On the direct and reverse multiplicative decompositions of deformation gradient in nonlinear anisotropic anelasticity

Yavari, Arash; Sozio, Fabio

doi:10.1016/j.jmps.2022.105101

Cited by 13 publications

(8 citation statements)

References 75 publications

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“…A few different but related measures of strain are usually used in nonlinear elasticity and anelasticity [47,50,61,62]. The right Cauchy–Green strain is defined as boldCnormal♭=φ∗g=boldF⋆gF, which is the pull-back of the spatial metric to the reference configuration.…”

Section: A Continuum Theory Of Accreting–ablating Bodiesmentioning

confidence: 99%

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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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Section: A Continuum Theory Of Accreting–ablating Bodiesmentioning

confidence: 99%

“…Stress-free or pre-stressed material can be added on the accretion boundary. The material metric is controlled by both the state of stress of the material before joining 1 For detailed historical accounts of this decomposition, see [49,50]. 2 See [50,51] for discussions on global intermediate configurations (manifolds).…”

Section: Introductionmentioning

confidence: 99%

Accretion–ablation mechanics

Pradhan,

Yavari

2023

Phil. Trans. R. Soc. A.

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“…The elastic–plastic decomposition of the deformation gradient, F, into an ‘elastic’ factor, Fe, and a ‘plastic’ factor, Fp, as F=FeFp, was introduced in 1960 by Kröner [1] and in 1967 by Lee & Liu [2,3], and has been used and studied extensively since then. For a comprehensive review of the subsequent work, see [4], and for more recent work see for example [5–13]. The plastic factor is viewed as the tensor field needed in order to release the residual stresses in the reference unloaded configuration of the body.…”

Section: Introductionmentioning

confidence: 99%

“…All rights reserved. and for more recent work see for example [5][6][7][8][9][10][11][12][13]. The plastic factor is viewed as the tensor field needed in order to release the residual stresses in the reference unloaded configuration of the body.…”

Section: Introductionmentioning

confidence: 99%

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Continuum kinematics with incompatible–compatible decomposition

Goldshtein,

Mariano,

Mucci

et al. 2023

Phil. Trans. R. Soc. A.

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We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities and non-injectivity of the deformations. In this framework, we construct an unambiguous decomposition into incompatible and compatible factors that includes the standard elastic–plastic decomposition in plasticity. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

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A nonlinear finite viscoelastic formulation relative to the viscous intermediate configuration applied to plants

Platen,

Pauls,

Anantheswar

et al. 2024

Numerical Meth Engineering

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In the contribution at hand, a new formulation for finite strain viscosity relative to the viscous intermediate configuration is presented. The evolution of the viscous deformations is based upon a new numerical approach, which allows for a consistent consideration of anisotropic finite strain viscoelasticity, according to the authors knowledge. A standard Maxwell model is used to describe viscous behaviour at finite deformations. Furthermore, the orthotropic Yeoh material model is extended to include a distinction between behaviour under tensile and compression loading. The proposed formulation is validated, and parameters of the model are identified by material tests on Sorghum bicolor plants. Subsequently, numerical examples are shown to demonstrate the capabilities of the model. In general, the proposed Yeoh material formulation is shown to accurately represent the inability of fibres to carry compression loading. Furthermore, the viscoelastic approach, developed relative to the viscous intermediate configuration, is demonstrated to be capable of producing plausible results. Additionally, the mechanical behaviour of Sorghum bicolor plants is simulated using the introduced formulation. The results show that the contribution at hand describes a novel methodology to simulate the viscoelastic behaviour of plant materials reliably.

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On the direct and reverse multiplicative decompositions of deformation gradient in nonlinear anisotropic anelasticity

Cited by 13 publications

References 75 publications

Accretion–ablation mechanics

Accretion–ablation mechanics

Continuum kinematics with incompatible–compatible decomposition

A nonlinear finite viscoelastic formulation relative to the viscous intermediate configuration applied to plants

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