An efficient plasticity algorithm for shell elements application to metal forming simulation

Zeng, Qiang; Combescure, Alain; Arnaudeau, F.

doi:10.1016/s0045-7949(01)00032-3

Cited by 24 publications

(17 citation statements)

References 6 publications

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“…which is closely related to approximations to Ilyushin condition applied by other researchers, as discussed in [22]. The relaxed form of the principle of maximum plastic work is…”

Section: Application Of Relaxation Methods To Derive Minimization Problemmentioning

confidence: 93%

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Rigid plastic model of incremental sheet deformation using second‐order cone programming

Raithatha

Duncan

2008

Numerical Meth Engineering

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SUMMARYThis paper describes a method for numerically modelling the incremental plastic deformation of shells and applies the method to incremental sheet forming (ISF). An upper bound finite element shell model is developed based on sequential limit analysis under the rigid plastic assumption, which is solved by manipulating the problem into the form of a second-order cone program (SOCP). Initially, the static upper bound plate problem is investigated and the results are compared with the existing literature. The approach is then extended to a shell formulation using a linearized form of the Ilyushin yield condition and two methods for treating the Ilyushin condition are presented. The model is solved efficiently using SOCP software. The resulting model shows good geometric agreement when validated against an elasto-plastic model produced using existing commercial software and with measurements from a real product produced using ISF.

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“…which is closely related to approximations to Ilyushin condition applied by other researchers, as discussed in [22]. The relaxed form of the principle of maximum plastic work is…”

Section: Application Of Relaxation Methods To Derive Minimization Problemmentioning

confidence: 93%

“…If required, anisotropic material behaviour can be included by modifying H using Hill anisotropy [22]. In either case, H is symmetric in structure and for the value of H in (12), the factorization H = C −1 C −T is defined, where for instance…”

Section: Bending Workmentioning

confidence: 99%

Rigid plastic model of incremental sheet deformation using second‐order cone programming

Raithatha

Duncan

2008

Numerical Meth Engineering

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“…In this manuscript, we use a standard elasto-plastic constitutive model as explained in detail in many references [36,37], [38,Sect. 5], [39,40].…”

Section: Constitutive Model and Fracture Criterionmentioning

confidence: 99%

Meshless study of dynamic failure in shells

Liu

2010

J Eng Math

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The dynamic fracture of a thin-walled structure that is mainly due to impact and explosive loading is studied. Use is made of a meshless SPH shell formulation based on Mindlin-Reissner's theory. The formulation is an extension of the continuum-corrected and stabilized SPH method allowing a thin structure to be modelled using only one particle characterizing the mean position of the shell surface. Fracture is based on an effective criterion similar to that of the visibility method. Four numerical examples are studied among which tearing of pre-notched plates, fracture due to impact loading and dynamic fracture of cylindrical shells.

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“…Matrix D in (8) In (8) we assumed a general (nonlinear) form of isotropic hardening and a linear form of kinematic hardening with hardening modulus H kin . The constants in (9) are k b = Eh 3 /(12(1 − 2 )), k s = cEh/(2(1 + )), where E is elastic modulus, is Poisson's ratio, h is plate thickness, and c is shear correction factor, usually set to 5 6 .…”

Section: Plate Elastoplasticitymentioning

confidence: 99%

“…[6] and references therein, and was later used e.g. Shi and Voyiadjis [7] for plates and Zeng et al [8] and Voyiadjis and Woelke [9] for shells. Another way to approximately describe the 3d effect of spreading of plasticity throughout the plate is to use the generalized plasticity model for plates, which is based on two functions (both defined in terms of stress resultants), the yield function and the limit function, see e.g.…”

Section: Introductionmentioning

confidence: 99%