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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 (

arash_yavari's picture

Nonlinear Mechanics of Thermoelastic Accretion

In this paper, we formulate a theory for the coupling of accretion mechanics and thermoelasticity. We present an analytical formulation of the thermoelastic accretion of an infinite cylinder and of a two-dimensional block.

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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