Circumferentially-symmetric finite eigenstrains in incompressible isotropic nonlinear elastic wedges

Golgoon, Ashkan; Sadik, Souhayl; Yavari, Arash

doi:10.1016/j.ijnonlinmec.2016.04.007

Cited by 24 publications

(15 citation statements)

References 29 publications

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“…In bulk growth material metric is explicitly time-dependent and is a function of the mass flux through the balance of mass [Yavari, 2010;. For inclusions (or inhomogeneities with eigenstrains) material metric explicitly depends on the distribution of (finite) eigenstrains [Yavari andGoriely, 2013b, 2015;Golgoon et al, 2016]. After solving the problem of surface growth of an infinitely-long cylindrical bar (or a hollow spherical ball) we will see that, as expected, the material manifold is time-dependent and has a metric that is determined by the history of loading and deformation during surface growth.…”

Section: Geometric Anelasticity and The Mechanics Of Growthmentioning

confidence: 99%

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Sozio

Yavari

2017

Journal of the Mechanics and Physics of Solids

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In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

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Section: Geometric Anelasticity and The Mechanics Of Growthmentioning

confidence: 99%

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Sozio

Yavari

2017

Journal of the Mechanics and Physics of Solids

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“…Contact mechanics is one of the most common problems in mechanical engineering and tribology, with a variety of applications in collision mechanics [1][2][3], joint structures [4,5], electrical contact [6], thermal contact [7], solid mechanics [8][9][10][11], seals and bearings [12], biomechanical systems [13,14], turbines [15], and additive manufacturing [16,17]. The studies in contact mechanics can be categorized into: single asperity spherical, elliptical, cylindrical and flat contacts, with single asperity spherical contact being the most employed one [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

Ghaednia

Brake

Berryhill

et al. 2018

Journal of Tribology

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For elastic contact, an exact analytical solution for the stresses and strains within two contacting bodies has been known since the 1880s. Despite this, there is no similar solution for elastic–plastic contact due to the integral nature of plastic deformations, and the few models that do exist develop approximate solutions for the elastic–perfectly plastic material model. In this work, the full transition from elastic–perfectly plastic to elastic materials in contact is studied using a bilinear material model in a finite element environment for a frictionless dry flattening contact. Even though the contact is considered flattening, elastic deformations are allowed to happen on the flat. The real contact radius is found to converge to the elastic contact limit at a tangent modulus of elasticity around 20%. For the contact force, the results show a different trend in which there is a continual variation in forces across the entire range of material models studied. A new formulation has been developed based on the finite element results to predict the deformations, real contact area, and contact force. A second approach has been introduced to calculate the contact force based on the approximation of the Hertzian solution for the elastic deformations on the flat. The proposed formulation is verified for five different materials sets.

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“…Also it is important to mention researches that combine wave propagation in non linear elasticity material where a specific strain field is applied allowing to modify the wave propagation conditions in the studied domain. This topic opens several possibilities of applications in Engineering and can be found in Shearer et al (2015), Golgoon et al (2016), Barnwell et. al.…”

Section: Bibliography Reviewmentioning

confidence: 99%

The dispersion curve applied in guided wave propagation in prismatic rods.

Groth

Iturrioz

Clarke

2018

Lat. Am. j. solids struct.

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The early detection of failures in structures is a subject of great interest in engineering; several of these techniques are linked with the elastic wave propagation, using guided waves is one of these alternatives. Several structures of interest in engineering are laminar arrangements; the wave propagation in this type of structures depends not only on the material properties, but also on the geometric parameters, such as the plate thickness. Tubular structures, pressure vessels, tanks and also parts of ships hulls could be considered laminar. The elastic wave propagation in laminar structures could be considered as a sum of modal shapes that have its wave length and frequencies defined. These mode families are characteristics of each structure and could be represented through the dispersion curves. The definition of these dispersion curves is of crucial importance to understand the propagation of guided waves in the structure studied. In the present work the dispersion curves were generated using three different methodologies, specific for metallic rectangular stems that compound the strengthening armor in flexible riser duct. Each approach presented in the analysis were carried out using standard finite element commercial packages and an experimental verification, as well. The premise is to present the topics in the simplest way, not only to understand how the dispersion curves are built but also how these curves must be interpreted.

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Circumferentially-symmetric finite eigenstrains in incompressible isotropic nonlinear elastic wedges

Cited by 24 publications

References 29 publications

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

The dispersion curve applied in guided wave propagation in prismatic rods.

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