We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations obtained from the Chapman–Enskog expansion for small relaxation times. Our results rely on the spectral theory of Jacobi operators with rank-one perturbations.

In this study, we approach the strain gradient thermoelasticity of bodies with microtemperatures. We define the internal energy corresponding to an arbitrary solution of the mixed problem with boundary and initial values, considered in the context of strain gradient thermoelasticity of bodies with microtemperatures. The Cesaro means of different parts of the internal energy are considered. In our main

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven

Motivated by the paradoxical results obtained from the differential nonlocal elasticity theory in some cases (e.g., bending and vibration problems of cantilevers), several attempts have been recently made to develop nonlocal beam models based on the integral (original) formulation of Eringen’s nonlocal theory. These models can be classified into two main groups including strain- and stress-driven ones

Lagrange’s equations represent the common approach in finite element analysis of an elastic multibody system. The most important step in this case is to write the governing equations. The work develops an alternative method to obtain these equations, using so-called Gibbs–Appell formalism. The advantage of this method is the decrease in the number of calculations to be made. The acceleration energy

Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of \(\varGamma \)-convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model features both Lagrangian and Eulerian terms. This calls for qualifying admissible three-dimensional deformations of planar domains in terms of injectivity. In addition

This paper presents an experimental study of the composite beams with elastic couplings subjected to the end-notched flexure (ENF) test. The object of research were carbon/epoxy composite laminates with specific stacking sequences exhibiting the bending–extension and the bending–twisting couplings. In addition, multidirectional laminates with different delamination interfaces were tested. Influence

A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization, and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional

The homogenization of viscoelastic composite materials gives rise to long-memory effects, reflected by the presence in the homogenized viscoelastic constitutive law of a delayed stress response expressed as a convolution integral involving the past material strain history. Computations reveal that the long-memory has the ability to delay or even absorb waves depending on the fraction of reinforcement

The indentation test is one of the most commonly employed techniques for the characterization of mechanical properties of materials. It is an efficient and useful tool for the evaluation of mechanical properties of small volumes of materials, e.g., hardness, elastic modulus and fracture toughness, etc., through analyzing the relationship between contact force and contact depth on the indented specimens

In this study, the large deformation analysis of the magnetoactive elastomers based on continuum mechanics approach has been conducted. First, the governing differential equations for the spatial configuration are presented. Stored energy density function defined with respect to the invariants of the right or left Cauchy–Green deformation tensor and the magnetic field induction vector is adopted to

Finite-plasticity theories often feature nonlocal energetic contributions in the plastic variables. By introducing a length-scale for plastic effects in the picture, these nonlocal terms open the way to existence results (Mainik and Mielke in J Nonlinear Sci 19(3):221–248, 2009). We focus here on a reference example in this direction, where a specific energetic contribution in terms of dislocation-density

The aim of this paper is to study a one-dimensional model system of equations for ionized gas dynamics at high temperature where the gas is a mixture of two kinds of monatomic gas. In addition to the mass density, pressure, temperature and particle velocity, degrees of ionization of both gases are also involved. The equations of motion are derived from conservation of mass, momentum and energy, which

Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined

The elastoplastic buckling behaviors of functionally graded material (FGM) beams under axial compression loading are studied in consideration of temperature dependence of material properties. Firstly, elastoplastic material properties are obtained on the basis of bilinear hardening model and temperature dependence, meanwhile the elastoplastic constitutive equations of the FGM are established as well

Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into

An investigation on the features of the shock structure solution of the 13-moment system of extended thermodynamics with a second-order closure based on the maximum entropy principle is presented. The results are compared to those obtained by means of the traditional first-order closure and to those obtained in the framework of kinetic theory by solving the Boltzmann equation with a BGK model for the

Limits of classical constitutive laws such as Fourier and Navier–Stokes equations are discovered since decades. However, the proper extensions—generalizations of these—are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based rational extended thermodynamics

Multi-scale and multi-physics are two important thematics when thinking to how next-generation materials will be engineered, aimed at delivering exceptional performances. This special issue attempts at collecting a representative sample of the interdisciplinary efforts that the scientific community is making towards the understanding and exploitation of the complex behaviours that can arise from multi-scale

The so-called minimal model is formulated for describing the enthalpy relaxation and recovery in glass transition. The model is based on the Arrhenius law for the enthalpy relaxation, which uses two-dimensional parameters, namely the activation energy and the so-called pre-factor (relaxation time at relatively high temperature). A numerically effective exact analytical solution is obtained for the

Future trends in predicting the fracture behaviour of rubber materials (products) are discussed. A complex methodology for the determination of rubber fracture behaviour from the energy viewpoint based on simulating realistic loading conditions in services applied to a rubber matrix in a laboratory test set-up is introduced. Because this is a pure rubber matrix investigation, additional effects such

Pantographic fabrics are presented as a paradigmatic example to discuss the research perspective on multiphysics and multiscale materials. Reduced-order modeling, obtained by introducing higher-gradient or microstructured continua, shows much smaller computational needs than those required by full-scale 3D modeling calculations and by equivalent discrete spring systems. Researches already available

The aim of this paper is to measure distances between autonomous underwater vehicles using power LED as light source and photodiode as receiver in unknown light water adsorption conditions. The method is based on the attenuation of the light signal, depending principally on distance and water characteristics. In a previous paper, we proposed the use of a cheap power LED system to support acoustic devices

This paper presents a poro-visco-elastic-plastic damageable model for saturated frozen soils within a rigorous theoretical framework. The effective fluid pressure, obtained considering the interfacial energy, is combined with the total Cauchy stress in order to formulate the hydro-mechanical effective stress applied to a soil skeleton. On the other hand, a two-stress variable constitutive relationship

Mechanical fatigue tests of unnotched, notched, and bending twin-roll cast AZ31B magnesium alloy specimens are performed in which strain fields are analyzed with digital image correlation. Clearly, delimited macroscopic bands of twinned grains (BTGs) in which the compressive strain is significantly higher compared to the adjacent regions are observed. Conventional fatigue parameters, e.g., the strain

Abstract A nonlinear analysis of the effect of viscous dissipation on the Rayleigh–Bénard instability in a fluid saturated porous layer is performed. The saturated medium is modelled through Darcy’s law, with the layer bounded by two parallel impermeable walls kept at different uniform temperatures, so that heating from below is supplied. While it is well known that viscous dissipation does not influence

Abstract A new mathematical model is presented for bone remodelling that includes a finite memory effect. In this new model, stimulus resulting from mechanical loading is separated from the signalling to grow or absorb bone. Also, a signal decaying exponentially to the distance from the point produced as well as an effect of decaying signal in time are considered. In addition, the model presented correctly

Abstract Additive manufacturing (AM) offers design freedom and ability to fabricate parts of complex shapes which are not often possible with the conventional methods of manufacturing. In an AM part, even with optimum build parameters, a complete elimination of defects is not possible and this makes it hard to fully deploy the AM technology to build load bearing parts operating under cyclic loading

Abstract In the framework of the couple stress theory, we discuss the effective elastic properties of a metal open-cell foam. In this theory, we have the couple stress tensor, but the microrotations are fully described by displacements. To this end, we performed calculations for a representative volume element which give the matrices of elastic moduli relating stress and stress tensors with strain

Abstract Fracture of normal strength concrete cylinder under static and dynamic loading is studied numerically. 3D finite element simulations are carried out at macro- and meso-scale. At meso-scale the analysis is performed with and without accounting for the interface zone (IZ) between aggregate and mortar. Aggregate is assumed to be linear elastic, and mortar is modeled using rate-dependent microplane

Abstract In this paper, we consider the role of functional kinetic equations in models of solid mechanics. It is shown that the choice of time-non-locality kernels allows both the finite speed of signal propagation and the inhomogeneity of material to be taken into account. Using analysis of the rheological kinetic equation for the entropy flux, we propose the motion energy, defined in the space of

Abstract An exact formulation and a solution of the stability problem for a three-dimensional elastic body containing distributed dislocations are given. The buckling phenomenon for a hollow nonlinear elastic sphere of the semi-linear (harmonic) material with edge dislocations is studied. The study is carried out within the framework of the continuum theory of continuously distributed dislocations

Abstract This work proposes a phenomenological level-set model for ferromagnetic shape-memory alloys (FSMAs), developed under consistent thermodynamic analysis. A set of adequate internal and external variables is chosen so as to describe the rate-independent magneto-mechanical response of a FSMA single crystal. Almost every phenomenological model in bibliography adopts martensitic volume fractions

Abstract In this paper, a diaphragm-type dielectric elastomer energy transducer is theoretically and numerically investigated by considering the viscoelastic behaviors of the material. The transducer is designed in the shape of a circular membrane. The buckling mode of the membrane is therefore harnessed to transform energy between its mechanical form and electrical form. It is shown that viscous dissipation

Abstract An effective fractional derivative-based visco-elastic model of tough, doubly cross-linked, single-network polyvinyl alcohol (PVA) hydrogels, embodying both chemical and physical cross-links, is developed using a Mittag–Leffler relaxation function of order 1/2 while applying only three material parameters that are physically quantifiable, namely frequency for maximum loss modulus, equilibrium

Abstract In our present paper, we approach the mixed problem with initial and boundary conditions, in the context of thermoelasticity without energy dissipation of bodies with a dipolar structure. Our first result is a reciprocal relation for the mixed problem which is reformulated by including the initial data into the field equations. Then, we deduce a generalization of Gurtin’s variational principle

Abstract In this work, we demonstrate the existence of rotational waves in deforming thermoelastic non-classical solid continua in which the conservation and balance laws consider internal rotations due to the deformation gradient tensor (Jacobian of deformation) as well as their time varying rates. In this non-classical continuum theory, time dependent deformation of solid continua results in time

Abstract Strain-induced crystallisation (SIC) is the phenomenon of elastomers to experience a pronounced nonlinearity under large deformations of several hundred percentages of strain, which is advantageous for industrial applications due to the resulting positive properties such as increasing crack growth resistance and fatigue behaviour. The overall objective of the current study is the constitutive

Abstract This article discusses several aspects of the curing process in polymers. First, we collect experimental data for an Araldite epoxy resin and calibrate the classical model of Kamal–Sourour. It is shown that there are strong correlations between the parameters in the material parameter identification process. Thus, a curing kinetics model with reduced number of parameters is proposed, which

Abstract We explore the formulation of nearly incompressible behaviors at finite strain in the context of a hybrid or a mixed energy. Such an energy is a function of both an isochoric deformation and a pressure-like quantity that can be considered as an internal variable. From thermodynamical and physical considerations, new energy functions are developed to correctly describe both nearly incompressible

Abstract The extreme stretching of dielectric elastomers in sensors, actuators and energy harvesting devices is a common phenomenon where the materials are prone to fracture under the influence of flaws and notches. In this work, we have investigated the length of flaw sensitivities of two widely used dielectric materials, acrylic (VHB) and silicone (Ecoflex) elastomers under a pure shear loading and

Abstract Various studies have reported the changes in the mechanical properties and the modification in morphology of polyamide due to the absorption of water. However, the relation between the local water content and the alteration in the properties has not been consolidated in a coupled model yet. In the current work, a simulation model is proposed that can capture the diffusion of water as well

Abstract Rubber components produced from nitrile butadiene rubber (NBR) are changing their material properties due to environmental influences. This is caused by irreversible changes occurring in the elastomer network which is known as chemical ageing. In this paper, ageing behaviour of NBR is investigated and modelled under the influence of different surrounding media as air and oil. Based on the

Abstract Even for a moderate actuation, a large electric voltage requirement hinders the application of electro-active polymers (EAPs) in many areas. Hence, among other mechanisms, the actuation enhancement in EAPs is performed via inclusions of high-dielectric-permittivity fillers in the matrix material in the uncured stage. Moreover, to obtain an optimum advantage from the high-dielectric-permittivity

Granular micromechanics approach (GMA) provides a predictive theory for granular material behavior by connecting the grain-scale interactions to continuum models. Here, we have used GMA to predict the closed-form expressions for elastic constants of macroscale chiral granular metamaterial. It is shown that for macroscale chirality, the grain-pair interactions must include coupling between normal and

Crack nucleation issue is addressed in a comprehensive micromechanics-based framework allowing to bridge the 2D model with the more realistic 3D representation of a crack. The sudden and abrupt nature of the nucleation process argues in favour of adiabatic conditions rather than isothermal so that the formulation of the energy balance is formulated in terms of internal energy instead of Helmholtz free

A geometrically exact nonlinear iso-parametric \(\mathrm {G}^1\)-conforming finite element formulation for the analysis of Kirchhoff rods, based on the cubic Bézier curve interpolation, is presented. In this work, the formulation is restricted to the planar 2D case. Introducing the \(\mathrm {G}^1\)-map, the interpolation preserves the continuity requirement during the deformation process of the rod

The presence of grain boundaries significantly influences the overall mechanical behavior of materials with an underlying crystalline microstructure. They act as an obstacle against the movement of dislocations and, thus, significantly contribute to size effects as for example the Hall–Petch effect. Hence, the thermodynamically consistent modeling of the behavior of the plastic slip at a grain boundary

The hyperbolicity of a model for relativistic extended thermodynamics of polyatomic gases is here proved for every time direction \(\xi _\alpha \); moreover, an expression for the production terms of the field equation is proposed which encloses as particular cases the variant of the Anderson–Witting model already known in the literature, but also a new variant of the Marle model. With these expressions

A framework for linear viscous gradient fluids as extensions of the Navier–Stokes law is derived. More precisely, the list of the independent variables is enlarged up to an Nth-order velocity gradient and, accordingly, also the list of the dependent variables up to dual hyperstress tensors of the same rank. It is shown that due to general invariance requirements, such models must be hemitropic functions

Magnetoelectric particle and laminate composites are investigated numerically, applying the finite element method in connection with microphysically or phenomenologically motivated constitutive models for ferroelectrics and soft as well as hard ferromagnetics. A micromechanical damage model is further introduced, accounting for micro-crack growth in the ferroelectric constituents, where the cracks

Thermal buckling problem of cylindrical shells made from functionally graded materials (FGM) is investigated under the framework of Donnell shell theory. The elastoplastic properties of FGM are described by Tamura–Tomota–Ozawa model, with a power law hardening model of metallic constituents, and the material-graded characteristic through the thickness is taken into account. \(J_{2}\) flow theory helps

A microstructure-based modelling approach was used to study the deformation behaviour of polycrystalline honeycomb structures under rubbing loading. Rubbing originates from the sliding contact between sealing surfaces in a gas turbine engine. As a stationary component of the sealing system, the honeycomb structure’s role is to prevent catastrophic failure of the rotating component. Therefore, normal

A possible strain energy density, incorporating Cosserat’s micro-rotations and Biot’s change in porosity conferred by the microstructure geometry, is proposed in an elastic, two-dimensional, nonlinear context. The nonlinearities are taken into account both extracting the exact macro-rotations by the polar decomposition of the standard deformation gradient \(\varvec{F}\) and evaluating the change in

Phenomena treated by non-equilibrium thermodynamics can be very effectively described by thermodynamic variational principles. The remarkable advantage of such an approach consists in possibility to account for an arbitrary number of constraints among state or kinetic variables stemming, e.g., from conservation laws or balance equations. As shown in the current paper, the variational principles can

The paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the

Devices made of Shape-Memory Alloys (SMA) often exhibit a superelasticity or a shape memory effect during the exploitation. Both effects include large deformations up to 10% or large rotations, and a large-strain stress integration procedure is necessary for a correct numerical simulation. For this purpose, a reformulation of the existing SMA phenomenological constitutive model is introduced to provide

Thick rods are employed in nanotechnology to build modern electromechanical systems. Design and optimization of such structures can be carried out by nonlocal continuum mechanics which is computationally convenient when compared to atomistic strategies. Bishop’s kinematics is able to describe small-scale thick rods if a proper mathematical model of nonlocal elasticity is formulated to capture size

We present a dynamical interpretation of the Monge–Kantorovich theory in a stationary regime. This new principle, akin to the Fermat principle of geometric optics, captures the geodesic character of many distribution networks such as plant roots, river basins and the physiological transportation network of metabolites in living systems. Our general continuum framework allows us to map a previously

For an electrically conducting rod that performs longitudinal oscillations, a self-consistent system is formulated that includes the equation of rod dynamics, the equation for the variation of the strength of the external magnetic field, and the kinetic equation for the accumulation of damages in the material of the rod. The linearized system and the system of equations, including geometrical and physical