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Schematic diagram for the compression test (Sec. 4.1.1). The initial configurations of the immersed structure and a fluid are denoted by Ω s 0 and Ω f 0 , respectively. The entire computational domain is Ω = Ω s 0 ∪Ω f 0 . Zero fluid velocity is enforced on the outer boundaries of the computational domain.
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This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incomp...
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... A downward uniaxial traction is loaded in the center of the top of the block. Zero horizontal and vertical displacements are respectively applied to the top and bottom boundaries of the block and all other boundaries have zero traction. This test was introduced by Reese et al. [37] to test a stabilization technique for low order finite elements. Fig. 3 Figure 5: Vertical displacements of the top center point of the compressed block, highlighted in Fig. 3, for different choices of peridynamic horizon size and numerical Poisson's ratio ν stab . The solid DoF range from 153 to 4753. Note that locking clearly occurs for ν stab = 0.49995. As in computational standard mechanics approaches, ...
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... displacements are respectively applied to the top and bottom boundaries of the block and all other boundaries have zero traction. This test was introduced by Reese et al. [37] to test a stabilization technique for low order finite elements. Fig. 3 Figure 5: Vertical displacements of the top center point of the compressed block, highlighted in Fig. 3, for different choices of peridynamic horizon size and numerical Poisson's ratio ν stab . The solid DoF range from 153 to 4753. Note that locking clearly occurs for ν stab = 0.49995. As in computational standard mechanics approaches, however, the IPD formulation ultimately converges under grid refinement even with high (but fixed) ...
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... even with high (but fixed) levels of volumetric penalization. 4 illustrates the material body after the deformation along with pointwise values of the non-local Jacobian determinant J, which is computed using the non-local deformation gradient tensor. Fig. 5 shows the vertical displacements of the top center material point, highlighted in Fig. 3, for various numerical Poisson's ratios ν stab and peridynamic horizon sizes under grid refinement. The maximum displacement of the point obtained using IPD method is in excellent agreement with that obtained using the standard FE method and it converges under grid refinement to approximately 3.92 cm. The maximum displacement of the ...
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... [48]. Fig. 22 shows the crack nucleation and propagation of the dynamic version of the elastic band benchmark with an Eulerian velocity field. The crack formulation is initiated near the junctions between the rigid blocks and the band, and the band gets entirely detached from the block when the bonds exceed the critical bond stretch s c . Fig. 23a shows the horizontal displacements of the point of interest, highlighted in Fig. 14, for different grid spacings. Fig. 23b shows the local damage growth at the top left corner of the detached band during the failure process under grid ...
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... an Eulerian velocity field. The crack formulation is initiated near the junctions between the rigid blocks and the band, and the band gets entirely detached from the block when the bonds exceed the critical bond stretch s c . Fig. 23a shows the horizontal displacements of the point of interest, highlighted in Fig. 14, for different grid spacings. Fig. 23b shows the local damage growth at the top left corner of the detached band during the failure process under grid ...
