Accretion Mechanics of Nonlinear Elastic Circular Cylindrical Bars Under Finite Torsion

Yavari, Arash; Pradhan, Satya Prakash

doi:10.1007/s10659-022-09957-6

Cited by 4 publications

(6 citation statements)

References 45 publications

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“…Following [Sozio and Yavari, 2017], we choose U g (t) = u g (t). Sozio and Yavari [2017] showed that other choices for U g (t) result in isometric material metrics (see also Yavari and Pradhan [2022]). In other words, this choice will not affect the calculation of deformation and stresses.…”

Section: Finite Extension Of An Accreting Circular Cylindrical Barmentioning

confidence: 99%

“…Accretion is a source of anelasticity (in the sense of Eckart [1948]), and hence, residual stresses. There are recent geometric formulations that model the accretion-induced anelasticity by a Riemannian material manifold whose metric explicitly depends on the history of deformation during accretion [Sozio and Yavari, 2017, Sozio et al, 2020, Yavari and Pradhan, 2022. In this paper we consider symmetric accretion of a finite solid circular cylinder made of an arbitrary incompressible isotropic solid.…”

Section: Introductionmentioning

confidence: 99%

“…Note that on the growth surface the entire Cauchy stress is known as the new material added to the boundary in the current configuration is stress-free.6 For definition of universal eigenstrains see[Yavari and Goriely, 2016]. See also[Yavari and Pradhan, 2022] for another class of universal deformations and eigenstrains in the case of an accreting circular cylindrical bar under finite torsion.…”

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confidence: 99%

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Finite extension of accreting nonlinear elastic solid circular cylinders

Yavari

Safa

Fallah

2023

Continuum Mech. Thermodyn.

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In this paper we formulate and solve the initial-boundary value problem of accreting circular cylindrical bars under finite extension. We assume that the bar grows by printing stress-free cylindrical layers on its boundary cylinder while it is undergoing a time-dependent finite extension. Accretion induces eigenstrains, and consequently residual stresses. We formulate the anelasticity problem by first constructing the natural Riemannian metric of the growing bar. This metric explicitly depends on the history of deformation during the accretion process. For a displacement-control loading during the accretion process we find the exact distribution of stresses. For a force-control loading, a nonlinear integral equation governs the kinematics. After unloading there are, in general, a residual stretch and residual stresses. For different examples of loadings we numerically find the axial stretch during loading, the residual stretch, and the residual stresses. We also calculate the stress distribution, residual stretch, and residual stresses in the setting of linear accretion mechanics. The linear and nonlinear solutions are numerically compared in a few accretion examples.

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Section: Finite Extension Of An Accreting Circular Cylindrical Barmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Finite extension of accreting nonlinear elastic solid circular cylinders

Yavari

Safa

Fallah

2023

Continuum Mech. Thermodyn.

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“…Recently, the nonlinear geometric accretion theory developed in [21,22] was used to solve two classes of problems: (i) time-dependent finite extension of incompressible isotropic accreting circular cylindrical bars [26] and (ii) time-dependent finite torsion of incompressible isotropic accreting circular cylindrical bars [59]. In the absence of accretion, these deformations are subsets of Family 3 universal deformations [60].…”

Section: Introductionmentioning

confidence: 99%

“…In the absence of accretion, these deformations are subsets of Family 3 universal deformations [60]. It was shown that even in the presence of cylindrically symmetric accretion these deformations are universal [26,59].…”

Section: Introductionmentioning

confidence: 99%

Accretion–ablation mechanics

Pradhan,

Yavari

2023

Phil. Trans. R. Soc. A.

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In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting–ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio & Yavari (Sozio & Yavari 2019 J. Nonlinear Sci. 29 , 1813–1863 (doi:10.1007/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads. In this formulation, the natural configuration of an accreting–ablating body is a time-dependent Riemannian 3 -manifold with a metric that is an unknown a priori and is determined after solving the accretion–ablation initial-boundary-value problem. In addition to the time of attachment map, we introduce a time of detachment map that along with the time of attachment map, and the accretion and ablation velocities, describes the time-dependent reference configuration of the body. The kinematics, material manifold, material metric, constitutive equations and the balance laws are discussed in detail. As a concrete example and application of the geometric theory, we analyse a thick hollow circular cylinder made of an arbitrary incompressible isotropic material that is under a finite time-dependent extension while undergoing continuous ablation on its inner cylinder boundary and accretion on its outer cylinder boundary. The state of deformation and stress during the accretion–ablation process, and the residual stretch and stress after the completion of the accretion–ablation process, are computed. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

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Controllable deformations in compressible isotropic implicit elasticity

Yavari,

Goriely

2024

Z. Angew. Math. Phys.

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For a given material, controllable deformations are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, universal deformations are those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress $$\varvec{\sigma }$$ σ and the left Cauchy-Green strain $$\textbf{b}$$ b , have the implicit form $$\varvec{\textsf{f}}(\varvec{\sigma },\textbf{b})=\textbf{0}$$ f ( σ , b ) = 0 . We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is constitutively admissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations.

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Accretion Mechanics of Nonlinear Elastic Circular Cylindrical Bars Under Finite Torsion

Cited by 4 publications

References 45 publications

Finite extension of accreting nonlinear elastic solid circular cylinders

Finite extension of accreting nonlinear elastic solid circular cylinders

Accretion–ablation mechanics

Controllable deformations in compressible isotropic implicit elasticity

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