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Nonlinear elasticity

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

Universal Deformations in Inhomogeneous Isotropic Nonlinear Elastic Solids

Universal (controllable) deformations of an elastic solid are those deformations that can be maintained for all possible strain-energy density functions and suitable boundary tractions. Universal deformations have played a central role in nonlinear elasticity and anelasticity. However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen. In this paper, we extend Ericksen's analysis of universal deformations to inhomogeneous compressible and incompressible isotropic solids.

arash_yavari's picture

Universal Deformations in Anisotropic Nonlinear Elastic Solids

Universal deformations of an elastic solid are deformations that can be achieved for all possible strain-energy density functions and suitable boundary conditions. They play a central role in nonlinear elasticity and their classification has been mostly accomplished for isotropic solids following Ericksen's seminal work. Here, we address the same problem for transversely isotropic, orthotropic, and monoclinic solids.

arash_yavari's picture

On Eshelby's Inclusion Problem in Nonlinear Anisotropic Elasticity

The recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby's inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of  combined finite radial, azimuthal, axial, and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed.

arash_yavari's picture

Transformation Cloaking in Elastic Plates

In this paper we formulate the problem of elastodynamic transformation cloaking for Kirchhoff-Love plates and elastic plates with both in-plane and out-of-plane displacements. A cloaking transformation maps the boundary-value problem of an isotropic and homogeneous elastic plate (virtual problem) to that of an anisotropic and inhomogeneous elastic plate with a hole surrounded by a cloak that is to be designed (physical problem). For Kirchhoff-Love plates, the governing equation of the virtual plate is transformed to that of the physical plate up to an unknown scalar field.

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.

MMSLab-CNR's picture

NOSA-ITACA code 1.1c is now available

The new version of the code presents an improved and more intuitive
management of the subroutine and an easier use of Job monitor dialogue.
Enjoy it

MMSLab-CNR's picture

NOSA-ITACA code version 1.1b is now available

The improved version of NOSA-ITACA is now available at A more friendly monitor analysis has been implemented. Bugs related to card creation are now fixed. At 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

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 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 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 ( 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

Choose a channel featured in the header of iMechanica: 

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.


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