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Research Papers

Systematic Integration of Finite Element Methods Into Multibody Dynamics Considering Hyperelasticity and Plasticity

[+] Author and Article Information
Graham Sanborn

FunctionBay, Inc.,
5F, Pangyo Seven Venture Valley 1 danji 2 dong,
625, Sampyeong-dong,
Bundang-gu, Seongnam-si,
Gyeonggi-do 463-400, South Korea
e-mail: gsanborn@functionbay.co.kr

Juhwan Choi

FunctionBay, Inc.,
5F, Pangyo Seven Venture Valley 1 danji 2 dong,
625, Sampyeong-dong,
Bundang-gu, Seongnam-si,
Gyeonggi-do 463-400, South Korea
e-mail: juhwan@functionbay.co.kr

Joon Shik Yoon

FunctionBay, Inc.,
5F, Pangyo Seven Venture Valley 1 danji 2 dong,
625, Sampyeong-dong,
Bundang-gu, Seongnam-si,
Gyeonggi-do 463-400, South Korea
e-mail: jueno@functionbay.co.kr

Sungsoo Rhim

Department of Mechanical Engineering,
KyungHee University,
1 Seochun-dong, Kihung-gu, YongIn-si,
Gyeonggi-do 449-701, South Korea
e-mail: ssrhim@khu.ac.kr

Jin Hwan Choi

Department of Mechanical Engineering,
KyungHee University,
1 Seochun-dong, Kihung-gu, YongIn-si,
Gyeonggi-do 449-701, South Korea
e-mail: jhchoi@khu.ac.kr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 31, 2013; final manuscript received April 30, 2014; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 041012 (Jul 11, 2014) (11 pages) Paper No: CND-13-1113; doi: 10.1115/1.4027580 History: Received May 31, 2013; Revised April 30, 2014

This study proposes a systematic extension of a multiflexible-body dynamics (MFBD) formulation that is based on a recursive formulation for rigid body dynamics. It is extended to include nonlinear plastic and hyperelastic material models for the flexible bodies. The flexible bodies in the existing MFBD formulation use a finite element formulation based on corotational elements. The rigid bodies and flexible bodies are coupled using the method of Lagrange multipliers. The extensions to add plasticity and hyperelasticity are outlined. A solid, brick-type element and a shell element are adapted from the literature for use with the plastic material, and a constant volume constraint is introduced to enforce the approximation of incompressibility with the hyperelastic materials. A brief overview of the MFBD formulation and the details required to extend the formulation to incorporate these nonlinear material models are presented. Numerical examples are presented to demonstrate the feasibility of the model.

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Figures

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Fig. 1

Two contiguous rigid bodies

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Fig. 2

Example shell element reference frame rl and Al=[xl yl zl]

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Fig. 3

The interpolation points for the out-of-plane shear strains of the MITC4

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Fig. 4

Cantilever model with plastic material and hexahedral element formulation. Traction load applied to free end. Displacement compared at point marked . Von Mises stress compared at point marked . (Model with 10 mm elements shown).

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Fig. 5

Distributed edge pressure load applied in the vertical direction to free end of cantilever plate model

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Fig. 6

Displacement of node at free end of cantilever, (a) time 0 to −2 sec, and (b) time 1.9 to −2.0 sec, for element sizes 2.5 and 5 mm, for abaqus (Ab) and the proposed formulation (Pr), for hexa-type solid elements

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Fig. 7

von Mises stress of node near base of cantilever, (a) time 0 to −2 sec, and (b) time 1.9 to −2.0 sec, for element sizes 2.5 and 5 mm, for abaqus (Ab) and the proposed formulation (Pr), for hexa-type solid elements

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Fig. 8

The model used for verification of the hyperelastic material behavior

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Fig. 9

Total force applied to Force applied to the free end of the hyperelastic model

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Fig. 10

(a) x-displacement and (b) von Mises stress of proposed versus. abaqus model for a Mooney–Rivlin material

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Fig. 11

A test model including rigid bodies modeled with the recursive formulation and flexible bodies that use plasticity and hyperelasticity

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Fig. 12

Configuration of the mechanism model between times 0.0 and 3.0 sec

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Fig. 13

Magnitude of contact forces between bodies B and E and between bodies C and E

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Fig. 14

Equivalent von Mises strain for total and plastic strain components on the top (inside of curvature after deformation) and bottom (outside of curvature after plastic deformation) of body E at the point of maximum strain

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Fig. 15

von Mises stress at a node near the midpoint of body F (hyperelastic body)

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