Nonlinear mechanics of accretion

Sozio, Fabio; Yavari, Arash

doi:10.1007/s00332-019-09531-w

Cited by 33 publications

(16 citation statements)

References 44 publications

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“…Thus, the problem is correctly stated with respect to unknown parameters 0 p 0, 0 and a 0, 0 . The solution of the system (21) allows to obtain the actual outer radius of the first layer: r e 0, 0 = [(r e 0 ) 3 + a 0, 0 ] 1/3 . In the next step, when the second layer is deposited to the first assembly, just before the solidification we have values:…”

Section: Incompressible Materialsmentioning

confidence: 99%

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Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

2021

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The present paper is intended to show the close interrelationship between non-linear models of solids, produced with additive manufacturing, and models of solids with distributed defects. The common feature of these models is the incompatibility of local deformations. Meanwhile, in contrast with the conventional statement of the problems for solids with defects, the distribution for incompatible local deformations in additively created deformable body is not known a priori, and can be found from the solution of the specific evolutionary problem. The statement of the problem is related to the mechanical and physical peculiarities of the additive process. The specific character of incompatible deformations, evolved in additive manufactured solids, could be completely characterized within a differential-geometric approach by specific affine connection. This approach results in a global definition of the unstressed reference shape in non-Euclidean space. The paper is focused on such a formalism. One more common factor is the dataset which yields a full description of the response of a hyperelastic solid with distributed defects and a similar dataset for the additively manufactured one. In both cases, one can define a triple: elastic potential, gauged at stress-free state, and reference shape, and some specific field of incompatible relaxing distortion, related to the given stressed shape. Optionally, the last element of the triple may be replaced by some geometrical characteristics of the non-Euclidean reference shape, such as torsion, curvature, or, equivalently, as the density of defects. All the mentioned conformities are illustrated in the paper with a non-linear problem for a hyperelastic hollow ball.

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Section: Incompressible Materialsmentioning

confidence: 99%

“…The general approach is based on the non-Euclidean geometry of the reference shape. This approach has been considerably developed in recent works [19][20][21]. Special attention is paid to non-linear theory of surface growth [22].…”

Section: Introductionmentioning

confidence: 99%

Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

2021

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“…Using a diffusion law of the general form j R = −M(F, φ R ) Grad µ with equation (12) and, specializing to the present setting, we can express the velocity v as…”

Section: Sperical Problem Settingmentioning

confidence: 99%

“…Most available studies of surface growth are based on kinematic assumptions [3,4,[7][8][9][10][11]. In that context, Sozio and Yavari [12] have recently presented a geometric theory that captures the nonlinear mechanics and incompatibilities induced by accretion. To couple between the kinematics and the kinetic laws that drive the growth, while requiring conservation of mass, Abi-Akl et al [13], take advantage of the notion of a reference configuration that can exist in a higher dimensional space, as described for the special case of growth on a spherical substrate in [14], and generalize it to develop a framework for surface growth in a material system composed of two species (i.e.…”

Section: Introductionmentioning

confidence: 99%

Surface growth on a deformable spherical substrate

Abi-Akl

Cohen

2020

Mechanics Research Communications

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“…Recent works [16,17] formalize the notion of an evolving material manifold based on a non-Euclidean material connection. In the same spirit, a material manifold is introduced in [28,29] endowed with a growth-dependent metric tensor that characterizes the coupling between surface accretion and deformation.…”

Section: Introductionmentioning

confidence: 99%

A finite element method for modeling surface growth and resorption of deformable solids

Bergel

Papadopoulos

2021

Comput Mech

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This work explores a continuum-mechanical model for a body simultaneously undergoing finite deformation and surface growth/resorption. This is accomplished by defining the kinematics as well as the set of material points that constitute the domain of a physical body at a given time in terms of an evolving reference configuration. The implications of spatial and temporal discretization are discussed, and an extension of the Arbitrary Lagrangian–Eulerian finite element method is proposed to enforce the resulting balance laws on the grown/resorbed body in two spatial dimensions. Representative numerical examples are presented to highlight the predictive capabilities of the model and the numerical properties of the proposed solution method.

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Nonlinear mechanics of accretion

Cited by 33 publications

References 44 publications

Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

Surface growth on a deformable spherical substrate

A finite element method for modeling surface growth and resorption of deformable solids

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