Internal symmetry in the constitutive model of perfect elastoplasticity

SUMMARYIn this communication we propose a new exponential-based integration algorithm for associative von-Mises plasticity with linear isotropic and kinematic hardening, which follows the ones presented by the authors in previous papers. In the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential-based schemes and, in particular, we address the yield consistency, exactness under proportional loading, accuracy and stability of the methods. In the second part of the contribution, we show a detailed numerical comparison between the new exponential-based method and two classical radial return map methods, based on backward Euler and midpoint integration rules, respectively. The developed tests include pointwise stress-strain loading histories, iso-error maps and global boundary value problems. The theoretical and numerical results reveal the optimal properties of the proposed scheme.

Section: A New Model Formulationmentioning

confidence: 82%

A novel ‘optimal’ exponential‐based integration algorithm for von‐Mises plasticity with linear hardening: Theoretical analysis on yield consistency, accuracy, convergence and numerical investigations

Artioli

Auricchio

Veiga

2006

“…In fact, as noted in the literature [1,2], an associative von-Mises plasticity model with linear kinematic hardening can be formulated as a di erential problem of the following type:…”

Section: Different Model Formulationmentioning

confidence: 99%

“…In fact, motivated by a work recently proposed in the literature [1,2], the numerical solution obtained with the new method is exact in the case of a material with a linear kinematic hardening, approximated in the case of a material with isotropic or mixed hardening.…”

Section: Introductionmentioning

confidence: 99%

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

Auricchio

Veiga

2003

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…In Equation (D4), f is the yield function defined in Equation (3). Equation (D2) shows that the deviatoric plastic strain vector is assumed to lie parallel to the trial deviatoric stress vector.…”

mentioning

confidence: 99%

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

Rezaiee‐Pajand

Nasirai

2007

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.