Nonlinear Finite Element Analysis using an Object-Oriented Philosophy – Application to Beam Elements and to the Cosserat Continuum

Lages, Eduardo Nobre; Paulino, Gláucio H.; Menezes, Ivan F. M.; Silva, Raul R.

doi:10.1007/s003660050006

Cited by 29 publications

(11 citation statements)

References 31 publications

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“…A similar problem was analyzed in [48] using a Cosserat continuum model and the results show 'reduced mesh sensitivity'. The Cosserat model includes a softening plastic behavior and other additional material parameters.…”

Section: Simple Traction Of a Rectangular Sheetmentioning

confidence: 99%

Modeling shear bands in J₂ plasticity using a two‐scale formulation via embedded strong discontinuity modes

D’hers

Dvorkin

2008

Numerical Meth Engineering

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SUMMARYA new two-scale finite element formulation was developed for modeling J 2 plastic deformation processes (2D) in which shear band localizations take place. The formulation is based on the use of embedded strong discontinuity modes, which are triggered using a stress-based criterion. The new formulation does not require a specific mesh refinement to model the localization phenomena and provides mesh-independent results. The shear bands constitutive behavior is derived from the continuum properties without the introduction of any ad hoc physical law.

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Section: Simple Traction Of a Rectangular Sheetmentioning

confidence: 99%

Modeling shear bands in J₂ plasticity using a two‐scale formulation via embedded strong discontinuity modes

D’hers

Dvorkin

2008

Numerical Meth Engineering

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“…The data structure also has potential applications in many other areas in solid or fluid mechanics. A few applications of particular interest include adaptive mesh refinement [32], support for non-linear finite element analysis [33] including graded material systems [34], and 3D fracture analysis using discrete approaches [35]. Automatic adaptive meshing requires extension of the data structure to treat non-manifold boundary representations.…”

Section: Resultsmentioning

confidence: 99%

A compact adjacency-based topological data structure for finite element mesh representation

Celes

Paulino

Espinha

2005

Int. J. Numer. Meth. Engng

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SUMMARYThis paper presents a novel compact adjacency-based topological data structure for finite element mesh representation. The proposed data structure is designed to support, under the same framework, both two-and three-dimensional meshes, with any type of elements defined by templates of ordered nodes. When compared to other proposals, our data structure reduces the required storage space while being 'complete', in the sense that it preserves the ability to retrieve all topological adjacency relationships in constant time or in time proportional to the number of retrieved entities. Element and node are the only entities explicitly represented. Other topological entities, which include facet, edge, and vertex, are implicitly represented. In order to simplify accessing topological adjacency relationships, we also define and implicitly represent oriented entities, associated to the use of facets, edges, and vertices by an element. All implicit entities are represented by concrete types, being handled as values, which avoid usual problems encountered in other reduced data structures when performing operations such as entity enumeration and attribute attachment. We also extend the data structure with the use of 'reverse indices', which improves performance for extracting adjacency relationships while maintaining storage space within reasonable limits. The data structure effectiveness is demonstrated by two different applications: for supporting fragmentation simulation and for supporting volume rendering algorithms.

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“…However, if thermal diffusion is considered, an intrinsic length scale forms and acts as a localization limiter, which has been shown to lead to mesh insensitive results [7][8][9]. Other regularization techniques reported in the literature include strain gradient theories [10][11][12], which have been used in the context of shear bands in [13][14][15] and nonlocal methods [16][17][18]. Mesh alignment is another form of sensitivity that can be improved using mesh-free formulations [19,20] or Isogeometric analysis [21].…”

Section: Background On Shear Bandsmentioning

confidence: 99%

Onset of shear band localization by a local generalized eigenvalue analysis

Arriaga

McAuliffe

Waisman

2015

Computer Methods in Applied Mechanics and Engineering

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Shear bands are material instabilities associated with highly localized intense plastic deformation zones which can form in materials undergoing high strain rates. Determining the onset of shear band localization is a difficult task and past work reported in the literature attempt to detect this instability by computing the eigenvalues of the acoustic tensor or by studying the linear stability of the perturbed governing equations. However, both methods have their limitations and are not suited for general rate dependent materials in multidimensions.In this work we propose a novel approach to determine the onset of shear band localization and alleviate the limitations of the above mentioned methods.Owing to the implicit mixed finite elements discretization employed in this work, we propose to cast the instability analysis as a generalized eigenvalue problem by employing a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases where no special simplifying assumptions ought to be made.To verify the accuracy of the proposed eigenvalue analysis, we first extend an analytical criterion by applying linear perturbation techniques to the continuous PDE model, considering an elastoplastic material with thermal diffusion and a nonlinear Taylor-Quinney coefficient. While this extension is novel on its own, it requires strenuous derivations and is not easily extended to general multidimension applications. Hence, herein it is only used for verification purposes in 1D.Numerical results on one-dimensional problems show that the eigenvalue analysis exactly recovers the instability point predicted by the analytical criterion with non-linear Taylor-Quinney coefficient. In addition, the proposed generalized eigenvalue analysis is applied on two-dimensional problems where propagation of the instability can be easily determined.

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Nonlinear Finite Element Analysis using an Object-Oriented Philosophy – Application to Beam Elements and to the Cosserat Continuum

Cited by 29 publications

References 31 publications

Modeling shear bands in J₂ plasticity using a two‐scale formulation via embedded strong discontinuity modes

Modeling shear bands in J₂ plasticity using a two‐scale formulation via embedded strong discontinuity modes

A compact adjacency-based topological data structure for finite element mesh representation

Onset of shear band localization by a local generalized eigenvalue analysis

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Nonlinear Finite Element Analysis using an Object-Oriented Philosophy – Application to Beam Elements and to the Cosserat Continuum

Cited by 29 publications

References 31 publications

Modeling shear bands in J2 plasticity using a two‐scale formulation via embedded strong discontinuity modes

Modeling shear bands in J2 plasticity using a two‐scale formulation via embedded strong discontinuity modes

A compact adjacency-based topological data structure for finite element mesh representation

Onset of shear band localization by a local generalized eigenvalue analysis

Contact Info

Product

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Modeling shear bands in J₂ plasticity using a two‐scale formulation via embedded strong discontinuity modes

Modeling shear bands in J₂ plasticity using a two‐scale formulation via embedded strong discontinuity modes