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Nonlinear elasticity

MMSLab-CNR's picture

NOSA-ITACA code version 1.1b is now available

The improved version of NOSA-ITACA is now available at www.nosaitaca.it/software/. A more friendly monitor analysis has been implemented. Bugs related to card creation are now fixed. At www.nosaitaca.it/software/ you can find also some tutorials that will guide you through the use of the code. Enjoy !

MMSLab-CNR's picture

NOSA-ITACA code now runs on UBUNTU 18.04

Running NOSA on Ubuntu 18.04 is not (yet) officially supported, but you may use the package for Ubuntu 16.04, as indicated at

http://www.nosaitaca.it/software/

See also the prevoius post about it ! Enjoy !

 

Arash_Yavari's picture

Nonlinear and Linear Elastodynamic Transformation Cloaking

In this paper we formulate the problems of nonlinear and linear elastodynamic transformation cloaking in a geometric framework. In particular, it is noted that a cloaking transformation is neither a spatial nor a referential change of frame (coordinates); a cloaking transformation maps the boundary-value problem of an isotropic and homogeneous elastic body (virtual problem) to that of an anisotropic and inhomogeneous elastic body with a hole surrounded by a cloak that is to be designed (physical problem).

MMSLab-CNR's picture

Modal analysis of historical masonry structures: Linear perturbation and software benchmarking

https://www.sciencedirect.com/science/article/pii/S0950061818322116 The mechanical behavior of masonry materials has a common feature: a nonlinear behavior with high compressive strength and very low tensile strength. As a consequence, old masonry buildings generally present cracks due to permanent loads and/or accidental events. Therefore, the characterization of the global dynamic behavior of masonry structures should take into account the presence of existing cracks.

MMSLab-CNR's picture

NOSA-ITACA: a free finite element software for structural analysis

NOSA-ITACA is a software product of the Mechanics of Materials and Structures Laboratory of ISTI-CNR, distributed via the http://www.nosaitaca.it/software/ website.
The package includes SALOME v8.3.0, and is available for Ubuntu 14.04 and 16.04.
NOSA-ITACA enables you to conduct both linear and nonlinear static analyses and modal analyses.
NOSA-ITACA can be used to study the static behavior of masonry buildings of historic and architectural interest and model the effectiveness of strengthening operations.

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.

Postdoc Positions Nonlinear Elasticty, Continuum Mechanics, Chile

The 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.

Sundaraelangovan selvam's picture

Validation of Numerical (INCS) method for Elastic wave case

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Dear mechanician,

Arash_Yavari's picture

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

In 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.

Arash_Yavari's picture

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

The 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.

Arash_Yavari's picture

Small-on-Large Geometric Anelasticity

In 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.

Arash_Yavari's picture

Hilbert Complexes of Nonlinear Elasticity

We 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.

Arash_Yavari's picture

Nonlinear Elasticity in a Deforming Ambient Space

In 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.

Amit Acharya's picture

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

Amit 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.

 

 

 

Arash_Yavari's picture

A Geometric Theory of Nonlinear Morphoelastic Shells

We 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.

Arash_Yavari's picture

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

The 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.

Payam Soltani's picture

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

 By :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 

liuliping's picture

Energy formulations of nonlinear elasticity including electric / magnetic couplings

Equilibrium theories for a continuum body may be formulated by either of the
following the classic paradigms: (1) We begin with the stress postulation (Cauchy’s formulation) and write down the kinematics, conservation laws, and
constitutive relations. In this way, one can obtain a system of field equations
which, presumably, can be solved upon specifying boundary conditions and
determine the equilibrium state of the body. (2) A second way is to start from
the energy postulation (Green’s

Arash_Yavari's picture

PhD Position in Geometric Mechanics at Georgia Tech

I 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.

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

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Dear all iMechanicians Smile,

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.

skumaar's picture

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

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.

Linear Elastic material behaves as Neo-Hookean in ANSYS?

I 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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