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  • Constrained Mixture Models of Soft Tissue Growth and Remodeling – Twenty Years After
    J. Elast. (IF 2.372) Pub Date : 2021-01-21
    J. D. Humphrey

    Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or

    更新日期:2021-01-21
  • Need the Uniform Stress Field Inside Multiple Interacting Inclusions Be Hydrostatic?
    J. Elast. (IF 2.372) Pub Date : 2021-01-20
    Ming Dai, Peter Schiavone

    Since the pioneering work of Eshelby on a single ellipsoidal inclusion embedded in an infinite space, much attention has been devoted in the literature to the question of the uniformity of the stress field inside inclusions surrounded by an elastic matrix. Over the last decade or so, researchers have established the existence of multiple (interacting) inclusions enclosing uniform internal stress distributions

    更新日期:2021-01-21
  • Insights into the Microstructural Origin of Brain Viscoelasticity
    J. Elast. (IF 2.372) Pub Date : 2021-01-20
    Nina Reiter, Biswaroop Roy, Friedrich Paulsen, Silvia Budday

    Mechanical aspects play an important role in brain development, function, and disease. Therefore, continuum-mechanics-based computational models are a valuable tool to advance our understanding of mechanics-related physiological and pathological processes in the brain. Currently, mainly phenomenological material models are used to predict the behavior of brain tissue numerically. The model parameters

    更新日期:2021-01-20
  • A Chemomechanical Model for Regulation of Contractility in the Embryonic Brain Tube
    J. Elast. (IF 2.372) Pub Date : 2021-01-20
    Alina Oltean, Larry A. Taber

    Morphogenesis is regulated by genetic, biochemical, and biomechanical factors, but the feedback controlling the interactions between these factors remains poorly understood. A previous study has found that compressing the brain tube of the early chick embryo induces changes in contractility and nuclear shape in the neuroepithelial wall. Assuming this response involves mechanical feedback, we used experiments

    更新日期:2021-01-20
  • A Morphoelastic Shell Model of the Eye
    J. Elast. (IF 2.372) Pub Date : 2021-01-20
    L. S. Kimpton, B. J. Walker, C. L. Hall, B. Bintu, D. Crosby, H. M. Byrne, A. Goriely

    The eye grows during childhood to position the retina at the correct distance behind the lens to enable focused vision, a process called emmetropization. Animal studies have demonstrated that this growth process is dependent upon visual stimuli, but dependent on genetic and environmental factors that affect the likelihood of developing myopia. The coupling between optical signal, growth, remodeling

    更新日期:2021-01-20
  • Swelling-Induced Interface Crease Instabilities at Hydrogel Bilayers
    J. Elast. (IF 2.372) Pub Date : 2021-01-20
    Berkin Dortdivanlioglu, Nil Ezgi Dincer Yilmaz, K. B. Goh, Xiaolin Zheng, Christian Linder

    Two dissimilar hydrogel layers bonded together become unstable when the compressive stresses due to diffusion-driven swelling of the layers reach a critical point and creases form at the interface. Although creasing instabilities observed on surfaces of soft solids subjected to large compressions are well studied, the transient nature and critical conditions for the emergence of interface creases as

    更新日期:2021-01-20
  • Analysis of Boundary Layer Effects Due to Usual Boundary Conditions or Geometrical Defects in Elastic Plates Under Bending: An Improvement of the Love-Kirchhoff Model
    J. Elast. (IF 2.372) Pub Date : 2021-01-05
    Andrés León Baldelli, Jean-Jacques Marigo, Catherine Pideri

    We propose a model of flexural elastic plates accounting for boundary layer effects due to the most usual boundary conditions or to geometrical defects, constructed via matched asymptotic expansions. In particular, considering a rectangular plate clamped at two opposite edges while the other two are free, we derive the effective boundary conditions or effective transmission conditions that the two

    更新日期:2021-01-05
  • Three-Dimensional Elastic Scattering Coefficients and Enhancement of the Elastic Near Cloaking
    J. Elast. (IF 2.372) Pub Date : 2021-01-05
    Hongyu Liu, Wing Yan Tsui, Abdul Wahab, Xianchao Wang

    This paper is concerned with the elastic near cloaking for the Lamé system in three-dimensions using the notion of elastic scattering coefficients (ESC). Accordingly, the ESC of arbitrary three-dimensional objects are designed and some of their properties are discussed using elements of the elastic layer potential theory. Then, near-cloaking structures, coined as ESC-vanishing-structures, are constructed

    更新日期:2021-01-05
  • BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension
    J. Elast. (IF 2.372) Pub Date : 2021-01-05
    Daniel E. Spector, Scott J. Spector

    In this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses

    更新日期:2021-01-05
  • Family of Continuous Strain-Consistent Convective Tensor Rates and Its Application in Hooke-Like Isotropic Hypoelasticity
    J. Elast. (IF 2.372) Pub Date : 2021-01-05
    S. N. Korobeynikov

    This paper presents a new family of objective (Lagrangian and Eulerian) continuous strain-consistent convective (corotational and non-corotational) tensor rates. Objective strain-consistent convective tensor rates are defined as having the property that there exist objective (Lagrangian and Eulerian) strain tensors from the Hill family such that the considered rates of these strain tensors are equal

    更新日期:2021-01-05
  • Incompressible Transversely Isotropic Hyperelastic Materials and Their Linearized Counterparts
    J. Elast. (IF 2.372) Pub Date : 2021-01-05
    C. O. Horgan, J. G. Murphy

    The strain-energy density \(W\) for incompressible transversely isotropic hyperelastic materials depends on four independent invariants of the strain tensor. For consistency with the infinitesimal theory, it is well known that there are three necessary conditions on the derivatives of \(W\) (evaluated in the undeformed state) that have to be to be satisfied in terms of the three independent elastic

    更新日期:2021-01-05
  • Discrete Kernel Functions for fcc Crystals Within Eringen’s Nonlocal Theory of Elasticity
    J. Elast. (IF 2.372) Pub Date : 2021-01-05
    H. M. Shodja, S. Shahvaghar-Asl

    The dilemma with the deficiencies of the nonlocal kernel functions as the building blocks of the Eringen’s nonlocal theory has been of concern. The aim of the current work is to provide a remedy for the calculation of the components of the nonlocal moduli tensor pertinent to face center cubic (fcc) crystals accounting for their true symmetry group. To this end, three new distinct nonlocal kernel functions

    更新日期:2021-01-05
  • A Naghdi Type Nonlinear Model for Shells with Little Regularity
    J. Elast. (IF 2.372) Pub Date : 2020-11-27
    Matko Ljulj, Josip Tambača

    In this paper a new nonlinear two-dimensional shell model of Naghdi’s type is formulated for shells which middle surface is parameterized by a \(W^{1, \infty}\) function. Therefore the model inherently contains undeformed geometries with corners, so the model also includes models of junctions of nonlinear shells. Deformation of the shell is described by a pair \((\boldsymbol{\psi}, {\mathbf{R}})\)

    更新日期:2020-11-27
  • Quasistatic Viscoelasticity with Self-Contact at Large Strains
    J. Elast. (IF 2.372) Pub Date : 2020-11-26
    Stefan Krömer, Tomáš Roubíček

    The frame-indifferent viscoelasticity in Kelvin-Voigt rheology at large strains is formulated in the reference configuration (i.e., using the Lagrangian approach) considering also the possible self-contact in the actual deformed configuration. Using the concept of 2nd-grade nonsimple materials, existence of certain weak solutions which are a.e. injective is shown by converging an approximate solution

    更新日期:2020-11-27
  • Equilibrium for Multiphase Solids with Eulerian Interfaces
    J. Elast. (IF 2.372) Pub Date : 2020-11-23
    Diego Grandi, Martin Kružík, Edoardo Mainini, Ulisse Stefanelli

    We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove existence of energy minimizing equilibrium states and \(\Gamma \)-convergence of diffuse-interface

    更新日期:2020-11-23
  • The Anelastic Ericksen Problem: Universal Deformations and Universal Eigenstrains in Incompressible Nonlinear Anelasticity
    J. Elast. (IF 2.372) Pub Date : 2020-10-07
    Christian Goodbrake, Arash Yavari, Alain Goriely

    Ericksen’s problem consists of determining all equilibrium deformations that can be sustained solely by the application of boundary tractions for an arbitrary incompressible isotropic hyperelastic material whose stress-free configuration is geometrically flat. We generalize this by first, using a geometric formulation of this problem to show that all the known universal solutions are symmetric with

    更新日期:2020-10-07
  • The Isotropic Cosserat Shell Model Including Terms up to O ( h 5 ) $O(h^{5})$ . Part II: Existence of Minimizers
    J. Elast. (IF 2.372) Pub Date : 2020-10-07
    Ionel-Dumitrel Ghiba, Mircea Bîrsan, Peter Lewintan, Patrizio Neff

    We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the convexity of the energy in the nonlinear strain and curvature measures. We first show the existence of the solution for the theory including \(O(h^{5})\) terms. The

    更新日期:2020-10-07
  • Pure Shearing and Pure Distortional Deformations Are Not Equivalent
    J. Elast. (IF 2.372) Pub Date : 2020-10-07
    M. B. Rubin

    This paper attempts to clarify the notions of a state of pure shear stress and pure shearing deformations. Specifically, it is shown that pure shearing deformations and pure distortional deformations are not equivalent. Attention is limited to isotropic, compressible, hyperelastic materials. Differences between the distortional deformations of pure shearing, pure shear caused by tension and compression

    更新日期:2020-10-07
  • The Isotropic Cosserat Shell Model Including Terms up to O ( h 5 ) $O(h^{5})$ . Part I: Derivation in Matrix Notation
    J. Elast. (IF 2.372) Pub Date : 2020-10-07
    Ionel-Dumitrel Ghiba, Mircea Bîrsan, Peter Lewintan, Patrizio Neff

    We present a new geometrically nonlinear Cosserat shell model incorporating effects up to order \(O(h^{5})\) in the shell thickness \(h\). The method that we follow is an educated 8-parameter ansatz for the three-dimensional elastic shell deformation with attendant analytical thickness integration, which leads us to obtain completely two-dimensional sets of equations in variational form. We give an

    更新日期:2020-10-07
  • A Screw Dislocation in a Monoclinic Tri-Material
    J. Elast. (IF 2.372) Pub Date : 2020-10-07
    Xu Wang, Peter Schiavone

    Employing primarily analytic continuation, we derive analytical solutions to the anti-plane problem associated with a screw dislocation located anywhere inside an anisotropic tri-material composed of an intermediate anisotropic elastic layer of finite thickness sandwiched between two semi-infinite anisotropic elastic media. All three phases of the tri-material are monoclinic with the symmetry plane

    更新日期:2020-10-07
  • Saint-Venant End Effects in the Plane Problem for Linearly Elastic Functionally Graded Materials
    J. Elast. (IF 2.372) Pub Date : 2020-09-23
    Aisa Biria

    An isotropic elastic strip, with a continuous inhomogeneity profile for Young’s modulus is considered, subject to a self-equilibrated load on one of its axial ends and free of traction on the remainder of its surface boundaries. By taking advantage of the analytical flexibility of an exponential inhomogeneity profile, the full equations of linear theory of elasticity are employed to find the two-dimensional

    更新日期:2020-09-23
  • Higher-Order Peridynamic Material Correspondence Models for Elasticity
    J. Elast. (IF 2.372) Pub Date : 2020-09-23
    Hailong Chen, WaiLam Chan

    Higher-order peridynamic material correspondence model can be developed based on the formulation of higher-order deformation gradient and constitutive correspondence with generalized continuum theories. In this paper, we present formulations of higher-order peridynamic material correspondence models adopting the material constitutive relations from the strain gradient theories. Similar to the formulation

    更新日期:2020-09-23
  • Asymptotics for Spectral Problems with Rapidly Alternating Boundary Conditions on a Strainer Winkler Foundation
    J. Elast. (IF 2.372) Pub Date : 2020-09-23
    Delfina Gómez, Sergei A. Nazarov, María-Eugenia Pérez-Martínez

    We consider a spectral homogenization problem for the linear elasticity system posed in a domain \(\varOmega \) of the upper half-space \(\mathbb{R}^{3+}\), a part of its boundary \(\varSigma \) being in contact with the plane \(\{x_{3}=0\}\). We assume that the surface \(\varSigma \) is traction-free out of small regions \(T^{\varepsilon }\), where we impose Winkler-Robin boundary conditions. This

    更新日期:2020-09-23
  • Stable Spatially Localized Configurations in a Simple Structure—A Global Symmetry-Breaking Approach
    J. Elast. (IF 2.372) Pub Date : 2020-09-23
    Shrinidhi S. Pandurangi, Ryan S. Elliott, Timothy J. Healey, Nicolas Triantafyllidis

    We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in many applications in mechanics. Instead of a numerical search for such solutions using arbitrary imperfections, we propose a systematic search using branch-following

    更新日期:2020-09-23
  • The Stokes Paradox in Inhomogeneous Elastostatics
    J. Elast. (IF 2.372) Pub Date : 2020-08-24
    Adele Ferone, Remigio Russo, Alfonsina Tartaglione

    We prove that the displacement problem of inhomogeneous elastostatics in a two–dimensional exterior Lipschitz domain has a unique solution with finite Dirichlet integral \(\boldsymbol{u}\), vanishing uniformly at infinity if and only if the boundary datum satisfies a suitable compatibility condition (Stokes paradox). Moreover, we prove that it is unique under the sharp condition \(\boldsymbol{u}=o(\log

    更新日期:2020-08-24
  • Invariance Under Superposed Rigid Body Motions with Constraints
    J. Elast. (IF 2.372) Pub Date : 2020-08-24
    M. B. Rubin

    The notion of invariance under Superposed Rigid Body Motions \((\mathit{SRBM})\) is enhanced by a restriction that explicitly states in what sense the responses of a material under \(\mathit{SRBM}\) are equivalent. This new restriction is used to develop expressions for the superposed values of the strain energy and the Cauchy stress, instead of assuming their forms. Moreover, it clarifies invariance

    更新日期:2020-08-24
  • Effective Resonant Model and Simulations in the Time-Domain of Wave Scattering from a Periodic Row of Highly-Contrasted Inclusions
    J. Elast. (IF 2.372) Pub Date : 2020-08-24
    Marie Touboul, Kim Pham, Agnès Maurel, Jean-Jacques Marigo, Bruno Lombard, Cédric Bellis

    The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions

    更新日期:2020-08-24
  • 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

    更新日期:2020-07-23
  • 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

    更新日期:2020-07-23
  • 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

    更新日期:2020-07-23
  • 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

    更新日期:2020-07-23
  • 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

    更新日期:2020-07-23
  • 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

    更新日期:2020-07-23
  • 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

    更新日期:2020-06-11
  • 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

    更新日期:2020-06-10
  • 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

    更新日期:2020-06-05
  • 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

    更新日期:2020-05-29
  • 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

    更新日期:2020-05-29
  • 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

    更新日期:2020-05-29
  • 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

    更新日期:2020-05-29
  • 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

    更新日期:2020-05-29
  • 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

    更新日期:2020-05-07
  • 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

    更新日期:2020-05-07
  • 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

    更新日期:2020-03-10
  • 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

    更新日期:2020-03-09
  • 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

    更新日期:2020-03-06
  • 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

    更新日期:2020-02-27
  • 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

    更新日期:2020-02-27
  • 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

    更新日期:2020-02-27
  • 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

    更新日期:2020-01-27
  • 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

    更新日期:2020-01-27
  • 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.

    更新日期:2020-01-27
  • 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

    更新日期:2020-01-10
  • 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

    更新日期:2020-01-10
  • 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

    更新日期:2020-01-09
  • 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

    更新日期:2020-01-09
  • 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

    更新日期:2020-01-09
  • 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

    更新日期:2020-01-08
  • 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 \(\mathbf{n}\)

    更新日期:2019-12-09
  • 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

    更新日期:2019-11-25
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