Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies
TLDR
In this article, the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework are formulated, where the body grows as a result of addition of new material on part of its boundary.Abstract:
In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.read more
Citations
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Mathematical Foundations Of Elasticity
TL;DR: The mathematical foundations of elasticity is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
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Nonlinear mechanics of accretion
Fabio Sozio,Arash Yavari +1 more
TL;DR: A geometric nonlinear theory of the mechanics of accretion of an accreting body is formulated and the incompatibilities induced by accretion are studied through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body.
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Nonlinear elasticity of incompatible surface growth.
Lev Truskinovsky,Giuseppe Zurlo +1 more
TL;DR: This development reveals the shortcomings of the linearized theory of incompatible surface growth, in particular its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities.
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Nonlinear Elastic Inclusions in Anisotropic Solids
Ashkan Golgoon,Arash Yavari +1 more
TL;DR: In this article, the authors studied the stress and deformation fields generated by nonlinear inclusions with finite eigenstrains in anisotropic solids and showed that the stress field in a spherical inclusion with uniform pure dilatational eigenstrain is uniform and hydrostatic.
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Inelastic surface growth
Giuseppe Zurlo,Lev Truskinovsky +1 more
TL;DR: In this paper, the authors extend the recently proposed stress-space-centered theory of surface growth (PRL 119, 048001, 2017) by shifting the focus towards growth induced strains.
References
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Book
Non-Linear Elastic Deformations
TL;DR: In this paper, the influence of non-linear elastic systems on a simple geometric model for elastic deformations is discussed, and the authors propose a planar and spatial euler introduction to nonlinear analysis.
Book
Mathematical foundations of elasticity
TL;DR: In this article, the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis are discussed. But the authors do not discuss the application of functional analysis to the problem of elasticity.
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Stress-dependent finite growth in soft elastic tissues
TL;DR: A general continuum formulation for finite volumetric growth in soft elastic tissues is proposed and it is shown that transmurally uniform pure circumferential growth, which may be similar to eccentric ventricular hypertrophy, changes the state of residual stress in the heart wall.
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Continuous Distributions of Dislocations: A New Application of the Methods of Non-Riemannian Geometry
TL;DR: In this article, the geometry of the continuously dislocated crystal is most conveniently analyzed by treating the manifold of lattice points in the final state as a non-Riemannian one with a single asymmetric connexion.
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Growth and instability in elastic tissues
TL;DR: In this article, the effect of growth on the stability of growing elastic materials is studied and numerical and analytical methods are combined to obtain explicit stability results and to identify the role of mechanical and geometric effects.