Nonlinear mechanics of thermoelastic accretion

Sozio, Fabio; Shojaei, Mostafa FaghihÂ; Sadik, Souhayl; Yavari, Arash

doi:10.1007/s00033-020-01309-5

Cited by 7 publications

(3 citation statements)

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“…Metlov [1985] proposed the first finite deformation theory of accretion and introduced a time of attachment map. There are many more works in the literature of the mechanics of accretion [Drozdov, 1998a,b, Arutyunyan et al, 1990, Manzhirov, 1995, Ong and O'Reilly, 2004, Kadish et al, 2005, Epstein, 2010, Lychev and Manzhirov, 2013, Manzhirov, 2014, Lychev, 2017, Lychev et al, 2021, Tomassetti et al, 2016, Sozio and Yavari, 2017, Sozio et al, 2020, Abi-Akl et al, 2019, Abi-Akl and Cohen, 2020, Truskinovsky and Zurlo, 2019, Bergel and Papadopoulos, 2021. For a detailed literature review of the mechanics of accretion see [Naumov, 1994, Sozio andYavari, 2017].…”

Section: Introductionmentioning

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%

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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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite extension of accreting nonlinear elastic solid circular cylinders

Yavari

Safa

Fallah

2023

Continuum Mech. Thermodyn.

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“…However, these studies did not consider deformation, and assumed that the body was rigid. Recent work has extended these ideas to account for deformation and stress [14][15][16][17][18][19][20][21][22][23]. These studies used a Lagrangian formulation, i.e., the kinematic description is roughly based on reference particles in an evolving reference configuration.…”

Section: Introductionmentioning

confidence: 99%

Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

Naghibzadeh

Walkington

Dayal

2021

Mathematics and Mechanics of Solids

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Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

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Nonlinear mechanics of accretion

Sozio

Yavari

2019

J Nonlinear Sci

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Nonlinear mechanics of thermoelastic accretion

Cited by 7 publications

References 50 publications

Finite extension of accreting nonlinear elastic solid circular cylinders

Finite extension of accreting nonlinear elastic solid circular cylinders

Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

Nonlinear mechanics of accretion

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