A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects
01 May 1988-Computer Methods in Applied Mechanics and Engineering (North-Holland)-Vol. 68, Iss: 1, pp 1-31
TL;DR: In this article, the authors proposed a hyperelastic J2-flow theory for elastoplastic tangent moduli, which reduces to a trivial modification of the classical radial return algorithm which is amenable to exact linearization.
About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1988-05-01. It has received 475 citations till now. The article focuses on the topics: Linearization & Hyperelastic material.
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17 Aug 2012
TL;DR: De Borst et al. as mentioned in this paper present a condensed version of the original book with a focus on non-linear finite element technology, including nonlinear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity.
Abstract: Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.
2,568 citations
TL;DR: In this paper, a framework is presented within which the augmented Lagrangians is readily applied to problems involving contact with friction, which is well-suited to finite element implementation, and a set of numerical examples is presented in which the utility of the method is demonstrated even in the presence of finite deformations and inelasticity.
828 citations
TL;DR: In this paper, a class of assumed strain mixed finite element methods for fully nonlinear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case.
Abstract: A class of ‘assumed strain’ mixed finite element methods for fully non-linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three-field variational formulation. The resulting class of mixed methods provides a possible extension to the non-linear regime of well-known incompatible mode formulations. In addition, this class of methods includes non-linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2-D, 3-D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.
763 citations
TL;DR: In this paper, a formulation and algorithmic treatment of static and dynamic plasticity at finite strains based on the multiplicative decomposition is presented which inherits all the features of the classical models of infinitesimal plasticity.
Abstract: A formulation and algorithmic treatment of static and dynamic plasticity at finite strains based on the multiplicative decomposition is presented which inherits all the features of the classical models of infinitesimal plasticity. The key computational implication is this: the closest-point-projection algorithm of any classical simple-surface or multi-surface model of infinitesimal plasticity carries over to the present finite deformation context without modification. In particular, the algorithmic elastoplastic tangent moduli of the infinitesimal theory remain unchanged. For the static problem, the proposed class of algorithms preserve exactly plastic volume changes if the yield criterion is pressure insensitive. For the dynamic problem, a class of time-stepping algorithms is presented which inherits exactly the conservation laws of total linear and angular momentum. The actual performance of the methodology is illustrated in a number of representative large scale static and dynamic simulations.
734 citations
TL;DR: In this paper, a complete formulation of a model of coupled associative thermoplasticity at finite strains is presented, addressing in detail the numerical analysis aspects involved in its finite element implementation, and assessing the performance of the proposed mechanical and finite element models in a comprehensive set of numerical simulations.
Abstract: This paper presents a complete formulation of a model of coupled associative thermoplasticity at finite strains, addresses in detail the numerical analysis aspects involved in its finite element implementation, and assesses the performance of the proposed mechanical and finite element models in a comprehensive set of numerical simulations. On the thermomechanical side, novel aspects of the proposed model of thermoplasticity are (1) the explicit characterization of the plastic (configurational) entropy as an independent internal variable, (2) a thermomechanical extension of the principle of maximum dissipation consistent with the multiplicative decomposition of the deformation gradient, and (3) the exploitation of this extended principle in the formulation of an associative flow which characterizes the evolution of the plastic entropy in terms of the change of the flow criterion with respect to temperature. On the numerical analysis side, salient features of the proposed approach are (4) a new global product formula algorithm constructed via an operator split of the nonlinear initial value problem, which leads to a two-step solution procedure, (5) a unified class of local return mapping algorithms which preserves exactly the incompressibility constraint on the plastic flow and reduces to the classical radial return method for isothermal J 2 - flow theory, and (6) the formulation of a mixed finite element method in terms of the elastic entropy and the temperature field which circumvents well-known difficulties associated with the incompressibility constraint on the plastic flow. The exact linearization of both the product formula algorithm and an alternative simulataneous solution scheme for the coupled thermomechanical problem is given in two appendices.
630 citations
References
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Book•
01 Jan 1989
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08
17,327 citations
Book•
01 Jan 1984
TL;DR: Strodiot and Zentralblatt as discussed by the authors introduced the concept of unconstrained optimization, which is a generalization of linear programming, and showed that it is possible to obtain convergence properties for both standard and accelerated steepest descent methods.
Abstract: This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities.New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters.From the reviews of the Third Edition: this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn. (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)
4,908 citations
1,792 citations
TL;DR: In this paper, it is shown that consistency between the tangent operator and the integration algorithm employed in the solution of the incremental problem plays crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon Newton's method.
1,702 citations
TL;DR: In this paper, a general criterion for testing a mesh with topologically similar repeat units is given, and it is shown that only a few conventional element types and arrangements are suitable for computations in the fully plastic range.
927 citations