A multidata method of approximate Laplace transform inversion

Cost, Thomas L.; Becker, Eric B.

doi:10.1002/nme.1620020206

Cited by 105 publications

(28 citation statements)

References 7 publications

(6 reference statements)

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“…In more general situations, the exact effective spectrum has a continuous part and the Prony series provide only a convenient approximation. The widely used collocation method and its extensions rely on this series approximation (Schapery, 1962;Cost and Becker, 1970;Bradshaw and Brinson, 1997;Turner and Tomé, 1993;Masson and Zaoui, 1999;Rekik and Brenner, 2011). New results have recently been obtained on the effective relaxation function of linear viscoelastic composites by considering its asymptotic behavior in time (Suquet, 2012).…”

Section: Introductionmentioning

confidence: 99%

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Brenner

Suquet

2013

International Journal of Solids and Structures

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This paper is devoted to the effective behavior of linear viscoelastic heterogeneous materials with a particular emphasis on their transient response. First, two new asymptotic relations for the overall creep function are derived at short and large times. They are related to the retardation spectrum of the composite and involve second-order moments per phase of the stress field for the purely elastic and purely viscous problems. In the context of harmonic loadings, these relations provide exact frequential asymptotic conditions on the overall storage and loss moduli. Second, by making use of these asymptotic results, an approximate model is proposed. It consists in approximating the retardation spectrum of the composite by a single discrete Dirac mass. Its accuracy is assessed by comparison with exact analytical results, fullfield simulations and collocation results for several classes of composites and polycrystals.

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Section: Introductionmentioning

confidence: 99%

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Brenner

Suquet

2013

International Journal of Solids and Structures

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“…For this #& goal, approaches relying on Dirichlet series expansion of the original time functions have #' been proposed, e.g. [13,16,17,18]. Among them, the so-called collocation method [13] $ has provided very good results for the homogenization of polycrystals [19,20,21].…”

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confidence: 99%

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

Vu¹,

Brenner²,

Castelnau³

et al. 2012

Modelling Simul. Mater. Sci. Eng.

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“…Based on a given set of respondance times, various numerical schemes have been developed to determine the corresponding spectrum lines: e.g. the collocation method of Schapery [34], the smoothness constraint approach of Clauser and Knauss [35], the multidata method of Cost and Becker [36] or the enhanced multidata method of Bradshaw and Brinson [37].…”

Section: Identification With Additional Informationmentioning

confidence: 99%

On parameter identification for material and microstructural properties

Gerlach

Matzenmiller

2007

GAMM-Mitteilungen

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The simulation of the mechanical behaviour of structures with the finite element method is one of the main tasks in engineering mechanics and requires both constitutive and structural parameters. In addition to a qualified geometrical approximation of the structure with the finite element discretization and the definition of initial and boundary conditions it is necessary to select material models for the realistic description of the mechanical system at hand. Furthermore, the material models chosen require reliable numerical data for the associated constitutive parameters, which are usually not known for most new materials like reinforced composites, if their properties are not listed in a database or if they consist of different constituents. Composites usually possess unknown microstructural properties, which cannot be assigned to typical specimen of homogeneous material distribution. Due to the imperfect manufacturing process the mechanical behaviour of composites can significantly vary and the associated material parameters must be determined from the overall behaviour of the composite. Therefore, the unknown material parameters, as the essential input data for the consitutive model for every finite element simulation, must be identified by solving an inverse problem before the complete structure is analyzed.

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A multidata method of approximate Laplace transform inversion

Cited by 105 publications

References 7 publications

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

On parameter identification for material and microstructural properties

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