger, (iii) when the contour-level approaches the minimum value of the state variable. The area with high-temperature may continue to increase even after the early compressive-waves have arrived at the downstream free surface and some rarefactive-waves have come back into the target body. In the case of energetic material needing a higher temperature for initiation, a higher porosity is preferred and the material may be initiated after the precursory compressive-waves have scanned all the target body. One may desire the fabrication of a porous body and choose appropriate shock strength according to what needed is scattered or connected hotspots. With the Minkowski measures, the dependence on experimental conditions is reflected simply by a few coefficients. They may be used as order parameters to classify the maps of physical variables in a similar way like thermodynamic phase transitions.Submitted to: J. Phys. D: Appl. Phys.

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Section: Theoretical Model Of the Materialsmentioning

confidence: 99%

Morphological characterization of shocked porous material

Xu¹,

Zhang²,

Pan³

et al. 2009

J. Phys. D: Appl. Phys.

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show abstract

“…If the numerical procedure can take the internal symmetry of the constitutive model into account, the plastic consistency condition is completely satisfied at the end of each time step [3][4][5]. Auricchio and Beirão da Veiga [6] converted the original non-linear differential problem of von-Mises' plasticity into a dynamical systemẊ = AX for an augmented stress vector X. Then they developed a new numerical scheme by employing an exponential map, exp(A n t), as an approximation to the above system.…”

Section: Introductionmentioning

confidence: 99%

On the integration schemes for Drucker–Prager's elastoplastic models based on exponential maps

Rezaiee‐Pajand

Nasirai

2007

Numerical Meth Engineering

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SUMMARYRate plasticity equations for the case of Drucker-Prager's model in small strain regime are considered. By defining an augmented stress vector, the formulations convert the original problem into a quasi-linear differential equation system. Two new exponential mapping schemes for integrating model equations are proposed. In addition, two traditional schemes for solving the dynamical system in an explicit manner are discussed. The two semi-implicit schemes developed pose higher accuracy and better convergency. Error contours are provided for all four methods to display the accuracy of each scheme. In order to compare the results, these contours for the classical one-step backward Euler integration method are also displayed. Accuracy and efficiency along with the rate of convergency of the existing and the proposed methods are examined by numerical examples.

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“…Solutions can be obtained for J2-Flow theory (Krieg and Krieg, 1977), kinematic hardening (Krieg and Xu, 1997;Auricchio and Beirão da Veiga, 2003;Arioli et al, 2006), the Drucker-Prager model (Rezaijee-Pajand and Nasirai, 2008;Szabó, 2009), and potentially other plasticity models. These methods have demonstrated accuracy advantages over purely numerical integration algorithms and do not suffer the return mapping direction issues, but the range of models which can be integrated analytically or semi-analytically is limited.…”

Section: Introductionmentioning

confidence: 99%

An alternative approach to integrating plasticity relations

Becker

2011

International Journal of Plasticity

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a b s t r a c tA new plasticity integration algorithm is proposed based upon observations from the closed form integration of a generalized quadratic yield function over a single time step. The key to the approach is specification of the normal to the plastic flow potential as a function of the current state and strain increment. This uniquely defines the direction of the stress tensor for a convex, non-faceted flow potential. The stress magnitude and plastic strain increment are computed to satisfy the yield function. A non-quadratic, isotropic, associative flow model is coded to demonstrate accuracy and time step convergence following a step change in loading path. The model is used in additional simulations of strain localization in an expanding ring and a perforated plate.Published by Elsevier Ltd.

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On a new integration scheme for von‐Mises plasticity with linear hardening

Cited by 49 publications

References 11 publications

Morphological characterization of shocked porous material

Morphological characterization of shocked porous material

On the integration schemes for Drucker–Prager's elastoplastic models based on exponential maps

An alternative approach to integrating plasticity relations

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