On a nonlinear inverse problem in viscoelasticity

Bui, Huy Duong; Chaillat, Stéphanie

doi:10.15625/0866-7136/31/3-4/5649

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…According to Bui's celebrated work [2], we regard the identification of local stress as an ill-posed problem; while data for strain are available, stress-strain relations are not known. It is true that stress is determined from strain if the stress-strain relations are known.…”

Section: Introductionmentioning

confidence: 99%

Stress inversion method and analysis of GPS array data

Hori

Iinuma

Kato

2008

Comptes Rendus. Mécanique

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The stress inversion method is developed to find a stress field which satisfies the equation of equilibrium for a body in a state of plane stress. When one stress-strain relation is known and data on the strain distribution on the body and traction along the boundary are provided, the method solves a well-posed problem, which is a linear boundary value problem for Airy's stress function, with the governing equation being the Poisson equation and the boundary conditions being of the Neumann type. The stress inversion method is applied to the Global Positioning System (GPS) array data of the Japanese Islands. The stress increment distribution, which is associated with the displacement increment measured by the GPS array, is computed, and it is found that the distribution is not uniform over the islands and that some regions have a relatively large increment. The elasticity inversion method is developed as an alternative to the stress inversion method; it is based on the assumption of linear elastic deformation with unknown elastic moduli and does not need boundary traction data, which are usually difficult to measure. This method is applied to the GPS array data of a small region in Japan to which the stress inversion method is not applicable. To cite this article: M.

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Section: Introductionmentioning

confidence: 99%

Stress inversion method and analysis of GPS array data

Hori

Iinuma

Kato

2008

Comptes Rendus. Mécanique

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Sensitivity analysis of truck tire tread material properties for on-road applications

Fathi,

Ly,

Pathak

et al. 2024

Trans. Can. Soc. Mech. Eng.

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This research delves into the sensitivity analysis of a truck tire rubber compound concerning its impact on tire–road interaction characteristics. Initially, the study employs finite element analysis to model a 315/80R22.5 truck tire, which is subsequently validated through static and dynamic response assessments via various simulation tests. Following validation, the established tire model is utilized to conduct a sensitivity analysis of the tire rubber compound specifically applied on the tread. This analysis encompasses several material definitions, including Mooney–Rivlin, visco-Mooney–Rivlin, linear viscoelastic, and nonlinear viscoelastic materials. By exploring the effects of these material models, the research scrutinizes their influence on tire–road interaction characteristics across diverse operating conditions. The tire–road interaction characteristics include the rolling resistance coefficient, and the cornering force at operating conditions including the longitudinal speed, vertical load, and slip angle. This comprehensive investigation offers insights into the intricate relationship between tire composition and performance, thereby enhancing our understanding of tire behavior and informing potential advancements in tire technology.

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On the mystery of Calderón’s formula for the geometry of an inclusion in elastic materials

Bui

2011

J. Mech. Mater. Struct.

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I write this paper to pay homage to Marie-Louise Steele and in honor of Charles R. Steele. I have had the pleasure and the honor to serve their journals IJSS and JoMMS, with George Herrmann. They have made Solids & Structures and now Material Sciences a subject of nobility to all of us.We consider the nonlinear inverse problem of determining an inclusion in an elastic body, in antiplane shear loading. The perturbation of the shear modulus due to the inclusion was determined by Calderón (1980) in the case of a small amplitude of perturbation. For the general nonlinear case, the problem is decomposed into two linear problems: a source inverse problem, which determines the geometry of the inclusion, and a Volterra integral equation of the first kind for determining the amplitude. In this paper, we deal only with the determination of the inclusion geometry in the two-dimensional problem. We derive a simple formula for determining the inclusion geometry. This formula enables us to investigate the mystery of Calderón's solution for the linearized perturbation h 0 , raised by Isaacson and Isaacson (1986), in the case of axisymmetry. By using a series method for numerical analysis, they found that the supports of the perturbation, in the linearized theory and the nonlinear theory in the axisymmetric case, are practically the same. We elucidate the mystery by discovering that both theories give exactly the same support of the perturbation, supp(h 0 ) ≡ supp(h), for the general case of geometry and loadings. Then, we discuss an application of the geometry method to locate an inclusion and solve the source inverse problem, which gives an indication of the amplitude of the perturbation.

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On a nonlinear inverse problem in viscoelasticity

Cited by 3 publications

References 16 publications

Stress inversion method and analysis of GPS array data

Stress inversion method and analysis of GPS array data

Sensitivity analysis of truck tire tread material properties for on-road applications

On the mystery of Calderón’s formula for the geometry of an inclusion in elastic materials

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