2019
DOI: 10.1007/s00332-019-09531-w
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Nonlinear mechanics of accretion

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Cited by 33 publications
(16 citation statements)
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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%
See 1 more Smart Citation
“…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%
“…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%
“…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%
“…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%