A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis

Liu, Wing Kam; Guo, Yuanyuan; Tang, S. C.; Belytschko, Ted

doi:10.1016/s0045-7825(97)00106-0

Cited by 112 publications

(98 citation statements)

References 35 publications

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“…Flanagan and Belytschko, 1981;Liu et al, 1998;Bonet et al, 2001;Reese, 2003;Puso and Solberg, 2006). In certain problems, such as the Rayleigh-Taylor instability with large abrupt viscosity variations (see Fig.…”

Section: Locking and Hourglassmentioning

confidence: 99%

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Popov

Sobolev

2008

Physics of the Earth and Planetary Interiors

187

159

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We describe a new technique for three-dimensional lithospheric-scale modeling of solid state deformation including strain localization processes. The new code, SLIM3D, includes a coupled thermo-mechanical treatment of deformation processes and allows for an elasto-visco-plastic rheology with diffusion, dislocation and Peierls creep mechanisms and Mohr-Coulomb plasticity. The code incorporates an Arbitrary Lagrangian Eulerian formulation with free surface and Winkler boundary conditions. SLIM3D is developed and implemented using the C++ objectoriented programming language. We describe aspects of physical models as well as details of the numerical implementation, including the Newton-Raphson solver, the stress update procedure, and the tangent operator. The applicability of the code to lithospheric-scale modeling is demonstrated by a number of benchmark problems that include: (i) the bending of an elastic plate, (ii) the sinking of a rigid cylinder into a viscous fluid, (iii) the initiation of shear bands in the brittle crust, (iv) triaxial compression test, and (v) lithospheric transpressional deformation. Finally, we discuss possible directions of further development.

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Section: Locking and Hourglassmentioning

confidence: 99%

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Popov

Sobolev

2008

Physics of the Earth and Planetary Interiors

187

159

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“…The best results obtained with reduced integration hexahedral elements (see References [9,14]) are presented for comparison in Figure 5. For Reference [9], the best results were obtained with their NUHEXIN-4 element, and these are presented here for comparison.…”

Section: Plate Problemsmentioning

confidence: 99%

“…The inspection of the accuracy of solid elements in the analysis of shell structures was carried out in References [8][9][10][11][12][13][14][15] with interesting conclusions for su ciently reÿned meshes.…”

Section: Introductionmentioning

confidence: 99%

“…The reduced=average integration technique with various stabilization approaches [9,14,[25][26][27][28][29][30] is a cost-e ective technique to improve elements' performance. Classical mixed formulations (assumed strains and=or stresses with internal variables) frequently result in high-accuracy solid elements (see References [1,7,12,13,[31][32][33][34][35]) but few non-linear examples have been presented using these techniques.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of 3D problems using a new enhanced strain hexahedral element

Areias¹,

Sá²,

Curnis³

et al. 2003

Numerical Meth Engineering

119

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SUMMARYThe now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell ÿnite elements, is here explored in a versatile 3D low-order element which is identiÿed as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including ÿnite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent sti ness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several ÿnite strain tests. Some examples involve ÿnite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples.

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“…The HEXDS element is an eight-node, four-point quadrature solid element (Liu et al, 1998). The H8-ct-cp element is presented in the PhD thesis of Lemosse (Lemosse, 2000).…”

Section: Pinched Hemispherical Shellmentioning

confidence: 99%

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

Abed‐Meraim

Combescure

2007

European Journal of Computational Mechanics

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A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis

Cited by 112 publications

References 35 publications

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Analysis of 3D problems using a new enhanced strain hexahedral element

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

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