On Finite Element Implementation of Polyconvex Incompressible Hyperelasticity: Theory, Coding and Applications

This work concerns mainly the finite element (FE) implementation of polyconvex incompressible hyperelastic models. A user material subroutine (UMAT) has been developed and can be utilized to define the aforementioned material behaviors in the FE system ABAQUS. The subroutine is written using a novel strategy in order to maximally simplify the relations for the analytical material Jacobian (MJ). The UMAT code is attached in the appendix. The developed subroutine allows to significantly decrease the time of computations and to avoid possible convergence difficulties. The structure of the code enables modifications which may lead to a rheological, damage or growth models, for instance.

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3D finite element model of dynamic material behaviors for multilayer ultrasonic metal welding

Journal of Manufacturing Processes ◽

10.1016/j.jmapro.2020.12.039 ◽

2021 ◽

Vol 62 ◽

pp. 302-312

Author(s):

Ninggang Shen ◽

Avik Samanta ◽

Wayne W. Cai ◽

Teresa Rinker ◽

Blair Carlson ◽

...

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Element Model ◽

3D Finite Element ◽

Ultrasonic Metal Welding ◽

3D Finite Element Model ◽

Material Behaviors ◽

Metal Welding

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Performance of a parallel mixed finite element implementation for fourth order clamped anisotropic plate bending problems in distributed memory environments

Applied Mathematics and Computation ◽

10.1016/s0096-3003(03)00816-6 ◽

2004 ◽

Vol 155 (3) ◽

pp. 753-777 ◽

Cited By ~ 4

Author(s):

Kshitij Kulshreshtha ◽

Neela Nataraj ◽

Michael Jung

Keyword(s):

Finite Element ◽

Fourth Order ◽

Distributed Memory ◽

Anisotropic Plate ◽

Mixed Finite Element ◽

Plate Bending ◽

Finite Element Implementation ◽

Bending Problems

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An uncoupled higher-order beam theory and its finite element implementation

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2017.10.041 ◽

2017 ◽

Vol 134 ◽

pp. 525-531 ◽

Cited By ~ 5

Author(s):

P.S. Geng ◽

T.C. Duan ◽

L.X. Li

Keyword(s):

Finite Element ◽

Beam Theory ◽

Higher Order ◽

Finite Element Implementation

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Stress concentration factors for the torsion of curved beams of arbitrary cross-section

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406jmes303 ◽

2006 ◽

Vol 220 (12) ◽

pp. 1709-1726 ◽

Cited By ~ 1

Author(s):

R E Cornwell

Keyword(s):

Finite Element ◽

Stress Concentration ◽

Cross Section ◽

Cross Sections ◽

Shear Stresses ◽

Curved Beams ◽

Finite Element Implementation ◽

Out Of Plane ◽

Concentration Factors ◽

Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

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