A new finite element based on the theory of a Cosserat point—extension to initially distorted elements for 2D plane strain

Boerner, Eiris F. I.; Löhnert, Stefan; Wriggers, Peter

doi:10.1002/nme.1954

Cited by 26 publications

(14 citation statements)

References 10 publications

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“…Developing a form for the strain energy of inhomogeneous deformations in the CPE formulation which predicts accurate results for thin irregularly shaped elements in their reference configurations has proven to be challenging 42, 43, 46. However, the generalized formulation in 45 includes dependence on the reference geometry of the element and has been shown to predict accurate results for a number of problems that include physical buckling, near incompressible response, problems which typically exhibit hourglass instabilities as well as problems of thin beams and thin shells.…”

Section: Discussionmentioning

confidence: 99%

Imaging of pancreatic islet cells

Arifin

Bulte

2011

Diabetes Metabolism Res

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At present, the onset and progress of diabetes, and the efficacy of potential treatments, can only be assessed through indirect means, i.e., blood glucose, insulin, or C-peptide measurements. The development of non-invasive and reliable methods for 1) quantification of pancreatic beta islet cell mass in vivo, 2) determining endogenous islet function and survival, and 3) visualizing the biodistribution, survival, and function of transplanted exogenous islets are critical to further advance both basic science research and islet cell therapy in diabetes. Islet cell imaging using magnetic resonance (MR), bioluminescence, positron emission tomography (PET), or single photon emission computed tomography (SPECT) may provide us with a direct means to interrogate islet cell distribution, survival, and function. Current state-of-the-art strategies for beta cell imaging are discussed and reviewed here in context of their clinical relevance.

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Section: Discussionmentioning

confidence: 99%

Imaging of pancreatic islet cells

Arifin

Bulte

2011

Diabetes Metabolism Res

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“…It is given in the theory of a Cosserat point, see e.g. [1,15,16] or [17]. Here, the expression forF above can be directly translated into the averaged deformation gradient used in the so-called Cosserat point element.…”

Section: Averaged Deformation Gradientmentioning

confidence: 99%

“…The main idea of this formulation is to use an averaged deformation gradient which is also described within the Cosserat theory, see e.g. [1,15,16] or [17]. Using only the averaged deformation gradient, however, would immediately yield hourglassing modes if no additional stabilization is applied.…”

Section: Introductionmentioning

confidence: 99%

A macro-element for incompressible finite deformations based on a volume averaged deformation gradient

Boerner

Wriggers

2008

Comput Mech

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A three-dimensional 8-node brick continuum finite element formulation for incompressible finite elasticity is presented. The core idea is to introduce a substructure consisting of eight sub-elements inside each finite element, further referred to as macro-element. For each of the subelements, the deformation is averaged. The weak form for each sub-element is based on the Hu-Washizu principle. The response of each sub-element is assembled and projected onto the eight external nodes of the macro-element. The introduction of deformable sub-elements in case of incompressible elasticity has two major advantages. Firstly, it is possible to suppress locking by evaluating the volumetric part of the response only in the macro-element instead of in each of the sub-elements. Secondly, no integration is necessary due to the use of averaged deformations on the sub-element level. The idea originates from the Cosserat point element developed in Nadler and Rubin (Int J Solids Struct 40:4585-4614, 2003). A consistent transition between the Cosserat point macro-element and a displacement macro-element formulation using a kinematical description from the enhanced strain element formulation (Flanagan, Belytschko in Int J Numer Methods Eng 17: 1981) or (Belytschko et al. in Comput Methods Appl Mech Eng 43:251-276, 1984) and the principle of Hu-Washizu is presented. The performance is examined by means of numerical examples.

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“…Recently, Boerner et al [2007] have proposed a numerical method for determining coefficients in a quadratic form of the strain energy function for inhomogeneous deformations which improve the response of the CPE for 2-D plane strain problems with irregular elements. In [Jabareen and Rubin 2007b] analytical expressions were developed for constitutive coefficients in an improved CPE for 3-D deformations by generalizing the quadratic form of the strain energy function for inhomogeneous deformations to include additional coupling of the inhomogeneous strains active in bending modes.…”

Section: Introductionmentioning

confidence: 99%

A generalized Cosserat point element (CPE) for isotropic nonlinear elastic materials including irregular 3-D brick and thin structures

Jabareen

Rubin

2008

JOMMS

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A generalized form for the strain energy of inhomogeneous deformations is developed for a 3-D brick Cosserat Point Element (CPE) which includes full coupling of bending and torsional modes of deformation. The constitutive coefficients, which depend on the reference geometry of the element, are determined by solving eighteen bending problems and six torsion problems on special elements that are parallelepipeds with two right angles. The resulting constitutive coefficients ensure that the strain energy for inhomogeneous deformations remains a positive definite function of the inhomogeneous strain measures for all reference element shapes. A number of example problems are considered which show that the generalized CPE produces results as accurate as enhanced strain and incompatible elements for thin structures and is free of hourglass instabilities typically predicted by these enhanced elements in regions experiencing combined high compression with bending.

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A new finite element based on the theory of a Cosserat point—extension to initially distorted elements for 2D plane strain

Cited by 26 publications

References 10 publications

Imaging of pancreatic islet cells

Imaging of pancreatic islet cells

A macro-element for incompressible finite deformations based on a volume averaged deformation gradient

A generalized Cosserat point element (CPE) for isotropic nonlinear elastic materials including irregular 3-D brick and thin structures

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