In this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young’s

A second strain gradient theory-based continuum model is presented for the mechanics of an elastic solid reinforced with extensible fibers in plane elastostatics. The extension and bending kinematics of fibers are formulated via the second and the third gradient of the continuum deformation. The Euler equations arising in the third gradient of virtual displacement are then formulated by means of iterated

We discuss some aspects of using the spatial description and the finite volume method as applied to the solid mechanics problems. The main objective is to study the differential equation relating the strain measure to the velocity gradient. We show that this equation can be reduced to an integral form and the obtained equation has the structure of the balance equation without a source term. On the

Starting from the three-dimensional theory of linear elasticity, we arrive at the exact plate problem by the use of Taylor series expansions. Applying the consistent-approximation approach to this problem leads to hierarchic generic plate theories. Mathematically, these plate theories are systems of partial-differential equations (PDEs), which contain the coefficients of the series expansions of the

Starting from a Cosserat-type model for curved rods, we derive analytical expressions for the effective stiffness coefficients of multilayered composite beams with an arbitrary number of layers. For this purpose, we employ the comparison with analytical solutions of some bending, torsion, and extension problems for three-dimensional beams and rods. The layers of the composite beam consist of different

The pure titanium, as a biomaterial destined for production of load-demanding prostheses, requires thermo-mechanical processing to increase its strength. The most common way to achieve this is the method of grain fragmentation. Thermo-mechanical deformation of titanium is a complex process, which makes it very difficult to describe it by means of constitutive equations. Such constitutive relations

Anisotropic materials are those that the value of a property depends on the direction of analysis. This article addresses both analytical and numerical stress computation for orthotropic beams under normal and shear loads. The analytical solution is based on potential polynomial functions and the present work establishes general strategies which allow systematic evaluation of the polynomial coefficients

In this paper we investigate the influence of rotational viscosity on the plane shear-rotational wave propagation in the linear isotropic reduced Cosserat medium. In such a continuum body points possess independent rotational and translational degrees of freedom, but the material does not resist to the gradient of microrotation. Stress tensor is asymmetric, but the couple stress is zero. For the elastic

Iron and steels are allotropes, meaning they exhibit different crystal configurations. The martensitic transformation is crucial for a variety of processes, such as hardening. It is induced by a combination of undercooling and mechanical deformation. Due to the changing material properties within the phases, and due to topological changes that might occur during the transformation, a phase field approach

Foamed rubber with a mixed cellular microstructure is a compressible material used for various sealing applications in the automotive industry. For technical optimization, a sufficiently precise material model is required. Here a material description for the porous elastic and viscoelastic response of low density foamed rubber is proposed and adapted to ethylene propylene diene monomer (EPDM)-based

In this paper, we discuss a theoretical approach to morphological instability analysis of the coherent interphase boundaries in strained heterostructures. Taking into account the fact that, under certain conditions, the atomic arrangement of solid–solid interfaces is thermodynamically unstable, the evolution equation describing the kinetics of the relief formation is obtained. The considered process

The paper presents experimental analysis of relation between friction coefficient and contact pressure of \(\hbox {MoS}_2\) film deposited on \(\hbox {Ti}_6\hbox {Al}_4\hbox {V}\) substrate in contact with sapphire ball during reciprocating sliding motion. It is shown that the value of friction coefficient decreases with increasing contact pressure. A microscale modeling approach is next developed

An extension of Boley’s continuum mechanics-based successive approximation method is presented for rectangular beams composed of two isotropic linear elastic layers. The solution is cast into the form of tables, in complete analogy to the tables originally presented by Boley and Tolins for single-layer strips. The first column in these tables corresponds to the classical Bernoulli–Euler theory of beams

The friction stir welding (FSW) process generally induces a gradient of properties and a softer behaviour along the welded joint. To design aeronautical structures welded by FSW in fatigue, it is necessary to study the impact of this localized soft behaviour on the overall structure. In this study, the 2198-T8 hardening structural aluminium alloy is considered. Monotonic and cyclic mechanical tests

The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two- and three-neighbour interactions

This paper studies weak solutions of the axial oscillations of the carbon nanotube modeled as an elastic nanobeam surrounded by an elastic medium. The model used combines Eringen’s theory of non-local elasticity and the equations of axial oscillations proposed by Aydogdu. Based on the Sturm–Liouville problem associated with this case, the weak solutions of the longitudinal waves in the carbon nanotube

Within the general approach to the modified Kirsch problem incorporating surface elasticity and residual surface stress (surface tension) by the original Gurtin–Murdoch model, the proper boundary conditions at an arbitrary cylindrical surface are derived in terms of complex variables for the plane strain and plane stress. In the case of the plane stress, the properties are allowed for not only of the

In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced

In this study, the effects of random laminate misalignment on the macroscopic and microscopic elastic/viscoplastic behaviors of ultrafine plate–fin structures are statistically investigated adopting Monte Carlo simulation. To this end, a multiscale method that analyzes the elastic–viscoplastic behavior of ultrafine plate–fin structures with random laminate misalignment both macroscopically and microscopically

A linear static problem of bending of a multilayer plate with homogeneous isotropic layers is considered. The deflection is assumed to have harmonic shape in the tangential directions. For calculation of the bending stiffness we introduce two dimensionless parameters: a small thickness parameter equal to the ratio of the thickness to the deformation wavelength in the tangential directions, and a large

Effective properties of fiber-reinforced composites can be estimated by applying the asymptotic homogenization method. Analytical solutions are possible for infinite long circular fibers based on the elliptic quasi-periodic Weierstrass Zeta function. This process leads to numerical convergences issues related to lattice sums calculations. The lattice sums original series converge slowly, which make

We here present a faithful translation of Carl Hermann’s important 1934 paper “Tensoren und Kristallsymmetrie”. This work, originally published in German language, is transferred into English while the preceding foreword summarizes Hermann’s achievements.

The thermodynamics of open systems exchanging mass, heat, energy and entropy with their environment is examined as a convenient unifying framework to describe the evolution of growing solid bodies subjected to electromechanical stimulations in the context of volumetric growth. Extending the framework of non-equilibrium thermodynamics to open systems, the balance laws for continuum solid bodies undergoing

Electroelastic piezoelectric transversely isotropic half-plane with a homogeneous or a functionally graded coating is considered. Independent arbitrary variation of electroelastic properties in depth is assumed for a functionally graded coating. A strip electrode is attached to the surface of the coating. Electric potential difference is applied through an electrode which leads to electroelastic deformation

In this paper, bending analysis of rectangular functionally graded nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory. The set of coupled equations are solved using the dynamic relaxation method combined with finite difference discretization

In this work, multi-principal element alloys (MPEAs) with the five base elements Al, Cr, Fe, Ni and Ti plus elements in minor amounts were produced by powder metallurgy and their microstructure and elastic behavior were analyzed via light and scanning electron microscopy, electron backscatter diffraction (EBSD) and synchrotron X-ray diffraction. The two studied compositions are an MPEA with Al, Cr

The mixed initial-boundary value problem in the context of elasticity of porous bodies having a dipolar structure is considered. By means of a semigroup of contractions, we can obtain some results regarding the existence and uniqueness of solutions for this mixed problem, after proving the equivalence between this problem and a Cauchy problem attached to an abstract equation of evolution. Also, by

This work is devoted to the problem of thermal fracture of a functionally graded coating on a homogeneous substrate (FGC/H) with an emphasis on the analysis of a special system of cracks that simulates a curved interface. The FGC/H structure contains the pre-existing crack system in the FGC, both edge cracks (which are often seen in FGC/H structures) and internal cracks. The stress intensity factors

We consider the cylindrical bending problem for an infinite plate as modeled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner specimens are comparatively stiffer. We provide the analytical solution for each case and exhibits the predicted bending stiffness. The relaxed micromorphic continuum

Materials and structures based on pantographic cells exhibit interesting mechanical peculiarities. They have been studied prevalently in the static case, both in linear and nonlinear regime. When the dynamical behavior is considered, available literature is scarce probably for the intrinsic difficulties in the solution of this kind of problems. The aim of this work is to contribute to filling of this

We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient

In this work, a thermodynamically consistent three-dimensional (3D) small strain-based theory to describe the deformation and fracture in quasi-brittle and brittle elastic solids is presented. The description of fracture at a material point resembles the microplane fracture approach developed by Bažant et al. (J Eng Mech 126(9):944–953, 2000, J Eng Mech 122(3): 245–254, 1996), but the present theory

In this paper, the bending behavior of nanoscale beams is studied using the 1D nonlocal integral Timoshenko beam theory (NITBT) and the 2D nonlocal integral elasticity theory (2D-NIET) using two types of nonlocal kernels, i.e., the two-phase kernel and a modified kernel which compensates the boundary effects. The governing equations are solved using the finite element method and the COMSOL code. Mesh

A finite element model based on continuum shell elements available in ABAQUS software has been developed for the free vibration analysis of FGM sandwich panels. Applications to sandwich plates with different combinations of FGM core and/or FGM face sheets satisfying through-the-thickness material gradations in the form of either power (P-FGM) or sigmoid (S-FGM) or exponential (E-FGM) distributions

Among the three heat conduction modes (diffusive, second sound, and ballistic propagation), the ballistic one is the most difficult to model. In the present paper, we discuss its physical interpretations and show different alternatives to its modelling. We highlight two of them: a thermo-mechanical model in which the generalized heat equation—the so-called Maxwell–Cattaneo–Vernotte equation—is coupled

Dynamic behavior of a material is essential in applications such as collision, explosion, ballistic impact, high-speed machining, and metal forming. As impact loadings, as well as accidental or malicious explosions, may impose high loading rates to engineering structures, estimating the dynamic response of a material accurately is crucial. Therefore, an analytical strain rate-dependent criterion on

An approximated theoretical model for linear hyperelastic materials with orthotropic inclusions is presented based on a mixture approach and orientation averaging of mechanical properties. In many modern composites, particle inclusions are used to achieve the desired properties. The properties of the resulting composite depend on the material, inclusion-density and also the shape and orientation of

Linear thermo-elasticity equations are derived in this paper for anisotropic, particle-reinforced composite structures at mesoscale. The full set of equations is first derived at microscale where the structure is represented as a three-dimensional body with spherical inclusions of known spatial distribution. Limiting the consideration by infinitesimal strains and assuming that the inclusions are embedded

Dual-phase steel shows a strong connection between its microstructure and its mechanical properties. This structure–property correlation is caused by the composition of the microstructure of a soft ferritic matrix with embedded hard martensite areas, leading to a simultaneous increase in strength and ductility. As a result, dual-phase steels are widely used especially for strength-relevant and energy-absorbing

In this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia tensor containing a production term. The constitutive

In this work, we consider a frictional contact between a thin-walled hyperelastic tube and a rigid body. One edge of the tube is partially worn on the body of revolution. The friction in the contact area obeys Coulomb law. An axial force is applied to the other end of the tube. In this paper, we analyze the relationship between the minimum contact length, the axial force and other parameters of the

Within the framework of the Cosserat continuum, the stability of a compressed circular rod with a two-layer coating is studied. It is assumed that the coating layers were fixed to each other and attached to the rod after preliminary deformations of axial extension–compression and contain internal stresses. For the physically linear model of a micropolar material, the linearized equilibrium equations

By relying on the Euler–Bernoulli beam model and energy variational formula, we indicate critical temperature causes in the buckling of piezo-flexomagnetic microscale beams. The corresponding size-dependent approach is underlying as a second strain gradient theory. Small deformations of elastic solids are assessed, and the mathematical discussion is linear. Regardless of the pyromagnetic effects, the

In the framework of the two-phase theory of nonlocal elasticity we study free high-frequency vibrations of nanobeams with varying cross section. Considering the Helmholtz kernel in the constitutive equation, we reduce the original integro-differential equation to an equivalent six-order differential equation with variable coefficients and derive the pair of additional boundary conditions accounting

We introduce two new concepts of convergence of gradient systems \(({\mathbf{Q}}, {{\mathcal {E}}}_\varepsilon ,{{\mathcal {R}}}_\varepsilon )\) to a limiting gradient system \(({\mathbf{Q}},{{\mathcal {E}}}_0,{{\mathcal {R}}}_0)\). These new concepts are called ‘EDP convergence with tilting’ and ‘contact–EDP convergence with tilting.’ Both are based on the energy-dissipation-principle (EDP) formulation

In this paper the process of polarization of transversally polarizable matter is investigated based on concepts from micropolar theory. The process is modeled as a structural change of a dielectric material. On the microscale it is assumed that it consists of rigid dipoles subjected to an external electric field, which leads to a certain degree of ordering. The ordering is limited, because it is counteracted

An asymmetric three-layered laminate with prescribed stresses along the faces is considered. The outer layers are assumed to be much stiffer than the inner one. The focus is on long-wave low-frequency anti-plane shear. Asymptotic analysis of the original dispersion relation reveals a low-frequency harmonic supporting a slow quasi-static (or static at the limit) decay along with near cut-off wave propagation

A common belief in phenomenological strain gradient plasticity modeling is that including the gradient of scalar variables in the constitutive setting leads to size-dependent isotropic hardening, whereas the gradient of second-order tensors induces size-dependent kinematic hardening. The present paper shows that it is also possible to produce size-dependent kinematic hardening using scalar-based gradient

A microcontinuum description of compressible liquid crystals is examined accounting for a constitutive model based on mass microdensity. As a first point, we discuss the effectiveness of the micropolar theory on compressible continua, which is limited to static problems. Then, by a micromorphic representation of mass density, we show the consistence of some classical constitutive models for compressible

We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker

A nonlinear spatial problem for an elastic micropolar liquid is formulated and solved. The problem describes a spherically symmetric equilibrium state of a liquid medium with couple stresses. Using the theory of spherically symmetric tensor fields, the original spatial problem is reduced to a system of ordinary differential equations. The boundary conditions consist in setting a distributed couples

The paper starts with a detailed investigation of the boundary conditions at free and fixed boundaries of any second gradient material and clarifies whether a surface tension is to be expected. The classical approach to the reaction stresses of higher gradient materials leaves a vast indeterminacy in most boundary value problems. An advanced approach is presented that yields much more definite distributions

An analytical model extending classical thermal elasticity is presented. It allows to introduce a correction to the attenuation of the mechanical waves at the higher frequency range. A material data set taken from experimental studies can be used to identify the attenuation rate as a function of frequency. An example is provided. The particular solution of the developed equations system in the form

An updated comprehensive exploratory survey of the literature on elastic cusped standard and prismatic shells and bars, in particular, cusped plates, and to the corresponding singular partial differential equations and systems is given. The governing systems of equations of statics and dynamics in the cases of compression–tension and bending are derived from I. Vekua’s hierarchical models of the generic

This paper aims to find parameters for the contribution of elements “\({-}\)F” and “\({=}\)C\({<}\)” on the dynamic liquid viscosity. The found contribution of the element “\({-}\)F” and “\(=\)C\({<}\)” for the dynamic liquid viscosity, 707.816 for \(\eta _{\mathrm {a }}\) and \(-2.3648\) for \(\eta _{\mathrm {b}}\) for element “\({-}\)F” and \(-919.101\) for \(\eta _{\mathrm {a }}\) and 2.21487 for

Working in the setting of Noll’s theory of materially uniform bodies, we develop a constitutive framework for plasticity that incorporates the gradient of plastic deformation.

Two formulae were developed to express sublimation enthalpy and Young’s modulus on a thermodynamic basis. The first formula reveals how the sublimation enthalpy is correlated with the thermal expansion coefficient and heat capacity of solids, whereas the second formula relates the Young’s modulus with sublimation enthalpy and equilibrium interatomic (intermolecular) distance. While the formulae themselves

In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism which describes several chemical reactions. In order to apply singular perturbation techniques, we determine an appropriate perturbation parameter \(\epsilon \) (which is related to the kinetic constants and initial conditions of the model), the inner and outer solutions and the matched expansions of the

The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These potentials are compared with the potentials for the non-rotating uniform system that have been found previously. The rotation leads to the appearance of vector potentials