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

This paper presents the determination of material hardening parameters with the use of the fuzzy set theory. The hardening parameters were initially predicted from measurements taken in the cyclic tension–compression test. The experimental hysteresis loop was compared to numerical one obtained by the integration of the plastic flow rule. The nonlinear combined hardening model—Voce isotropic hardening

The deterioration of the musculoskeletal system is a serious health concern for long-term space missions. The accumulated information over the past decades of space flights showed that microgravity impacts significantly the musculoskeletal system with muscle atrophy and bone loss. Until now, it has been difficult to make reasonable predictions of the bone loss for prolonged space missions due to the

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration

The interaction between magnetic field and thermal field in an elastic half-space, homogeneous and isotropic under two temperature and initial stress are investigated using a normal mode method in the framework of the Lord–Şhulman theory, with thermal shock and rotation. The medium rotates with a uniform angular velocity, and it is considered to be permeated by a uniform magnetic field and hydrostatic

Gradient plasticity theories are of utmost importance for accounting for size effects in metals, especially on the grain scale. Today, there are several methods used to derive the governing equations for the additional degrees of freedom in gradient plasticity theories. Here, the equivalence between an extended principle of virtual power and an extended energy balance is shown. The energy balance of

In this work, we considered the new parametrization of a multilayer thin domain. In particular, in contrast to classic approaches, we used several base surfaces and an analytic method with the application of orthogonal polynomial systems. We gave the vector parametric equation of each layer and the system of vector parametric equations of a multilayer thin domain and introduced the geometric characteristics

This paper presents an analysis of wave propagation in a microstretch elastic medium in the context of the Green–Naghdi (GN) theory. Moreover, the dissipation and the influence of gravity on reflected waves have also been investigated. In the present article, five reflected waves propagate into the medium for any incident wave. The problem is solved numerically, and the amplitude ratios are graphically

Mathematical models of micropolar plates and shells are considered within the framework of the approximation approach. The governing equations of the theories are written in a thermodynamically consistent form of the conservation laws. This ensures hyperbolicity and correctness of the initial boundary value problems. For numerical solution, we propose parallel algorithms for supercomputers with graphics

We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects

This work discusses some alternate models of a mixed assumed strain finite element which has been developed for laminated plates. After a brief theoretical review about this kind of plates and their possible finite element formulation, specifically devised for predicting the mechanical behavior of such structures, we discuss four possible assumptions for strains generating four kinds of mixed assumed

The paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the

In this paper, elastic wave propagation in a one-dimensional micromorphic medium characterized by two internal variables is investigated. The evolution equations are deduced following two different approaches, namely using: (i) the balance of linear momentum and the Clausius–Duhem inequality, and (ii) an assumed Lagrangian functional (including a gyroscopic coupling) together with a variational principle