Lorentz group on Minkowski spacetime for construction of the two basic principles of plasticity

Hong, Hong‐Ki; Liu, Chein‐Shan

doi:10.1016/s0020-7462(00)00033-0

Cited by 21 publications

(4 citation statements)

References 8 publications

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“…For later references we may call the dynamic system derived so far * mainly represented by the non-linear state equation (29) * as the primitive model [15]. To summarize, the principle of causal-ity in Minkowski spacetime ,L> implies the Lorentz group SO M (n, 1)UG, which gives uniquely the real Lie algebra so(n, 1)UA, which in turn gives the #ow X(t).…”

Section: Abstract Dynamic System * a Primitive Modelmentioning

confidence: 99%

“…where X : "(X, X, X) is the spatial part of X. We note that the event observation transformation formula (36), the boost transformation (37), the event observation equation (38), and the (constant) control matrix (39) of special relativity are math-ematically analogous to, respectively, the augmented state transition formula (17), the augmented state fundamental matrix (21), the augmented state equation (15), and the (constant) control matrix (16) of perfect elastoplasticity under rectilinear generalized strain paths, with the following similarities: vKq , vK""q "", "cosh Ka,…”

Section: Comparison With Special Relativitymentioning

confidence: 99%

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Some physical models with Minkowski spacetime structure and Lorentz group symmetry

Hong

Liu

2001

International Journal of Non-Linear Mechanics

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Section: Abstract Dynamic System * a Primitive Modelmentioning

confidence: 99%

Section: Comparison With Special Relativitymentioning

confidence: 99%

Some physical models with Minkowski spacetime structure and Lorentz group symmetry

Hong

Liu

2001

International Journal of Non-Linear Mechanics

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“…Investigating the characteristics of the Minkowski space-time. Hong and Liu [46][47][48] argued that the constitutive equations of the von-Mises plasticity with linear kinematic hardening could be represented by a system of linear differential equations. Liu [49][50][51] developed the method for the vonMises mixed-hardening and Drucker-Prager plasticity.…”

Section: Introductionmentioning

confidence: 99%

Integrating the Pressure-Sensitive Nonassociative Plasticity by Exponential-Based Methods

Rezaiee‐Pajand

Sharifian

2013

Journal of Engineering Materials and Technology

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A nonassociative plasticity model of Drucker-Prager yield surface coupled with a generalized nonlinear kinematic hardening is considered. Conforming to the plasticity model, two exponential-based methods, called fully explicit and semi-implicit, are recommended for integrating its constitutive equations. These techniques are proposed for the first time to solve nonlinear hardening materials. The integrations are thoroughly investigated by utilizing stress and strain-updating tests along with a boundary value problem in diverse grounds of accuracy, convergence rate, and efficiency. The results indicate that the fully explicit scheme is more accurate and efficient than the Euler's, but the same convergence rate as the classical integrations is also perceived. Having a quadratic convergence, the semi-implicit is noticeably the most accurate and efficient procedure to use for this plasticity model among the algorithms in question. Since the plasticity model is in a great consistency with discontinuously reinforced aluminum (DRA) composites, the suggested formulations can be utilized pragmatically. The tangent moduli of the proposed and Euler's strategies are derived and examined, as well, due to their vital role in achieving the asymptotic quadratic convergence rate of the Newton-Raphson solution in nonlinear finite-element analyses.

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“…In the past several years, new integration techniques based on the internal symmetries of simple constitutive models have been developed. The internal symmetry group of the constitutive model ensures that the plastic consistency condition will be exactly satisfied at the end of each time step if the numerical process can take it into account ͑Hong and Liu 1999Liu , 2000Liu , 2001Liu 2003. Auricchio and Beirão da Veiga ͑2003͒ converted the original nonlinear differential problem of von-Mises plasticity with linear hardening into a dynamical system Ẋ = AX for an augmented stress vector X.…”

Section: Introductionmentioning

confidence: 99%

Application of Exponential-Based Methods in Integrating the Constitutive Equations with Multicomponent Nonlinear Kinematic Hardening

2010

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The von-Mises plasticity model, in the small strain regime, along with a class of multicomponent nonlinear kinematic hardening rules is considered. The material is assumed to be stabilized after several load cycles and therefore, isotropic hardening will not be accounted for. Application of exponential-based methods in integrating plasticity equations is provided, which is based on defining an augmented stress vector and using exponential maps to solve a system of quasi-linear differential equations. The solutions obtained by this new technique give very accurate updated stress values that are consistent with the yield surface. The classical forward Euler method is reformulated in details and applied to the multicomponent form of the nonlinear kinematic hardening in order to provide a comparison for the suggested technique. Moreover, a consistent tangent operator for the exponential-based integration strategy and also for the classical forward Euler algorithm is presented. In order to show the robustness and performance of the proposed formulation, an extensive numerical investigation is carried out.

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Lorentz group on Minkowski spacetime for construction of the two basic principles of plasticity

Cited by 21 publications

References 8 publications

Some physical models with Minkowski spacetime structure and Lorentz group symmetry

Some physical models with Minkowski spacetime structure and Lorentz group symmetry

Integrating the Pressure-Sensitive Nonassociative Plasticity by Exponential-Based Methods

Application of Exponential-Based Methods in Integrating the Constitutive Equations with Multicomponent Nonlinear Kinematic Hardening

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