p-FEM for finite deformation powder compaction

Heisserer, Ulrich; Hartmann, Stefan; Düster, Alexander; Bier, Wolfgang; Yosibash, Zohar; Rank, Ernst

doi:10.1016/j.cma.2007.09.001

Cited by 26 publications

(9 citation statements)

References 25 publications

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“…Hence the elastic part of the solution is known as the relation between the radius δ and the pressure Π δ is known. The solution for the plasticized zone (a ≤ r ≤ δ) is obtained from the algebraic-differential system composed by the equilibrium equations (23), the boundary conditions (31), and the yield condition (25) or (26) (depending on the criterion assumed). This system writes as…”

Section: The Elasto-plastic Solutionmentioning

confidence: 99%

Integration algorithms of elastoplasticity for ceramic powder compaction

Penasa

Argani

Bigoni

2014

Journal of the European Ceramic Society

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Inelastic deformation of ceramic powders (and of a broad class of rock-like and granular materials), can be described with the yield function proposed by Bigoni and Piccolroaz (2004, Yield criteria for quasibrittle and frictional materials. Int. J. Solids and Structures, 41, 2855-2878). This yield function is not defined outside the yield locus, so that 'gradient-based' integration algorithms of elastoplasticity cannot be directly employed. Therefore, we propose two ad hoc algorithms: (i.) an explicit integration scheme based on a forward Euler technique with a 'centre-of-mass' return correction and (ii.) an implicit integration scheme based on a 'cutoff-substepping' return algorithm. Iso-error maps and comparisons of the results provided by the two algorithms with two exact solutions (the compaction of a ceramic powder against a rigid spherical cup and the expansion of a thick spherical shell made up of a green body), show that both the proposed algorithms perform correctly and accurately.

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Section: The Elasto-plastic Solutionmentioning

confidence: 99%

Integration algorithms of elastoplasticity for ceramic powder compaction

Penasa

Argani

Bigoni

2014

Journal of the European Ceramic Society

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“…Quite arbitrary polynomials may be used to enrich the approximation, so relatively often the Legendre polynomials are chosen e.g. [8,18,21]. The hierarchical approximation with Legendre polynomials enables to achieve high order elements, however they do not exceed p = 10, anyway.…”

Section: Introductionmentioning

confidence: 99%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

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The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

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“…Exponential convergence rates for the energy norm are achievable if the exact solution to be approximated is smooth. The p-FEM approach also extends to nonlinear problems such as hyperelasticity [4,11,24] and elastoplasticity [12,13,23,26,39].…”

Section: High-order Femmentioning

confidence: 98%

A comparison of the h-, p-, hp-, and rp-version of the FEM for the solution of the 2D Hertzian contact problem

Franke

Düster

Nübel³

et al. 2010

Comput Mech

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A comparison of the h-, p-, hp-, and r p-version of the FEM for the solution of the 2D Hertzian contact problemDavid Franke · A. Düster · V. Nübel · E. Rank Abstract Even after more than three decades of intensive research in the field of contact mechanics, there is still a great need for improving the numerical methods. Recent investigations on the 2D Hertzian contact problem clearly showed significantly varying results for different finite element versions. In this paper we will compare the analytical solution of the 2D Hertzian contact problem with the numerical results of the classical h-version with uniform and locally refined meshes, as well as with the p-, the hp-, and the r p-version of the FEM. The penalty method is used to incorporate the contact constraints.

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p-FEM for finite deformation powder compaction

Cited by 26 publications

References 25 publications

Integration algorithms of elastoplasticity for ceramic powder compaction

Integration algorithms of elastoplasticity for ceramic powder compaction

Very high order discontinuous Galerkin method in elliptic problems

A comparison of the h-, p-, hp-, and rp-version of the FEM for the solution of the 2D Hertzian contact problem

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