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# Nonlinear elasticity

## Nonlinear elasticity of incompatible surface growth

Fri, 2019-01-18 06:49 - peppezurloIn 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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## Postdoc Positions Nonlinear Elasticty, Continuum Mechanics, Chile

Fri, 2018-06-08 11:21 - Roger BustamanteThe Superior Councils for Science and Technological Development of Chile (CONICYT) will call soon for the FONDECYT Postdoctoral Grants Competition.

The available grants are for 2 or 3 years. The applicants must have obtained their Doctorate degrees approximately not before January of 2015 and after the end of September of 2018 (the exact dates will appear in the page of the agency later on).

If there is a person interested in doing research in nonlinear elasticity and continuum mechanics with me as a sponsoring researcher, please feel free to contact me for further enquiries (rogbusta@ing.uchile.cl). My recent research interests are on the developing of some new constitutive models for elastic and inelastic bodies (especially for rocks), nonlinear magneto and electro-elasticity and also on the modelling of residual stresses in arteries. I do mostly theoretical work.

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## How to define the spatial frequency in Matlab?

Tue, 2018-01-30 10:49 - Sundaraelangova...- Read more about How to define the spatial frequency in Matlab?
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## Validation of Numerical (INCS) method for Elastic wave case

Tue, 2018-01-09 09:27 - Sundaraelangova...Dear mechanician,

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## On the Stress Field of a Nonlinear Elastic Solid Torus with a Toroidal Inclusion

Thu, 2016-12-22 19:24 - Arash_YavariIn this paper we analyze the stress field of a solid torus made of an incompressible isotropic solid with a toroidal inclusion that is concentric with the solid torus and has a uniform distribution of pure dilatational finite eigenstrains. We use a perturbation analysis and calculate the residual stresses to the first order in the *thinness* ratio (the ratio of the radius of the generating circle and the overall radius of the solid torus). In particular, we show that the stress field inside the inclusion is not uniform.

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## The Anelastic Ericksen's Problem: Universal Eigenstrains and Deformations in Compressible Isotropic Elastic Solids

Mon, 2016-11-07 18:51 - Arash_YavariThe elastic Ericksen's problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains.

## Small-on-Large Geometric Anelasticity

Wed, 2016-10-12 10:19 - Arash_YavariIn this paper we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems.

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## Hilbert Complexes of Nonlinear Elasticity

Mon, 2016-10-10 15:32 - Arash_YavariWe introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors.

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## Nonlinear Elasticity in a Deforming Ambient Space

Fri, 2016-05-27 13:02 - Arash_YavariIn this paper we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space.

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## Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions

Sun, 2016-05-22 20:23 - Amit AcharyaAmit Acharya, Gui-Qiang Chen, Siran Li, Marshall Slemrod, and Dehua Wang

(To appear in Archive for Rational Mechanics and Analysis)

We are concerned with underlying connections between fluids,

elasticity, isometric embedding of Riemannian manifolds, and the existence of

wrinkled solutions of the associated nonlinear partial differential equations. In

this paper, we develop such connections for the case of two spatial dimensions,

and demonstrate that the continuum mechanical equations can be mapped into

a corresponding geometric framework and the inherent direct application of

the theory of isometric embeddings and the Gauss-Codazzi equations through

examples for the Euler equations for fluids and the Euler-Lagrange equations

for elastic solids. These results show that the geometric theory provides an

avenue for addressing the admissibility criteria for nonlinear conservation laws

in continuum mechanics.

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## A Geometric Theory of Nonlinear Morphoelastic Shells

Thu, 2016-03-17 11:15 - Arash_YavariWe formulate a geometric theory of nonlinear morphoelastic shells that can model the time evolution of residual stresses induced by bulk growth. We consider a thin body and idealize it by a representative orientable surface. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell (material manifold). We consider the evolution of both the first and second fundamental forms in the material manifold by considering them as dynamical variables in the variational problem.

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## The Geometry of Discombinations and its Applications to Semi-Inverse Problems in Anelasticity

Wed, 2014-06-11 10:46 - Arash_YavariThe geometric formulation of continuum mechanics provides a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects, or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometric structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space.

## Nonlinear free and forced vibration analysis of a single-walled carbon nanotube using shell model

Mon, 2013-11-04 07:00 - Payam SoltaniBy :Payam SOLTANI, J SABERIAN, R BAHRAMIAN, A FARSHIDIANFAR

In this Paper, the nonlinear free and force vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is

investigated based on von Karman’s geometric nonlinearity. The SWCNT described as an individual shell and the Donnell’s

equations of cylindrical shells are used to obtain the governing equations. The Galerkin's procedure is used to discretized partial

## Energy formulations of nonlinear elasticity including electric / magnetic couplings

Tue, 2013-09-24 11:32 - liuliping- Read more about Energy formulations of nonlinear elasticity including electric / magnetic couplings
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## Giant and universal magneto-electric coupling in soft materials

Mon, 2013-09-23 19:37 - liuliping- Read more about Giant and universal magneto-electric coupling in soft materials
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## PhD Position in Geometric Mechanics at Georgia Tech

Sun, 2013-09-22 14:34 - Arash_YavariI am looking for a new Ph.D. student to work on discretization of nonlinear elasticity using geometric and topological ideas. Requirements for this position are a strong background in solid mechanics and some background in differential geometry and analysis. If interested please email me your CV.

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## Is it possible to model nonlinear elasticity in ANSYS with SOLID 18x elements?

Sun, 2013-02-24 16:50 - FreemanDear all iMechanicians ,

Since several days I am trying to simulate a granular material very similar to sand. The uniaxial compression test performed to the material shows a nonlinear elasticity behavior during the unloading curve.

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## Joint Post-doctoral position: Masdar Institute (MI) and MIT

Fri, 2013-02-15 04:01 - skumaar
Applications are invited for the position of

Post‐doctoral Research

Fellow as part of a joint research project between Masdar Institute of Science

& Technology and Massachusetts Institute of Technology (MIT). Details of the position are given in the attachement.

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## Linear Elastic material behaves as Neo-Hookean in ANSYS?

Mon, 2013-02-11 12:23 - BreslavskyI solve the static bending problem for thin plate under uniformly distributed load acting orthogonally to the plate. I

need the solution up to quite large values of deflection (100

thicknesses, which implies the strains about 100%), but I want to take

into account only geometric nonlinearity and not the material

nonlinearity. I use elements which support large strains (SHELL181,

SHELL281). The software is ANSYS Mechanical APDL 12 and 13. Also, I use "Large displacement static" option for

solution.

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## Compatibility Equations of Nonlinear Elasticity for Non-Simply-Connected Bodies

Sun, 2013-02-03 11:15 - Arash_YavariCompatibility equations of elasticity are almost 150 years old. Interestingly they do not seem to have been rigorously studied for non-simply-connected bodies to this date. In this paper we derive necessary and sufficient compatibility equations of nonlinear elasticity for arbitrary non-simply-connected bodies when the ambient space is Euclidean. For a non-simply-connected body, a measure of strain may not be compatible even if the standard compatibility equations ("bulk" compatibility equations) are satisfied.

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## Jacobian matrix of Mooney-Rivlin model

Sun, 2012-09-02 15:56 - augustusHi,

does anyone know where I can find the analytical expressions for the components

of the Jacobian matrix of the Mooney-Rivlin model.

I know the compact form of the matrix, with the tensor products, deviators etc,

but I'm looking for the explicit expressions of each component of the matrix.

many thanks!

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## Periodic Solution for Nonlinear Vibration of a Fluid- Conveying Carbon Nanotube

Fri, 2011-11-11 09:21 - Payam Soltani- Read more about Periodic Solution for Nonlinear Vibration of a Fluid- Conveying Carbon Nanotube
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## Nonlinear free and forced vibration analysis of a single-walled carbon nanotube using shell model

Fri, 2011-10-07 23:39 - payam.soltaniPayam Soltani, J. Saberian, R. Bahramian, and A. Farshidianfar

http://fundamentaljournals.org/ijfps/archive.html#A14

In this Paper, the nonlinear free and force vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is

investigated based on von Karman’s geometric nonlinearity. The SWCNT described as an individual shell and the Donnell’s

equations of cylindrical shells are used to obtain the governing equations. The Galerkin's procedure is used to discretized partial

## Characterization of residual stress fields in nonlinear elasticity; a question posed by Sebastien Turcaud

Wed, 2010-12-22 10:07 - Amit Acharya## Three Postdoctoral positions at the University of Oxford: Brain modelling, soft-tissues, and water filtration

Sun, 2010-12-12 06:33 - gorielyThe Mathematical Institute at Oxford is advertising three post-doctoral positions within the Oxford Centre for Collaborative Applied Mathematics for(ideally) a 1st April 2011 start. The project titles (with links for more information) are:

1. Brain Mechanics, Cortex Folding, and Pattern Formation in Growing Tissues.

http://www.maths.ox.ac.uk/node/1405

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