Variational principles and convergence of finite element approximations of a holonomic elastic-plastic problem

Reddy, B. D.; Griffin, T. B.

doi:10.1007/bf01401024

Cited by 19 publications

(10 citation statements)

References 13 publications

(11 reference statements)

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“…In [12], the convergence of the regularization procedure is proved. More precisely, it is proved that there exists a constant c, such that…”

Section: Where a ~ H = U~ H --Il H ~(0)mentioning

confidence: 99%

“…Then, it is proved in [12] that the bilinear form a: Vx V~]R is V-elliptic, continuous, the linear form l: P~R is continuous, the non-differentiable functional j:L~, is convex and Lipschitz-continuous. Furthermore, the solution t~=(u,p)~V of the problem (2.1), (2.2), (2.3) and (2.4) is the unique solution of the following variational inequality of the second kind:…”

Section: Cijkl Akt Aij> Ct Aij Aijmentioning

confidence: 99%

“…A typical step in such an incremental procedure is described by a variational inequality of the second kind, involving a non-differentiable term. In [12], a regularization procedure is used replacing the non-differentiable term by suitable differentiable ones. Solutions of the regularized problems are shown to converge to the solution of the original problem.…”

Section: Introductionmentioning

confidence: 99%

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Finite element analysis of a holonomic elastic-plastic problem

Han

1991

Numer. Math.

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“…In [12], the convergence of the regularization procedure is proved. More precisely, it is proved that there exists a constant c, such that…”

Section: Where a ~ H = U~ H --Il H ~(0)mentioning

confidence: 99%

Section: Cijkl Akt Aij> Ct Aij Aijmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite element analysis of a holonomic elastic-plastic problem

Han

1991

Numer. Math.

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“…This may be seen in work presented in [25] and [26]; the former contains an analysis of a problem which has an identical structure to that which is under discussion, while the latter treats a broad class of problems with unilateral constraints, so that the problem being discussed here is a special case. Secondly, it has been demonstrated in [19,20,21] that this same variational framework, when time-discretised in a rational way, gives rise to a problem which in discrete form is amenable to solution by the use of simple algorithms.…”

Section: Fp = Ifmentioning

confidence: 99%

An internal variable finite-strain theory of plasticity within the framework of convex analysis

Eve¹,

Gültop²,

Reddy³

1990

Quart. Appl. Math.

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Abstract. An internal variable constitutive theory for elastic-plastic materials undergoing finite strains is presented. The theory is based on a corresponding study in the context of small strains [6], and has the following features: first, with a view to embracing the classical notions of convex yield surfaces and the normality law, the evolution law is developed within the framework of nonsmooth convex analysis, which proves to be a powerful unifying tool; secondly, the special case of elastic materials is recovered from the theory in a natural manner. After presentation of the theory a concrete example is discussed in detail.1. Introduction. The theory of plasticity in its classical small-strain form is wellestablished, especially that form which the theory takes in its application to metals. The finite-strain theory, on the other hand, while showing indications that it is on the way to becoming an established branch of mechanics, is still nevertheless the subject of considerable effort and debate, and certain of its aspects remain unsettled. The literature on the subject has in the meantime acquired voluminous proportions; without attempting a comprehensive survey we mention as important contributions the early work of Green and Naghdi [7] and of Lee [17] in which were addressed, inter alia, the question of the decomposition of deformation into elastic and plastic parts, the former proposing an additive decomposition of strain and the latter a multiplicative decomposition of deformation gradient. The multiplicative decomposition has proved more popular, and forms the basis for a number of alternative theories; as examples we mention the works of Mandel [18], Halphen and Nguyen [8], Simo and

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“…The regularization method has been widely used in applications (cf. [7], [8], [12], [14]). An approximating differentiable sequence in the regularization method depends on a small parameter ε > 0.…”

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confidence: 99%

The regularization method for an obstacle problem

1994

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We give a relatively complete analysis for the regularization method, which is usually used in solving non-differentiable minimization problems. The model problem considered in the paper is an obstacle problem. In addition to the usual convergence result and a-priori error estimates, we provide a-posteriori error estimates which are highly desired for practical implementation of the regularization method.

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Variational principles and convergence of finite element approximations of a holonomic elastic-plastic problem

Cited by 19 publications

References 13 publications

Finite element analysis of a holonomic elastic-plastic problem

Finite element analysis of a holonomic elastic-plastic problem

An internal variable finite-strain theory of plasticity within the framework of convex analysis

The regularization method for an obstacle problem

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