Consistent tangent matrices for substepping schemes

Foguet, Agustí Pérez; Ferran, Antonio Rodríguez; Huerta, Antonio

doi:10.1016/s0045-7825(00)00336-4

Cited by 81 publications

(48 citation statements)

References 21 publications

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“…This situation is related to the strong nonlinearity of the equations which may arise, for example, from the high curvature of the yield function, as it can be found in typical practical applications. The numerical results reported in de Souza Neto et al [1994], Bićanić & Pearce [1996], Pérez-Foguet et al [2000a] and herein illustrate these difficulties. These observations identify clearly the goal of this work: the development of efficient globally convergent algorithms for the solution of the closest-point projection equations in elastoplasticity.…”

Section: Introductionmentioning

confidence: 58%

On the formulation of closest‐point projection algorithms in elastoplasticity—part II: Globally convergent schemes

Foguet

Armero

2001

Numerical Meth Engineering

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This paper presents the formulation of numerical algorithms for the solution of the closest-point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity. The main motivation behind this work is to avoid the poor global convergence properties of a straight application of a Newton scheme in the solution of these equations, the socalled Newton-CPPM. The mathematical structure behind the closest-point projection equations identified in Part I of this work delineates clearly different strategies for the successful solution of these equations. In particular, primal and dual closest-point projection algorithms are proposed, in non-augmented and augmented Lagrangian versions for the imposition of the consistency condition. The primal algorithms involve a direct solution of the original closest-point projection equations, whereas the dual schemes involve a two level structure by which the original system of equations is staggered, with the imposition of the consistency condition driving alone the iterative process. Newton schemes in combination with appropriate line search strategies are considered, resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes. These properties, together with the computational performance of the different schemes, are evaluated through representative numerical examples involving different models of finite strain plasticity. In particular, the avoidance of the large regions of no convergence in the trial state observed in the standard Newton-CPPM is clearly illustrated.

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Section: Introductionmentioning

confidence: 58%

On the formulation of closest‐point projection algorithms in elastoplasticity—part II: Globally convergent schemes

Foguet

Armero

2001

Numerical Meth Engineering

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“…where A and B stand for the individual surface parameters of Eqs (26)- (27), as detailed in Table 1. The three material variables C,  t , tan associated with surface F 1 have explicit physical meaning as they represent the cohesion, the tensile strength and the friction angle at either mortar or brick interfaces.…”

Section: Variables Plastic Surfaces and Potentialsmentioning

confidence: 99%

“…When the number of iterations required to solve Eq. (40) is greater than a prescribed value n max1 , the substepping procedure is activated and the total increment of local strains du n , as determined from the increment of global displacements, is divided into m local substeps [27]: local iterations, the sum of the iterations required at each substep, is greater than a prescribed maximum value n max2 . In the former case, the local solution for the total increment of local strains du n , is determined, while in the latter case, step reduction at the global structural level may be required.…”

Section: Solution Of the Plasticity Problemmentioning

confidence: 99%

A non‐linear interface element for 3D mesoscale analysis of brick‐masonry structures

Macorini

Izzuddin

2010

Numerical Meth Engineering

169

154

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This paper presents a novel interface element for the geometric and material nonlinear analysis of unreinforced brick-masonry structures. In the proposed modelling approach, the blocks are modelled using 3D continuum solid elements, while the mortar and brick-mortar interfaces are modelled by means of the 2D nonlinear interface element. This enables the representation of any 3D arrangement for brick-masonry, accounting for the in-plane stacking mode and the through-thickness geometry, and importantly it allows the investigation of both the in-plane and the out-of-plane response of unreinforced masonry panels. A co-rotational approach is employed for the interface element, which shifts the treatment of geometric nonlinearity to the level of discrete entities, and enables the consideration of material nonlinearity within a simplified local framework employing first-order kinematics. In this respect, the internal interface forces are modelled by means of elasto-plastic material laws based on work-softening plasticity and employing multi-surface plasticity concepts.Following the presentation of the interface element formulation details, several experimentalnumerical comparisons are provided for the in-plane and out-of-plane static behaviour of brick-masonry panels. The favourable results achieved demonstrate the accuracy and the significant potential of using the developed interface element for the nonlinear analysis of brick-masonry structures under extreme loading conditions. Keywords: non linear interface element, cohesive model, multi-surface plasticity, geometric nonlinearity, brick-masonry, in-plane and out-of-plane behaviour.

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“…Reference [18] presents an analysis of different numerical differentiation schemes to compute these derivatives and references [23,26] show the application to different nontrivial elastoplastic models and time-integration rules. The main conclusion of these works is that simple first and second order difference schemes do not disturb the quadratic convergence of the Newton-Raphson method provided that the stepsize is fixed in a relative way.…”

Section: Numerical Differentiationmentioning

confidence: 99%

Efficient and accurate approach for powder compaction problems

Foguet¹,

Ferran²,

Huerta³

2003

Computational Mechanics

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In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian-Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations.

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Consistent tangent matrices for substepping schemes

Cited by 81 publications

References 21 publications

On the formulation of closest‐point projection algorithms in elastoplasticity—part II: Globally convergent schemes

On the formulation of closest‐point projection algorithms in elastoplasticity—part II: Globally convergent schemes

A non‐linear interface element for 3D mesoscale analysis of brick‐masonry structures

Efficient and accurate approach for powder compaction problems

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