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Effect of a thermodynamically consistent interface stress on thermal-induced nanovoid evolution in NiAl Math. Mech. Solids (IF 2.04) Pub Date : 2021-01-18 Mohammad Sadegh Ghaedi; Mahdi Javanbakht
In the present work, the effect of a thermodynamically consistent inelastic interface stress on nanovoid evolution in NiAl is studied. Such interface stress is introduced for the solid–gas interface of nanovoids within the concept of the phase field approach. The Cahn–Hilliard (CH) equation using the Helmholtz free energy describes the evolution of nanovoid concentration. The interface stress changes
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Influence of non-local diffusion in avascular tumour growth Math. Mech. Solids (IF 2.04) Pub Date : 2021-01-04 Ariel Ramírez-Torres; Salvatore Di Stefano; Alfio Grillo
The availability and evolution of chemical agents play an important role in the growth of a tumour and, therefore, the mathematical description of their consumption is of special interest. Usually, Fick’s law of diffusion is adopted for describing the local character of the evolution of chemicals. However, in a highly complex, heterogeneous medium, as is a tumour, the progression of chemical species
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A non-classical model for first-ordershear deformation circular cylindrical thin shells incorporating microstructure and surface energy effects Math. Mech. Solids (IF 2.04) Pub Date : 2021-01-04 GY Zhang; X-L Gao
A new non-classical model for first-order shear deformation circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. Through a variational formulation based on Hamilton’s principle, the equations of motion and boundary conditions are simultaneously obtained, and the microstructure and surface energy effects are treated in a unified manner
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A new approach to curvature measures in linear shell theories Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-27 Miroslav Šilhavý
The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of
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Diffuse approximation for identification of the mechanical properties of microcapsules Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-25 Carlos Quesada; Claire Dupont; Pierre Villon; Anne-Virginie Salsac
A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first involves experimentally acquiring the deformed shape that a given microcapsule takes
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In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-25 Ivan Giorgio; Mario Spagnuolo; Ugo Andreaus; Daria Scerrato; Alberto Maria Bersani
In this review paper, some relevant models, algorithms, and approaches conceived to describe the bone tissue mechanics and the remodeling process are showcased. Specifically, we briefly describe the hierarchical structure of the bone at different levels and underline the geometrical substructure characterizing the bone itself. The mechanical models adopted to describe the bone tissue at different levels
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Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-25 Maziar Kalantari; Naser Khaji; Morteza Eskandari-Ghadi
Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static analysis is accurate enough, as the rocking motion is the dominant mode of their interaction with the surrounding soil (i.e. soil–structure interaction problem). In this study, the soil–structure interaction
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Elastohydrodynamic lubrication line contact in couple-stress elasticity Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-25 Jie Su; Hong-Xia Song; Liao-Liang Ke
By using the couple-stress elasticity theory, this article firstly analyzes the size-dependent elastohydrodynamic lubrication (EHL) line contact between a deformable half-plane and a rigid cylindrical punch. The size effect that emerged from the material microstructures is described by the characteristic material length. It is assumed that the viscosity and density of the lubricant vary with the fluid
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Variational principles of nonlinear magnetoelastostatics and their correspondences Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-22 Basant Lal Sharma; Prashant Saxena
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo certain boundary integrals or constant integrals, between these formulations using the Legendre transform and properties of Maxwell’s equations. Bifurcation equations
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A hole of irregular shape interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-06 Xu Wang; Ping Yang; Peter Schiavone
We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity
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Upscaling and spatial localization of non-local energies with applications to crystal plasticity Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-06 José Matias; Marco Morandotti; David R. Owen; Elvira Zappale
We describe multiscale geometrical changes via structured deformations (g,G) and the non-local energetic response at a point x via a function Ψ of the weighted averages of the jumps [un](y) of microlevel deformations un at points y within a distance r of x. The deformations un are chosen so that limn→∞un=g and limn→∞∇un=G. We provide conditions on Ψ under which the upscaling “n→∞” results in a macroscale
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A simplified metaelastic model for coated sphere-filled random composites Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-04 CQ Ru
A simplified metaelastic model is presented to study long-wavelength dynamics of random composites filled with coated rigid spheres under the condition that the characteristic wavelength of the displacement field is much larger than the average distance between adjacent coated rigid spheres. The model is characterized by a simple differential relation between the displacement field of the composite
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High-order three-scale computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales Math. Mech. Solids (IF 2.04) Pub Date : 2020-12-02 Hao Dong; Junzhi Cui; Yufeng Nie; Ke Jin; Xiaofei Guan; Zihao Yang
A novel high-order three-scale (HOTS) computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales is developed in this paper. The multiple heterogeneities of axisymmetric composite structures we investigated are taken into account by periodic distributions of representative unit cells on the mesoscale and microscale. First
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Mathematical analysis of static and dynamic three-dimensional models of thermo-electro-magneto-elastic solids Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-30 Gia Avalishvili; Mariam Avalishvili; Ayech Benjeddou
This paper is devoted to the investigation of three-dimensional models of thermo-electro-magneto-elastic solids made of a multidomain inhomogeneous anisotropic material. General boundary and initial boundary value problems corresponding to the static and dynamic models are studied where, on certain parts of the boundary, mechanical displacement, electric and magnetic potentials and temperature vanish
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Linear peridynamics for triclinic materials Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-23 Yozo Mikata
The governing equation of linear peridynamics is developed for the most general anisotropic materials (triclinic materials). As a departure from the standard peridynamic theory, the linear constitutive equation in the form of a micromodulus is determined by directly requiring the resulting peridynamic equation to converge to a comparable classical elastodynamic equation for a triclinic material as
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Theoretical solution for the axial vibration of functionally graded double-lap adhesive joints Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-17 Shadi A Sindi; Ramzi Othman; Khalid H Almitani
Adhesively bonded joints have widely been used in a number of engineering applications, owing to their improved mechanical performance as compared with other mechanical joining techniques, such as rivets or bolts. In this study, a theoretical solution of double-lap joints is established, with functionally graded adhesive and isotopic adherends, under harmonic loads. Assuming a parabolic distribution
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Hilbert transform approach to solve a problem of collinear Griffith crack in the mid-plane of an infinite orthotropic strip Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-17 Priti Mondal; Jagabandhu De
In this paper, an integral transformation of the displacement is employed to determine the solution of the elastodynamics problem of two collinear Griffith cracks with constant velocity situated in a mid-plane of an infinite orthotropic strip where the boundaries are assumed to be stress-free. By use of the integral transformation of the displacement, the problem is reduced to a solution of the triple
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Stick-slip and wear phenomena at the contact interface between an elastic beam and a rigid substrate Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-17 Francesco D’Annibale; Arnaldo Casalotti; Angelo Luongo
In this paper, the static behavior of an elastic beam resting on a rigid substrate is investigated. The structure lies on a rigid substrate and exchanges with it tangential forces, in correspondence with a finite number of contact points. These actions entail extension of the beam in the longitudinal direction together with a negligible bending, owing to the small eccentricity between the beam’s axis
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Solution to Bending Problem of Trapezoid Composite Laminates Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-17 Da Cui; Daokui Li; Shiming Zhou; Anfeng Zhou; Xuan Zhou
The optimized design of composite adaptive structures puts forward higher requirements and challenges to the actual configuration of the structural section. In this paper, a trapezoidal laminate model of composite materials is established. Based on the classical laminates theory, the bending problem of trapezoidal laminates is solved by using the Kantorovich method and the principle of minimum potential
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Lagrangian descriptions of dissipative systems: a review Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-11 Alberto Maria Bersani; Paolo Caressa
In this paper, we review classical and recent results on the Lagrangian description of dissipative systems. After having recalled Rayleigh extension of Lagrangian formalism to equations of motion with dissipative forces, we describe Helmholtz conditions, which represent necessary and sufficient conditions for the existence of a Lagrangian function for a system of differential equations. These conditions
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Wave propagation in micromorphic anisotropic continua with an application to tetragonal crystals Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-11 Fabrizio Daví
We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic
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Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution Math. Mech. Solids (IF 2.04) Pub Date : 2020-11-02 Dmitry Timofeev; Emilio Barchiesi; Anil Misra; Luca Placidi
Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology
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The Poynting effect in elastomeric bars undergoing chemo-mechanical evolution Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-25 Alan S Wineman
This work considers a rubber cylinder under zero axial force that elongates in response to the normal stresses produced during torsion (the Poynting effect). The combined elongation and twisting deformation occurs at an elevated temperature at which the rubber undergoes time-dependent scission and re-crosslinking of its macromolecular network junctions. A constitutive theory accounting for this microstructural
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A damaged non-homogeneous Timoshenko beam model for a dam subjected to aging effects Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-25 Bernardino Chiaia; Valerio De Biagi; Luca Placidi
A hemi-variational formulation for a damaged non-homogeneous Timoshenko beam is proposed here for the purpose of fast simulation of the properties of a dam. The dam is therefore modeled as a damaged non-homogeneous Timoshenko beam embedded in 2D space. The damage evolution and the mechanics of the beam are governed both by the hemi-variational principle and by the assumption on the form of the deformation
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Surface and interfacial anti-plane waves in micropolar solids with surface energy Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-25 Mriganka Shekhar Chaki; Victor A Eremeyev; Abhishek K Singh
In this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for
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Modelling and analysis of piezoelectric actuators with partially debonded adhesive layers Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-25 Huan Hu; Zhengwei Li; Xiaodong Wang
In the modelling of thin-sheet piezoelectric actuators, the bonding condition between the actuator and the host structure can place a significant influence on the behaviour of the actuator. This paper provides a comprehensive theoretical study of the electromechanical behaviour of a thin-sheet piezoelectric actuator bonded to a host structure through a partially debonded adhesive layer under in-plane
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Symmetry-adapted tight-binding electronic structure analysis of carbon nanotubes with defects, kinks, twist, and stretch Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-23 Soumya Mukherjee; Hossein Pourmatin; Yang Wang; Timothy Breitzman; Kaushik Dayal
In this paper, a symmetry-adapted method is applied to examine the influence of deformation and defects on the electronic structure and band structure in carbon nanotubes. First, the symmetry-adapted approach is used to develop the analog of Bloch waves. Building on this, the technique of perfectly matched layers is applied to develop a method to truncate the computational domain of electronic structure
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Elastic and elasto-plastic analysis of Ti6Al4V micro-lattice structures under compressive loads Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-20 Prashant Athanker; Amit Kumar Singh
This article aims to study the modeling and simulation of Ti6Al4V micro-lattice structures under the same compressive loads. Initially, five distinct unit cell topologies (Grid, X, Star, Cross, and Tesseract) were used to design lattice structures. For the modeling of these lattice structures, both three-dimensional wireframe and solid (homogeneous and heterogeneous gradient) meshing were employed
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Modeling the dynamic bending of rigid-plastic fiber-reinforced laminated curvilinear doubly connected thin plates with free outer contour Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-20 Tatiana Pavlovna Romanova
A theoretical model of the dynamic bending of rigid-plastic hybrid composite, arbitrary curvilinear doubly connected thin plates is developed. Inner contour of the plate is simply supported or clamped and outer one is free. The plates are on a viscous basis and under the action of uniformly distributed loads of explosive type. The plates are laminated and fibrous, with layers arranged symmetrically
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Electric features of dislocations and electric force between dislocations Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-20 Yuanjie Huang
Dislocations and dislocation dynamics are the cores of material plasticity. In this work, the electric features of dislocations were investigated theoretically. An intrinsic electric field around a single dislocation was revealed. In addition to the well-known Peach–Koehler force, it was established that an important intrinsic electric force exists between dislocations, which is uncovered here for
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Compatibility conditions of continua using Riemann–Cartan geometry Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-19 Christian G Böhmer; Yongjo Lee
The compatibility conditions for generalised continua are studied in the framework of differential geometry, in particular Riemann–Cartan geometry. We show that Vallée’s compatibility condition in linear elasticity theory is equivalent to the vanishing of the three-dimensional Einstein tensor. Moreover, we show that the compatibility condition satisfied by Nye’s tensor also arises from the three-dimensional
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Local gradient Bernoulli–Euler beam model for dielectrics: effect of local mass displacement on coupled fields Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-19 Olha Hrytsyna
The size-dependent behaviour of a Bernoulli–Euler nanobeam based on the local gradient theory of dielectrics is investigated. By using the variational principle, the linear stationary governing equations of the local gradient beam model and corresponding boundary conditions are derived. In this set of equations the coupling between the strain, the electric field and the local mass displacement is taken
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Peridynamics boundary condition treatments via the pseudo-layer enrichment method and variable horizon approach Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-16 Jingkai Chen; Yiyu Jiao; Wenchun Jiang; Yanting Zhang
Peridynamics is a nonlocal theory that applies an integral term to represent the material response. Without a spatial differential term involved, peridynamics possesses certain advantages for solving discontinuity-involved problems. However, due to the reduction of stiffness, the deformation near the boundary region by peridynamics has a low accuracy compared to the local elastic deformation. Previous
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Estimates for the constant in two nonlinear Korn inequalities Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-14 Maria Malin; Cristinel Mardare
A nonlinear Korn inequality estimates the distance between two immersions from an open subset of Rn into the Euclidean space Rk, k⩾n⩾1, in terms of the distance between specific tensor fields that determine the two immersions up to a rigid motion in Rk. We establish new inequalities of this type in two cases: when k = n, in which case the tensor fields are the square roots of the metric tensor fields
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Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-13 JF Ganghoffer; XN Do; G Maurice
The Hill macrohomogeneity condition is revisited in the context of strain gradient homogenization for heterogeneous materials prone to interfacial displacement jumps. The consideration of strain gradient effects is motivated by their use as a regularization method for strain-softening constitutive damage models leading to strain localization and displacement discontinuity. Starting from the weak form
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A state-based peridynamic formulation for functionally graded Kirchhoff plates Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-13 Zhenghao Yang; Erkan Oterkus; Selda Oterkus
Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler–Lagrange equation and
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Dual fat boundary method: the fat boundary method in elasticity with an extension of the application scope Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-13 Kui Liu; Ang Zhao; Zhendong Hu
The fat boundary method (FBM) is a fictitious domain method, proposed to solve Poisson problems in a domain with small perforations. It can achieve higher accuracy around holes, which makes it very suitable to solve elasticity problems because stress concentrations often appear around holes. However, there are some strict restrictions of the FBM limiting the wide range of applications. For example
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Partial slip contact analysis for a monoclinic half plane Math. Mech. Solids (IF 2.04) Pub Date : 2020-10-11 İ Çömez; Y Alinia; MA Güler; S El-Borgi
In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the
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A generalized mechanical model using stress–strain duality at large strain for amorphous polymers Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-28 CA Bernard; D George; S Ahzi; Y Rémond
Numerous models have been developed in the literature to simulate the thermomechanical behavior of amorphous polymers at large strain. These models generally show a good agreement with experimental results when the material is submitted to uniaxial loadings (tension or compression) or in the case of shear loadings. However, this agreement is highly degraded when they are used in the case of combined
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Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-21 Giulio Maria Tonzani; Isaac Elishakoff
This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations
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Local sensitivity analysis of the “membrane shape equation” derived from the Helfrich energy Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-21 P Rangamani; A Behzadan; M Holst
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well studied in the axisymmetric framework. However, the Helfrich energy
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Computation of brittle fracture propagation in strain gradient materials by the FEniCS library Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-21 E Barchiesi; H Yang; CA Tran; L Placidi; WH Müller
Strain gradient continuum damage modelling has been applied to quasistatic brittle fracture within an approach based on a maximum energy-release rate principle. The model was implemented numerically, making use of the FEniCS open-source library. The considered model introduces non-locality by taking into account the strain gradient in the deformation energy. This allows for stable computations of crack
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Quality factor of circular microdiaphragm with surface effects in contact with liquids Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-21 RM Zhang; SS Zhou; AQ Li
This paper reports an investigation of the influences of surface effects and residual stress on the quality factor of a circular microdiaphragm in contact with liquids on one side. Acoustic radiation, as the main source of energy dissipation, can decrease the quality factor of a circular microdiaphragm. An approximate solution for the natural frequency can be obtained based on the Rayleigh–Ritz energy
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A domain of influence theorem under MGT thermoelasticity theory Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-15 Komal Jangid; Santwana Mukhopadhyay
The purpose of this article is to discuss domain of influence results under the Moore–Gibson–Thompson (MGT) thermoelasticity theory. We employ a mixed initial–boundary value problem concerning a homogeneous and isotropic material in view of the MGT thermoelasticity theory and establish the domain of influence theorem for potential–temperature disturbance. This theorem implies that the coupling of potential
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Four states of matter and centrally symmetric de Broglie particle–wave mechanical systems Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-15 James M Hill
The dark issues of cosmological mechanics imply that our accounting for mass and energy at this scale is incorrect. On the other hand, existing theory not only accounts for atomic physics, but does so to a very high degree of accuracy. de Broglie was first to propose a concrete physical picture of the co-existence of both particle and its associated wave. We have previously proposed a Lorentz invariant
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Two Versions of the Extended Hill’s Lemma for Non-Cauchy Continua Based on the Couple Stress Theory Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-09 A. I. Gad; X.-L. Gao
Two versions of the extended Hill’s lemma for non-Cauchy continua satisfying the couple stress theory are proposed. Each version can be used to determine two effective elasticity (stiffness) tensors: one classical and the other higher order. The classical elasticity tensor relates the symmetric part of the force stress to the symmetric strain, whereas the higher-order elasticity tensor links the deviatoric
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A model for a solid undergoing rate-independent dissipative mechanical processes Math. Mech. Solids (IF 2.04) Pub Date : 2020-09-01 Umakanthan Saravanan; Kumbakonam R Rajagopal; Roshan M Tom; Keshav Bharadwaj
A thermodynamic framework is proposed to capture the dissipative response of metals. In contrast to the conventional practice, a stressed reference configuration is assumed instead of a stress-free configuration. The second law of thermodynamics is converted into equality by prescribing a non-negative rate of dissipation function. Stress in the reference configuration evolves with time to satisfy the
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On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-27 Xiaoyi Chen; Hui-Hui Dai; Erick Pruchnicki
An asymptotic reduction method is introduced to construct a rod theory for a linearized general anisotropic elastic material for space deformation. The starting point is Taylor expansions about the central line in rectangular coordinates, and the goal is to eliminate the two cross-section spatial variables in order to obtain a closed system for displacement coefficients. This is first achieved, in
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Ramberg–Osgood material behavior expression and large deflections of Euler beams Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-24 Ronald J Giardina; Dongming Wei
Several assumptions are commonly made throughout the literature with regard to the mechanical expression of material behavior under a Ramberg–Osgood material model; specifically, the negligible effects of nonlinearity on the elastic behavior of the material. These assumptions do not reflect the complicated nonlinearity implied by the Ramberg–Osgood expression, which can lead to significant differences
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Periodic tilings and auxetic deployments Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-24 Ciprian S Borcea; Ileana Streinu
We investigate geometric characteristics of a specific planar periodic framework with three degrees of freedom. While several avatars of this structural design have been considered in materials science under the name of chiral or missing rib models, all previous studies have addressed only local properties and limited deployment scenarios. We describe the global configuration space of the framework
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A variational property of the von Kármán plate problem Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-24 Cesare Davini; Roberto Paroni
The solution of the boundary value problem of anisotropic Föppl–von Kármán plates is shown to be a critical point for a suitable energy functional. Moreover, under the assumption that the minimum of the total energy exists, we prove a saddle-point property and also deduce from it the form of the boundary conditions for plates clamped on part of the boundary and loaded on the complementary part.
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RETRACTION NOTICE: Flexural wave dispersion of nonlocal bi-Helmholtz-type stress gradient theory Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-19
At the request of the Journal Editor(s) and SAGE Publishing, the following article has been retracted.
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Some comparisons between heterogeneous and homogeneous layers for nonlinear SH waves in terms of heterogeneous and nonlinear effects Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-17 Dilek Demirkuş
This paper aims to make some comparative studies between heterogeneous and homogeneous layers for nonlinear shear horizontal (SH) waves in terms of the heterogeneous and nonlinear effects. Therefore, with this aim, two layers are defined as follows: on the one hand, one layer consists of hyperelastic, isotropic, heterogeneous, and generalized neo-Hookean materials; on the other hand, another layer
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Stiffness optimization in nonlinear pantographic structures Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-11 Boris Desmorat; Mario Spagnuolo; Emilio Turco
Mechanical metamaterials are microstructured mechanical systems showing an overall macroscopic behaviour that depends mainly on their microgeometry and microconstitutive properties. Moreover, their exotic properties are very often extremely sensitive to small variations of mechanical and geometrical properties in their microstructure. Clearly, the methods of structural optimization, once combined with
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Asymptotic derivation of refined dynamic equations for a thin elastic annulus Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-11 Nihal Ege; Barış Erbaş; Julius Kaplunov
Low-frequency vibrations of a thin elastic annulus are considered. The dynamic equations of plane strain are subjected to asymptotic treatment beyond the leading-order approximation. The main peculiarity of the considered problem is a specific degeneration associated with the effect of the almost inextensible midline of the annulus, resulting in a few unexpected features of the mechanical behaviour
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Discussion on the conformal mapping of a half-plane onto a unit disk in anisotropic elasticity and related applications Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-08 Ming Dai; Jian Hua
The conformal mapping, which transforms a half-plane into a unit disk, has been used widely in studies involving an isotropic elastic half-plane under anti-plane shear or plane deformation. However, very little attention has been paid to the possibility of utilizing this mapping in the study of an anisotropic elastic half-plane under the same deformation. In this paper, we discuss a general case of
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The effect of a pre-existing nanovoid on martensite formation and interface propagation: a phase field study Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-06 Mahdi Javanbakht; Mohammad Sadegh Ghaedi; Emilio Barchiesi; Alessandro Ciallella
In the present work, the effect of a pre-existing nanovoid on martensitic phase transformation (PT) is investigated using the phase field approach. The nanovoid is created as a solution of the coupled Cahn–Hilliard and elasticity equations. The coupled Ginzburg–Landau and elasticity equations are solved to capture the martensitic nanostructure. The above systems of equations are solved using the finite
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Commented translation of Erwin Schrödinger’s paper ‘On the dynamics of elastically coupled point systems’ (Zur Dynamik elastisch gekoppelter Punktsysteme) Math. Mech. Solids (IF 2.04) Pub Date : 2020-08-05 Uwe Mühlich; Bilen Emek Abali; Francesco dell’Isola
The paper ‘Zur Dynamik elastisch gekoppelter Punktsysteme’ by Schrödinger (1914) does not seem to have attracted the attention that it deserves. We translate it into English here and we discuss its results in detail, with a view to its possible influence in the modern theories of generalised continua. The clever solution found, in terms of Bessel functions, by Schrödinger of the problem of the vibrations
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Stepwise analysis of pantographic beams subjected to impulsive loads Math. Mech. Solids (IF 2.04) Pub Date : 2020-07-28 Emilio Turco
Materials based on pantographic unit cells have very interesting mechanical peculiarities. For these reasons they are largely studied from a theoretical, experimental, and numerical point of view. Numerical simulations furnish an important contribution for the the design and optimization of such materials and, more generally, for metamaterials. Here, we consider the influence of inertial forces, removing
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Determination of the stress concentration in the corner point of the wedge-shaped region reinforced by a more rigid thin coating Math. Mech. Solids (IF 2.04) Pub Date : 2020-07-28 AN Soloviev; BV Sobol; EV Rashidova; AI Novikova
We analysed the problem of determining the exponents in the asymptotic solution of the isotropic theory of elasticity problem at the top of the wedge-shaped region where its sides (or one of them) are supported by a thin coating and lean without friction on the rigid bases. On the other side of the wedge-shaped region, it is assumed that there are various boundary conditions, including when there is
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