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Surface growth

arash_yavari's picture

Accretion-Ablation Mechanics

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 and Yavari (2019). 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.

arash_yavari's picture

Finite Extension of Accreting Nonlinear Elastic Solid Circular Cylinders

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.

arash_yavari's picture

Accretion Mechanics of Nonlinear Elastic Circular Cylindrical Bars Under Finite Torsion

In this paper we formulate the initial-boundary value problem of accreting circular cylindrical bars under finite torsion. It is assumed that the bar grows as a result of printing stress-free cylindrical layers on its boundary while it is under a time-dependent torque (or a time-dependent twist) and is free to deform axially. In a deforming body, accretion induces eigenetrains, and consequently residual stresses. We formulate the anelasticity problem by first constructing the natural Riemannian metric of the growing bar.

Kiana Naghibzadeh's picture

Accretion and Ablation in Deformable Solids with an Eulerian Description: Examples using the Method of Characteristics

Dear colleagues,

We invite you to see the preprint of our new paper "Accretion and Ablation in Deformable Solids with an Eulerian Description: Examples using the Method of Characteristics" which will appear in Mathematics and Mechanics of Solids. Recent work has proposed an Eulerian approach to the surface growth problem, enabling the side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid. 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. Here, we applied the method of characteristics to solve concrete simplified problems motivated by surface growth in biomechanics and manufacturing (https://journals.sagepub.com/doi/10.1177/10812865211054573)

peppezurlo's picture

Nonlinear elasticity of incompatible surface growth

In this manuscript with Lev Truskinovsky, we developed a new nonlinear theory of large-strain incompatible surface growth. Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems, surface growth is usually accompanied by the development of geometrical incompatibility leading to residual stresses and triggering various instabilities. Here we developed a nonlinear theory of incompatible surface growth which quantitatively linkes deposition protocols with post-growth states of stress.

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