Multimaterial Eulerian finite element formulation for pressure‐sensitive adhesives

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Summary We propose a full Eulerian incompressible solid‐fluid interaction scheme capable of achieving high parallel efficiency and easily generating meshes for complex solid geometries. While good scalability of a full Eulerian solid‐fluid interaction formulation has been reported by Sugiyama et al, their analysis was carried out using uniform Cartesian mesh and an artificial compressibility method. Typically, it is more challenging to achieve good scalability for hierarchical Cartesian meshes and a fully incompressible formulation. In addition, the conventional full Eulerian methods require a large computational cost to resolve complex solid geometries due to the usage of uniform Cartesian meshes. In an attempt to overcome the aforementioned issues, we employ the building‐cube method, where the computational domain is divided into cubic regions called cubes. Each cube is divided at equal intervals, the same number of cubes is assigned to each core, and the spatial loop processing is executed for each cube. The numerical method is verified by computing five numerical examples. In the weak scaling test, the parallel efficiency at 32768 cores with 32 cores as a reference is 93.6%. In the strong scaling test, the parallel efficiency at 32768 cores with 128 cores as a reference is 70.2%.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Full Eulerian deformable solid‐fluid interaction scheme based on building‐cube method for large‐scale parallel computing

Nishiguchi

Bale

Okazawa

et al. 2018

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Eulerian finite volume formulation using Lagrangian marker particles for incompressible fluid–structure interaction problems

Shimada

Nishiguchi

Bale

et al. 2021

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We propose a monolithic fluid-structure interaction (FSI) method that uses the cell-centered finite volume formulation in the Eulerian description, Lagrangian marker particles allocated in the solid region, and the incompressible mixture formulation. In the proposed method, we compute all the basic equations and spatial derivatives, except the solid constitutive equations, on an Eulerian mesh to avoid neighboring particle search. Although full Eulerian methods that use a Cartesian mesh are attractive for FSI problems that require large-scale computing and include complex geometries and the large deformation of the solid, they cannot avoid the numerical dissipation of the interfaces or internal variables of the solid caused by their advection. This computational problem has been a barrier to the industrial application of full Eulerian mesh methods. In the numerical examples, we confirmed that the proposed method retains sharp interfaces, such as the corners of a square solid, and yields more accurate numerical results for the deformation, energy, and incompressibility of a solid in fluid than our conventional Eulerian FSI method.

Arbitrary mesh‐moving velocity‐based space‐time finite element method for large deformation analysis of solids

Shimizu,

Sharma,

Fujisawa

2023

SummaryThis paper presents a new velocity‐based space‐time finite element method for computing the large deformation of solids over arbitrary Lagrange/Eulerian moving meshes. The proposed method is oriented toward quasi‐static deformation problems with hypoelastic and neo‐Hookean hyperelastic constitutive models. The Cauchy stress in the weak form of the linear momentum equation is explicitly described in terms of deformation velocity through consistent time integration of objective stress rates transferred in the arbitrary moving mesh. Consequently, the resultant system equation only contains the space‐time nodal velocity as the primary unknown. An iterative algorithm for solving the discretized system equation is implemented, whereby the nonlinearities induced by geometrical change in the computational domain as well as nonlinear constitutive equations are computed in an iterative manner updating the stress and the strain over the moving mesh of the deforming domain. Three benchmark problems, such as uniform beam compression, thick‐cylinder compression with superimposed rigid body rotation and extrusion of a column involving material loss, have been solved in order to examine the accuracy of the proposed numerical scheme. The numerical results have revealed the proper computation of the stress and the displacement of the solids undergoing the large deformation and rotation over the arbitrary Lagrange/Eulerian moving meshes, and have shown the validity and applicability of the proposed method with linear convergence of the iterative algorithm.