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  • Stochastic Approach to the Solution of Boussinesq-Like Problems in Discrete Media
    J. Elast. (IF 2.372) Pub Date : 2020-07-23
    Ignacio G. Tejada

    A vertical surface load acting on a half-space made of discrete and elastic particles is supported by a network of force chains that changes with the specific realization of the packing. These force chains can be transformed into equivalent stress fields, but the obtained values are usually different from those predicted by the unique solution of the corresponding boundary value problem. In this research

  • The Asymptotically Sharp Geometric Rigidity Interpolation Estimate in Thin Bi-Lipschitz Domains
    J. Elast. (IF 2.372) Pub Date : 2020-07-23
    D. Harutyunyan

    This work is part of a program of development of asymptotically sharp geometric rigidity estimates for thin domains. A thin domain in three dimensional Euclidean space is roughly a small neighborhood of regular enough two dimensional compact surface. We prove an asymptotically sharp geometric rigidity interpolation inequality for thin domains with little regularity. In contrast to that celebrated Friesecke

  • Maximum-Entropy Based Estimates of Stress and Strain in Thermoelastic Random Heterogeneous Materials
    J. Elast. (IF 2.372) Pub Date : 2020-07-23
    Maximilian Krause, Thomas Böhlke

    Mean-field methods are a common procedure for characterizing random heterogeneous materials. However, they typically provide only mean stresses and strains, which do not always allow predictions of failure in the phases since exact localization of these stresses and strains requires exact microscopic knowledge of the microstructures involved, which is generally not available. In this work, the maximum

  • Recovering the Normal Form and Symmetry Class of an Elasticity Tensor
    J. Elast. (IF 2.372) Pub Date : 2020-07-23
    S. Abramian, B. Desmorat, R. Desmorat, B. Kolev, M. Olive

    We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor. We produce a rotation which brings an Elasticity tensor onto its normal form, given its components in any orthonormal frame, and this for any tensor of any symmetry class. Our methodology relies on the use of specific covariants and on the geometric characterization of each symmetry class using these

  • Distances of Stiffnesses to Symmetry Classes
    J. Elast. (IF 2.372) Pub Date : 2020-07-23
    Oliver Stahn, Wolfgang H. Müller, Albrecht Bertram

    For a given elastic stiffness tetrad an algorithm is provided to determine the distance of this particular tetrad to all tetrads of a prescribed symmetry class. If the particular tetrad already belongs to this class then the distance is zero and the presentation of this tetrad with respect to the symmetry axes can be obtained. If the distance turns out to be positive, the algorithm provides a measure

  • Bond-Based Peridynamics Does Not Converge to Hyperelasticity as the Horizon Goes to Zero
    J. Elast. (IF 2.372) Pub Date : 2020-07-23
    J. C. Bellido, J. Cueto, C. Mora-Corral

    Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in the reference and deformed configurations. It is known how to calculate the \(\Gamma \)-limit of this model when the horizon (maximum interaction distance between the particles) tends to zero, and the limit turns out to be

  • U=C1/2${\mathbf{U}} = \mathbf{C}^{1/2}$ and Its Invariants in Terms of C$\mathbf{C}$ and Its Invariants
    J. Elast. (IF 2.372) Pub Date : 2020-06-11
    N. H. Scott

    We consider \(N\times N\) tensors for \(N= 3,4,5,6\). In the case \(N=3\), it is desired to find the three principal invariants \(i_{1}, i_{2}, i_{3}\) of \({\mathbf{U}}\) in terms of the three principal invariants \(I_{1}, I_{2}, I_{3}\) of \({\mathbf{C}}={\mathbf{U}}^{2}\). Equations connecting the \(i_{\alpha }\) and \(I_{\alpha }\) are obtained by taking determinants of the factorisation $$ \lambda

  • On Structural Theories for Ionic Polymer Metal Composites: Balancing Between Accuracy and Simplicity
    J. Elast. (IF 2.372) Pub Date : 2020-06-10
    Alain Boldini, Lorenzo Bardella, Maurizio Porfiri

    Ionic polymer metal composites (IPMCs) are soft electroactive materials that are finding increasing use as actuators in several engineering domains, where there is a need of large compliance and low activation voltage. Similar to traditional sandwich structures, an IPMC comprises a hydrated ionomer core that is sandwiched by two stiffer electrodes. The application of a voltage across the electrodes

  • Homogenization of Perforated Elastic Structures
    J. Elast. (IF 2.372) Pub Date : 2020-06-05
    Georges Griso, Larysa Khilkova, Julia Orlik, Olena Sivak

    The paper is dedicated to the asymptotic behavior of \(\varepsilon\)-periodically perforated elastic (3-dimensional, plate-like or beam-like) structures as \(\varepsilon \to 0\). In case of plate-like or beam-like structures the asymptotic reduction of dimension from \(3D\) to \(2D\) or \(1D\) respectively takes place. An example of the structure under consideration can be obtained by a periodic repetition

  • On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity
    J. Elast. (IF 2.372) Pub Date : 2020-05-29
    M. Olive, B. Desmorat, B. Kolev, R. Desmorat

    We formulate necessary and sufficient conditions for a unit vector \(\pmb{\nu }\) to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four in the components of \(\pmb{\nu }\). Compared to Cowin–Mehrabadi conditions, this is an improvement, since these equations involve only the normal vector

  • Dynamics of Two Linearly Elastic Bodies Connected by a Heavy Thin Soft Viscoelastic Layer
    J. Elast. (IF 2.372) Pub Date : 2020-05-29
    Elena Bonetti, Giovanna Bonfanti, Christian Licht, Riccarda Rossi

    In this paper, we extend the asymptotic analysis in (Licht et al. in J. Math. Pures Appl. 99:685–703, 2013) performed, in the framework of small strains, on a structure consisting of two linearly elastic bodies connected by a thin soft nonlinear Kelvin–Voigt viscoelastic adhesive layer to the case in which the total mass of the layer remains strictly positive as its thickness tends to zero. We obtain

  • Gel Debonding from a Rigid Substrate
    J. Elast. (IF 2.372) Pub Date : 2020-05-29
    M. Carme Calderer, Carlos Garavito, Duvan Henao, Lorenzo Tapia, Suping Lyu

    We consider the problem of debonding of a thin gel domain from a rigid substrate. Starting with a variational approach involving the total energy of a gel, we formulate the boundary value problem of the governing equations in two-space dimensions. We consider the case that the aspect ratio, \(\eta \), the quotient of the thickness of the film with respect to its length, is very small. We assume that

  • Derivation of a Homogenized Bending–Torsion Theory for Rods with Micro-Heterogeneous Prestrain
    J. Elast. (IF 2.372) Pub Date : 2020-05-29
    Robert Bauer, Stefan Neukamm, Mathias Schäffner

    In this paper we investigate rods made of nonlinearly elastic, composite–materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that is small compared to the length of the rod. As a main result we derive a homogenized bending–torsion theory for rods as \(\Gamma \)-limit from 3D nonlinear elasticity by simultaneous homogenization and dimension reduction

  • An Approach to Isotropic Tensor Functions and Their Derivatives Via Omega Matrix Calculus
    J. Elast. (IF 2.372) Pub Date : 2020-05-29
    Antônio Francisco Neto

    In this work we show how to obtain a closed form expression of any isotropic tensor function \(F\left (\boldsymbol{A}\right )\) and their associated derivatives with \(\boldsymbol{A}\) a second order tensor in a finite dimensional space. Our approach is based on a recent work of the author (SIAM Rev. 62(1):264–280, 2020) extending the Omega operator calculus, originally devised by MacMahon to describe

  • Indentation of a Periodically Layered, Planar, Elastic Half-Space
    J. Elast. (IF 2.372) Pub Date : 2020-05-07
    Deepak Sachan, Ishan Sharma, T. Muthukumar

    We investigate indentation by a smooth, rigid indenter of a two-dimensional half-space comprised of periodically arranged linear-elastic layers with different constitutive responses. Identifying the half-space’s material parameters as periodic functions in space, we utilize the theory of periodic homogenization to approximate the layered heterogeneous material by a linear-elastic, homogeneous, but

  • An Equivalent Indentation Method for the External Crack with a Dugdale Cohesive Zone
    J. Elast. (IF 2.372) Pub Date : 2020-05-07
    Fan Jin, Donghua Yue

    An equivalent indentation method is developed for the external crack problem with a Dugdale cohesive zone in the both axisymmetric and two-dimensional (2D) cases. This is achieved based on the principle of superposition by decomposing the original problem into two simple boundary value problems, with one considering action of a constant traction within the cohesive zone, and the other corresponding

  • On the Orientation Average Based on Central Orientation Density Functions for Polycrystalline Materials
    J. Elast. (IF 2.372) Pub Date : 2019-11-25
    Mauricio Fernández

    The present work continues the investigation first started by Lobos et al. (J. Elast. 128(1):17–60, 2017) concerning the orientation average of tensorial quantities connected to single-crystal physical quantities distributed in polycrystals. In Lobos et al. (J. Elast. 128(1):17–60, 2017), central orientation density functions were considered in the orientation average for fourth-order tensors with

  • Identification of Scale-Independent Material Parameters in the Relaxed Micromorphic Model Through Model-Adapted First Order Homogenization
    J. Elast. (IF 2.372) Pub Date : 2019-10-16
    Patrizio Neff, Bernhard Eidel, Marco Valerio d’Agostino, Angela Madeo

    We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new procedure involving the concept of apparent material stiffness of a unit-cell under affine Dirichlet boundary conditions and Neumann’s principle on the overall representation

  • Topological Defects and Metric Anomalies as Sources of Incompatibility for Piecewise Smooth Strain Fields
    J. Elast. (IF 2.372) Pub Date : 2019-10-04
    Animesh Pandey, Anurag Gupta

    The incompatibility of linearized piecewise smooth strain field, arising out of volumetric and surface densities of topological defects and metric anomalies, is investigated. First, general forms of compatibility equations are derived for a piecewise smooth strain field, defined over a simply connected domain, with either a perfectly bonded or an imperfectly bonded interface. Several special cases

  • Boundary Value Problems for Euler-Bernoulli Planar Elastica. A Solution Construction Procedure
    J. Elast. (IF 2.372) Pub Date : 2019-11-25
    Josu J. Arroyo, Óscar J. Garay, Álvaro Pámpano

    We consider the problem of finding a curve minimizing the Bernoulli bending energy among planar curves of the same length, joining two fixed points and possibly carrying orientations at the endpoints (Euler elastica). We focus on the problem of constructing closed form elasticae for given boundary data and show that, rather than employing complicated numerical algorithms, it suffices to use easily

  • Effective Description of Anisotropic Wave Dispersion in Mechanical Band-Gap Metamaterials via the Relaxed Micromorphic Model
    J. Elast. (IF 2.372) Pub Date : 2019-10-16
    Marco Valerio d’Agostino, Gabriele Barbagallo, Ionel-Dumitrel Ghiba, Bernhard Eidel, Patrizio Neff, Angela Madeo

    In this paper the relaxed micromorphic material model for anisotropic elasticity is used to describe the dynamical behavior of a band-gap metamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy, Cosserat, second gradient, classical Mindlin–Eringen micromorphic etc.), the relaxed micromorphic model is endowed to capture the main microscopic and macroscopic characteristics of the

  • Discrete Cosserat Rod Kinematics Constructed on the Basis of the Difference Geometry of Framed Curves—Part I: Discrete Cosserat Curves on a Staggered Grid
    J. Elast. (IF 2.372) Pub Date : 2019-07-25
    Joachim Linn

    The theory of Cosserat rods provides versatile models to simulate large spatial deformations of slender flexible structures. As the strain measures of the mechanical theory are given in terms of the differential invariants of Cosserat curves, the kinematics of Cosserat rods is closely related to the differential geometry of framed curves. We utilize ideas from the difference geometry of framed curves

  • On Purely Mechanical Simple Kinematic Internal Constraints
    J. Elast. (IF 2.372) Pub Date : 2019-09-02
    Adam Zdunek

    The classic purely mechanical approach to materials with simple kinematic internal constraints is supplemented. A right Cauchy–Green tensor which locally represents the kinematically admissible restricted domain of a finite hyperelastic stress response function is constructed explicitly. It satisfies all imposed constraints identically. It is obtained by a procedure which annihilates the banned modes

  • Non-local Thermoelasticity Based on Equilibrium Statistical Thermodynamics
    J. Elast. (IF 2.372) Pub Date : 2019-07-22
    Giacomo Po, Nikhil Chandra Admal, Bob Svendsen

    The purpose of this work is the formulation of energetic constitutive relations for thermoelasticity of non-simple materials based on atomistic considerations and equilibrium statistical thermodynamics (EST). In particular, both (unrestricted) canonical, and (restricted) quasi-harmonic, formulations are considered. In the canonical case, (spatial) non-locality results from relaxation of the assumption

  • Homogenization Approach and Bloch-Floquet Theory for Band-Gap Prediction in 2D Locally Resonant Metamaterials
    J. Elast. (IF 2.372) Pub Date : 2019-07-25
    Claudia Comi, Jean-Jacques Marigo

    This paper provides a detailed comparison of the two-scale homogenization method and of the Bloch-Floquet theory for the determination of band-gaps in locally resonant metamaterials. A medium composed by a stiff matrix with soft inclusions with 2D periodicity is considered and the equivalent mass density of the homogenized medium is explicitly obtained both for in-plane and out-of-plane wave propagation

  • Exponential Stability in Three-Dimensional Type III Thermo-Porous-Elasticity with Microtemperatures
    J. Elast. (IF 2.372) Pub Date : 2019-09-02
    Antonio Magaña, Ramón Quintanilla

    We study the time decay of the solutions for the type III thermoelastic theory with microtemperatures and voids. We prove that, under suitable conditions for the constitutive tensors, the solutions decay exponentially. This fact is in somehow striking because it differs from the behaviour of the solutions in the classical model of thermoelasticity with microtemperatures and voids, where the exponential

  • The Bending of Beams in Finite Elasticity
    J. Elast. (IF 2.372) Pub Date : 2019-08-29
    Luca Lanzoni, Angelo Marcello Tarantino

    In this paper the analysis for the anticlastic bending under constant curvature of nonlinear solids and beams, presented by Lanzoni, Tarantino (J. Elast. 131:137–170, 2018), is extended and further developed for the class of slender beams. Following a semi-inverse approach, the problem is studied by a three-dimensional kinematic model for the longitudinal inflexion, which is based on the hypothesis

  • Rayleigh Waves in Isotropic Viscoelastic Solid Half-Space
    J. Elast. (IF 2.372) Pub Date : 2019-10-01
    M. D. Sharma

    Propagation of harmonic plane waves is considered in a linear viscoelastic isotropic medium. Complex-valued velocities define the attenuated propagation of two bulk waves in this medium. The ratio of these velocities, as a complex-valued parameter, decides the number of Rayleigh waves in the medium. An empirical relation is derived to bifurcate the domain of this parameter, which identifies the necessary

  • The Complementing and Agmon’s Conditions in Finite Elasticity
    J. Elast. (IF 2.372) Pub Date : 2019-06-18
    Henry C. Simpson

    We consider the complementing condition and Agmon’s condition for linearized elasticity in two-dimensions. With an elasticity tensor \(\mathsf{C}\) derived from a compressible, isotropic stored energy \(W\), linearized about a homogeneous deformation \(\mathbf{f}_{0}\), we apply the complementing and Agmon’s conditions to a traction portion of the surface of a body with unit normal \(\mathbf{n}\).

  • Energy Minimising Configurations of Pre-strained Multilayers
    J. Elast. (IF 2.372) Pub Date : 2020-03-10
    Miguel de Benito Delgado, Bernd Schmidt

    We investigate energetically optimal configurations of thin structures with a pre-strain. Depending on the strength of the pre-strain we consider a whole hierarchy of effective plate theories with a spontaneous curvature term, ranging from linearised Kirchhoff to von Kármán to linearised von Kármán theories. While explicit formulae are available in the linearised regimes, the von Kármán theory turns

  • Extension-Torsion-Inflation Coupling in Compressible Magnetoelastomeric Thin Tubes with Helical Magnetic Anisotropy
    J. Elast. (IF 2.372) Pub Date : 2020-03-09
    Darius Diogo Barreto, Ajeet Kumar, Sushma Santapuri

    An axisymmetric and axially homogenous variational formulation is presented for coupled extension-torsion-inflation deformation in compressible magnetoelastomeric tubes in the presence of azimuthal and axial magnetic fields. The tube’s material is assumed to have a preferred magnetization direction which lie in the radial plane but at an angle from the tube’s axial direction - this imparts helical

  • On the Wave Propagation in the Thermoelasticity Theory with Two Temperatures
    J. Elast. (IF 2.372) Pub Date : 2020-03-06
    Ciro D’Apice, Vittorio Zampoli, Stan Chiriţă

    This paper considers the thermoelastic theory with two temperatures that involves higher gradients of thermal and mechanical effects. The wave propagation question is addressed within the class of waves of assigned wavelength. Considering harmonic in time wave solutions, it is found that the transverse waves are undamped in time and non-dispersive, and they are not altered by the thermal effects. Conversely

  • A Hyperelastic Model for Soft Polymer Foam Including Micromechanics of Porosity
    J. Elast. (IF 2.372) Pub Date : 2019-05-14
    M. B. Rubin, L. Dorfmann

    This paper proposes a new isotropic hyperelastic model for polymer foam, which explicitly models the micromechanical influence of changes in porosity. The foam is treated as a matrix of compressible solid material with evacuated pores that cause soft response for low pressures. In its general form, the strain energy of the foam depends on the strain energy of the solid material and on the porosity

  • Equilibrium Paths for von Mises Trusses in Finite Elasticity
    J. Elast. (IF 2.372) Pub Date : 2019-03-27
    Matteo Pelliciari, Angelo Marcello Tarantino

    This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress

  • Finite Third-Order Gradient Elastoplasticity and Thermoplasticity
    J. Elast. (IF 2.372) Pub Date : 2019-04-17
    Jörg Christian Reiher, Albrecht Bertram

    A general format for a third-order gradient elasto-plasticity under finite deformations is suggested. The basic assumptions are the principle of Euclidean invariance and the isomorphy of the elastic behaviour before and after yielding. The format allows for isotropy and anisotropy. Both the elastic and the plastic laws include the second and third deformation gradient. The starting point is an objective

  • Generalized Euclidean Distances for Elasticity Tensors
    J. Elast. (IF 2.372) Pub Date : 2019-06-24
    Léo Morin, Pierre Gilormini, Katell Derrien

    The aim of this short paper is to provide, for elasticity tensors, generalized Euclidean distances that preserve the property of invariance by inversion. First, the elasticity law is expressed under a non-dimensional form by means of a gauge, which leads to an expression of elasticity (stiffness or compliance) tensors without units. Based on the difference between functions of the dimensionless tensors

  • Growth and Non-Metricity in Föppl-von Kármán Shells
    J. Elast. (IF 2.372) Pub Date : 2020-02-27
    Ayan Roychowdhury, Anurag Gupta

    The non-homogeneous Föppl-von Kármán equations for growing thin elastic shallow shells are revisited by deriving the inhomogeneity source terms directly from the non-metricity tensor associated with growth. This is in contrast with the existing literature where the source terms are obtained using the extensional and curvature growth strains after exploiting the additive decomposition of the total strain

  • Spectral Properties of Neumann-Poincaré Operator and Anomalous Localized Resonance in Elasticity Beyond Quasi-Static Limit
    J. Elast. (IF 2.372) Pub Date : 2020-02-27
    Youjun Deng, Hongjie Li, Hongyu Liu

    This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within finite frequency regime beyond the quasi-static approximation. We first derive the complete spectral system of the Neumann-Poincaré operator associated with the elastic system in \(\mathbb{R}^{3}\) within the finite frequency regime. Based

  • Generalization of Plane Stress and Plane Strain States to Elastic Plates of Finite Thickness
    J. Elast. (IF 2.372) Pub Date : 2020-02-27
    Xian-Fang Li, Zhen-Liang Hu

    This paper presents a novel method to establish a general solution for an isotropic homogeneous elastic plate of finite thickness. Under the assumption of vanishing out-of-plane shear stresses, a necessary condition of solvability of elastic problems is obtained. Moreover, a general solution dependent on the thickness-wise coordinate is derived, where the unknown function is still governed by a two-dimensional

  • Analysis of the Antiplane Problem with an Embedded Zero Thickness Layer Described by the Gurtin-Murdoch Model
    J. Elast. (IF 2.372) Pub Date : 2020-01-27
    S. Baranova, S. G. Mogilevskaya, V. Mantič, S. Jiménez-Alfaro

    The antiplane problem of an infinite isotropic elastic medium subjected to a far-field load and containing a zero thickness layer of arbitrary shape described by the Gurtin-Murdoch model is considered. It is shown that, under the antiplane assumptions, the governing equations of the complete Gurtin-Murdoch model are inconsistent for non-zero surface tension. For the case of vanishing surface tension

  • New Classes of Traveling Waves in a Planar Kirchhoff Beam with Nonlinear Bending Stiffness
    J. Elast. (IF 2.372) Pub Date : 2020-01-27
    P. Rosenau, M. B. Rubin

    New traveling wave solutions are presented for motion of an inextensible, unshearable, planar Kirchhoff beam endowed with rotary inertia and a generalized strain energy function for bending which models nonlinear stiffening and softening. It is shown that although sonic waves (i.e., wave traveling at the bar speed in the beam) do not exist for constant bending stiffness, nonlinear bending stiffness

  • Dimensional Reduction of the Kirchhoff-Plateau Problem
    J. Elast. (IF 2.372) Pub Date : 2020-01-27
    Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi

    We obtain the minimal energy solution of the Plateau problem with elastic boundary as a variational limit of the minima of the Kirchhoff-Plateau problems with a rod boundary when the cross-section of the rod vanishes. The limit boundary is a framed curve that can sustain bending and twisting.

  • Multi-criteria Estimation of Load-Bearing Capacity of Solids
    J. Elast. (IF 2.372) Pub Date : 2020-01-10
    Igor A. Brigadnov

    The article discusses the problem of the load-bearing capacity of a deformable solid in the current configuration, which may be either reference (undeformed) or actual (deformed). An original variational approach is proposed, where, depending on different engineering considerations, the root-mean-square values (rms) of any stress components in various sub-domains are calculated and used to estimate

  • Mechanics of High-Flexible Beams Under Live Loads
    J. Elast. (IF 2.372) Pub Date : 2020-01-10
    Luca Lanzoni, Angelo Marcello Tarantino

    In this paper the mathematical formulation of the equilibrium problem of high-flexible beams in the framework of fully nonlinear structural mechanics is presented. The analysis is based on the recent model proposed by L. Lanzoni and A.M. Tarantino: The bending of beams in finite elasticity in J. Elasticity (2019) doi:10.1007/s10659-019-09746-8 2019. In this model the complete three-dimensional kinematics

  • The Degenerate Scales for Plane Elasticity Problems in Piecewise Homogeneous Media Under General Boundary Conditions
    J. Elast. (IF 2.372) Pub Date : 2020-01-09
    Alain Corfdir, Guy Bonnet

    The degenerate scale issue for 2D-boundary integral equations and boundary element methods has been already investigated for Laplace equation, antiplane and plane elasticity, bending plate for Dirichlet boundary condition. Recently, the problems of Robin and mixed boundary conditions and of piecewise heterogeneous domains have been considered for the case of Laplace equation. We investigate similar

  • Closed-Form Saint-Venant Solutions in the Koiter Theory of Shells
    J. Elast. (IF 2.372) Pub Date : 2020-01-09
    Mircea Bîrsan

    In this paper we investigate the deformation of cylindrical linearly elastic shells using the Koiter model. We formulate and solve the relaxed Saint-Venant’s problem for thin cylindrical tubes made of isotropic and homogeneous elastic materials. To this aim, we adapt a method established previously in the three-dimensional theory of elasticity. We present a general solution procedure to determine closed-form

  • A Note on the Extreme Points of the Cone of Quasiconvex Quadratic Forms with Orthotropic Symmetry
    J. Elast. (IF 2.372) Pub Date : 2020-01-09
    Davit Harutyunyan

    We study the extreme points of the cone of quasiconvex quadratic forms with linear elastic orthotropic symmetry. We prove that if the determinant of the acoustic matrix of the associated forth order tensor of the quadratic form is an extremal polynomial, then the quadratic form is an extreme point of the cone in the same symmetry class. The extremality of polynomials and quadratic forms here is understood

  • Equivalence of a Constrained Cosserat Theory and Antman’s Special Cosserat Theory of a Rod
    J. Elast. (IF 2.372) Pub Date : 2020-01-08
    M. B. Rubin

    The general nonlinear Cosserat theory of a rod allows for tangential shear deformation, axial extension and a deformable cross-section. Simplified equations are obtained by introducing kinematic constraints and associated constraint responses which force the cross-section to remain rigid. The equations of motion of this constrained Cosserat rod are shown to be equivalent to those of Antman’s nonlinear

  • The Complementing and Agmon’s Conditions in Finite Elasticity, Three Dimensions
    J. Elast. (IF 2.372) Pub Date : 2019-12-09
    Henry C. Simpson

    We consider the complementing condition and Agmon’s condition for linearized elasticity in three-dimensions. With an elasticity tensor \(\mathsf{C}\) derived from a compressible, isotropic stored energy \(W\), linearized about a homogeneous deformation \(\mathbf{f}_{0}\), we apply the complementing and Agmon’s conditions to a traction portion of the surface of a body with unit normal \(\mathbf{n}\)

  • Utilization of the Theory of Small on Large Deformation for Studying Mechanosensitive Cellular Behaviors.
    J. Elast. (IF 2.372) Pub Date : 2019-10-11
    Seungik Baek,Chun Liu,Kun Gou,Jungsil Kim,Hamidreza Gharahi,Christina Chan

    Recent studies suggest that cells routinely probe their mechanical environments and that this mechanosensitive behavior regulates some of their cellular activities. The finite elasticity theory of small-on-large deformation (SoL) has been shown to be effective in interpreting the mechanosensitive behavior of cells on a substrate that has been subjected to a prior large static stretch before the culturing

  • A Comparison of Phenomenologic Growth Laws for Myocardial Hypertrophy.
    J. Elast. (IF 2.372) Pub Date : 2018-04-11
    Colleen M Witzenburg,Jeffrey W Holmes

    The heart grows in response to changes in hemodynamic loading during normal development and in response to valve disease, hypertension, and other pathologies. In general, a left ventricle subjected to increased afterload (pressure overloading) exhibits concentric growth characterized by thickening of individual myocytes and the heart wall, while one experiencing increased preload (volume overloading)

  • Bulging brains.
    J. Elast. (IF 2.372) Pub Date : 2017-11-21
    J Weickenmeier,P Saze,C A M Butler,P G Young,A Goriely,E Kuhl

    Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy

  • Multi-Scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia.
    J. Elast. (IF 2.372) Pub Date : 2017-10-03
    Rafael Grytz,Mustapha El Hamdaoui

    The sclera uses unknown mechanisms to match the eye's axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the

  • Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth.
    J. Elast. (IF 2.372) Pub Date : 2017-09-13
    D Ambrosi,S Pezzuto,D Riccobelli,T Stylianopoulos,P Ciarletta

    The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties (the "constitutive equations") of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the "growth law") that relates stress and mitotic-apoptotic rate is far to be identified. We address these questions on the basis of

  • A Note on Evaluation of Temporal Derivative of Hypersingular Integrals over Open Surface with Propagating Contour.
    J. Elast. (IF 2.372) Pub Date : 2015-08-28
    Dawid Jaworski,Aleksandr Linkov,Liliana Rybarska-Rusinek

    The short note concerns with elasticity problems involving singular and hypersingular integrals over open surfaces, specifically cracks, with the contour propagating in time. Noting that near a smooth part of a propagating contour the state is asymptotically plane, we focus on 1D hypersingular integrals and employ complex variables. By using the theory of complex variable singular and hypersingular

  • Effect of the boundary conditions and influence of the rotational inertia on the vibrational modes of an elastic ring.
    J. Elast. (IF 2.372) Pub Date : 2014-05-06
    Nicolas Clauvelin,Wilma K Olson,Irwin Tobias

    We present the small-amplitude vibrations of a circular elastic ring with periodic and clamped boundary conditions. We model the rod as an inextensible, isotropic, naturally straight Kirchhoff elastic rod and obtain the vibrational modes of the ring analytically for periodic boundary conditions and numerically for clamped boundary conditions. Of particular interest are the dependence of the vibrational

  • The anisotropic Hooke's law for cancellous bone and wood.
    J. Elast. (IF 2.372) Pub Date : 2001-09-07
    G Yang,J Kabel,B van Rietbergen,A Odgaard,R Huiskes,S C Cowin

    A method of data analysis for a set of elastic constant measurements is applied to data bases for wood and cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable

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