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Research Papers

Peridynamic Modeling of Hyperelastic Membrane Deformation

[+] Author and Article Information
D. J. Bang, E. Madenci

Department of Aerospace and
Mechanical Engineering,
University of Arizona,
Tucson, AZ 85721

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received October 25, 2016; final manuscript received January 18, 2017; published online March 27, 2017. Assoc. Editor: Huiling Duan.

J. Eng. Mater. Technol 139(3), 031007 (Mar 27, 2017) (10 pages) Paper No: MATS-16-1305; doi: 10.1115/1.4035875 History: Received October 25, 2016; Revised January 18, 2017

This study concerns the development of peridynamic (PD) strain energy density functions for a Neo-Hookean type membrane under equibiaxial, planar, and uniaxial loading conditions. The material parameters for each loading case are determined by equating the PD strain energy density to that of the classical continuum mechanics. The PD equations of motion are derived based on the Neo-Hookean model under the assumption of incompressibility. Numerical results concern the deformation of a membrane with a defect in the form of a hole, a crack, and a rigid inclusion under equibiaxial, planar, and uniaxial loading conditions. The PD predictions are verified by comparison with those of finite element analysis.

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Figures

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Fig. 1

Force densities and kinematics of PD material points x(k) and x(j)

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Fig. 2

Pairwise interaction of force densities at material points x(k) and x(j)

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Fig. 3

Material point x(k) interacting with others in its immediate vicinity

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Fig. 4

Equibiaxial loading condition

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Fig. 5

Planar loading condition

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Fig. 6

Uniaxial loading condition

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Fig. 7

Comparison of PD and ansys forces predictions under equibiaxial loading

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Fig. 8

Comparison of PD and ansys force predictions under planar loading

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Fig. 9

Comparison of PD and ansys force predictions under uniaxial loading

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Fig. 10

Displacement contours of membrane with a hole under equibiaxial loading for λ=1.5 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 11

Displacement contours of membrane with a hole under equibiaxial loading for λ=3.0 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 12

Displacement contours of membrane with a hole under planar loading in the x-direction for λ=1.5 in deformed configuration (left: PD and right: ansys)

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Fig. 13

Displacement contours of membrane with a hole under planar loading in the x-direction for λ=3.0 in deformed configuration (left: PD and right: ansys)

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Fig. 14

Displacement contours of membrane with a hole under uniaxial loading for λ=1.5 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 15

Displacement contours of membrane with a hole under uniaxial loading for λ=3.0 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 16

Displacement contours of membrane with a crack under equibiaxial loading for λ=1.5 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 17

Displacement contours of membrane with a crack under equibiaxial loading for λ=3.0 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 18

Displacement contours of membrane with a crack under planar loading in the x-direction for λ=1.5 in deformed configuration (left: PD and right: ansys)

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Fig. 19

Displacement contours of membrane with a crack under planar loading in the x-direction for λ=3.0 in deformed configuration (left: PD and right: ansys)

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Fig. 20

Displacement contours of membrane with a crack under uniaxial loading for λ=1.5 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 21

Displacement contours of membrane with a crack under uniaxial loading for λ=3.0 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 22

Displacement contours of membrane with a solid inclusion under equibiaxial loading for λ=1.5 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 23

Displacement contours of membrane with a solid inclusion under equibiaxial loading for λ=3.0 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 24

Displacement contours of membrane with a rigid inclusion under planar loading for in the x-direction λ=1.5 in deformed configuration (left: PD and right: ansys)

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Fig. 25

Displacement contours of membrane with a rigid inclusion under planar loading in the x-direction for λ=3.0 in deformed configuration (left: PD and right: ansys)

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Fig. 26

Displacement contours of membrane with a rigid inclusion under uniaxial loading for λ=1.5 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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Fig. 27

Displacement contours of membrane with a rigid inclusion under uniaxial loading for λ=3.0 in deformed configuration: (a) x-direction and (b) y-direction (left: PD and right: ansys)

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