Three-dimensional finite elements for large deformation micropolar elasticity

Bauer, Steffen; Schäfer, Michael; Grammenoudis, P.; Tsakmakis, Ch.

doi:10.1016/j.cma.2010.05.002

Cited by 36 publications

(19 citation statements)

References 33 publications

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“…The finite element method remains the most common tool of numerical analysis Li and Xie [2004], Jeong et al [2009], Bauer et al [2010], Natarajan et al [2012], Natarajan [2014].…”

Section: Introductionmentioning

confidence: 99%

Micro-structured materials: Inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach

Atroshchenko

Hale

Videla

et al. 2017

Engineering Analysis with Boundary Elements

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Abstract. In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an inclusion of one plane strain micropolar phase into another micropolar phase and reduce the problem to a system of boundary integral equations, which is subsequently solved by the boundary element method. The inclusion interface condition is assumed to be imperfect, which permits jumps in both displacements/microrotations and tractions/couple tractions, as well as a linear dependence of jumps in displacements/microrotations on continuous across the interface tractions/couple traction (model known in elasticity as homogeneously imperfect interface). These features can be directly incorporated into the boundary element formulation.The BEM-results for a circular inclusion in an infinite plate are shown to be in an excellent agreement with the analytical solutions. The BEM-results for inclusions in finite plates are compared with the FEM-results obtained with FEniCS.

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“…The finite element method remains the most common tool of numerical analysis Li and Xie [2004], Jeong et al [2009], Bauer et al [2010], Natarajan et al [2012], Natarajan [2014].…”

Section: Introductionmentioning

confidence: 99%

Micro-structured materials: Inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach

Atroshchenko

Hale

Videla

et al. 2017

Engineering Analysis with Boundary Elements

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“…The authors have taken into account these kinematical relations in providing a very robust and highly parallel non-linear 3D-FEM Cosserat models [20]. Some relevant works pertaining to the non-linear Cosserat can be also addressed in [56,58,[61][62][63][64]. 4 Some benchmark experimental efforts have been made by Lakes [43,44,69,45] for extracting the material unknowns (four supplementary material parameters, i.e., l c , a, b and c).…”

Section: Paper Organizationmentioning

confidence: 99%

On parallel simulation of a new linear Cosserat elasticity model with grid framework model assumptions

Ramézani¹,

Jeong²,

Feng³

2011

Applied Mathematical Modelling

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a b s t r a c tIn the present paper, the linear Cosserat elasticity involving the grid framework model for micro-rotations as boundary condition or side-condition has been taken into account. Theassumption or so called case 4, altogether case 1 (a = b = 0 and c ¼ lL 2 c ), case 2 a ¼ 0 andare examined by means of some numerical experiments for torsion test with a circular bar. The presence of m 33 (stress moment in z direction) on the top of specimen is confirmed numerically and analytically via a missing term R @Xt ðr Â t ðnÞ Þ Á d/ dS . By considering this term, m 33 is non-zero, whereas, the Dirichlet boundary condition for displacements on the top of bar is used to apply the torque (M T ). The outcomes reveal that the case 4 as well as other cases is still bounded. This property is found out for curvature stiffness as well. These cases are presented in Torque-Log (L c ) diagram. In this diagram, two non-size affected zones (zones I and III) and one size affected zone would be inferred. By taking advantage of this curve, we can probably consider Cosserat theory as a multi-scale tool and some outlooks for a fresh experimental departure are discussed.

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“…These studies conclude that K c , instead of having the constant value of 3, depends on geometry and material properties, namely the Poisson's ratio ν, the ratio of r to the material characteristic length l and a coupling number N . The micropolar material parameters are explained in details in [33].…”

Section: Numerical Examplesmentioning

confidence: 99%

A Semi-Implicit Microplar Discrete-to-Continuum Method for Granular Materials

Wang¹,

Sun²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. A micropolar discrete-continuum coupling model is proposed to link the collectively particulate mechanical simulations at high-order representative elementary volume to field-scale boundary value problems. By incorporating high-order kinematics to the homogenization procedure, contact moment and force exerted on grain contacts are homogenized into a non-symmetric Cauchy stress and higher-order couple stress. These stress measures in return become the constitutive updates for the macroscopic finite element model for micropolar continua. Unlike the non-lcoal weighted averaging models in which the intrinsic length scale must be a prior knowledge to compute the nonlocal damage or strain measures, the proposed model introduces the physical length scale directly through the higher-order kinematics. As a result, there is no need to tune or adjust the intrinsic length scale. Furthermore, since constitutive updates are provided directly from micro-structures, there is also no need to calibrate any high-order material parameters that are difficult to infer from experiments. These salient features are demonstrated by numerical examples. The classical result from Mindlin is used as a benchmark to verify the proposed model.

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Three-dimensional finite elements for large deformation micropolar elasticity

Cited by 36 publications

References 33 publications

Micro-structured materials: Inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach

Micro-structured materials: Inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach

On parallel simulation of a new linear Cosserat elasticity model with grid framework model assumptions

A Semi-Implicit Microplar Discrete-to-Continuum Method for Granular Materials

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