In this work, the mechanical behaviour of composite materials consisting of fly ash-based geopolymer reinforced with wood fibres is investigated for compressive and flexural loadings. The gathered test data were used to calibrate constitutive models for the geopolymer, consisting of the exponential Drucker–Prager yield criterion coupled with the concrete damage plasticity model. The numerical analyses

A new nonlinear lattice model for an influence of the hydrogen concentration on the elastic constants of the lattice model of a material is developed. A weakly nonlinear long-wavelength continuum model is considered, and a model nonlinear equation for the dynamics of concentration of hydrogen is obtained asymptotically. The model predicts a decrease in the stiffness coefficient as well as a light local

During most metal manufacturing processes, the medium deforms by generating large quantities of plastic strain at relatively high strain rates, inevitably inducing rises in temperature. Metals characterized by low thermal conductivity properties might locally retain high temperatures, consequently undergoing thermal softening. The classical balance laws governing the continuum equilibrium show severe

In this work we investigate the buckling response of sandwich plates with a polymeric core and two face sheets reinforced by carbon nanotubes (CNTs). The problem is tackled analytically by means of a higher-order sandwich plate theory, where the face sheets are modeled according to a classical plate theory and modified strain gradient theory with temperature-dependent and moisture-dependent material

The complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic

The analytical formulas for spectrum of turbulence on the basis of the new theory of stochastic hydrodynamics are presented. This theory is based on the theory of stochastic equations of continuum laws and equivalence of measures between random and deterministic movements. The purpose of the article is to present a solutions based on these stochastic equations for the formation of the turbulence spectrum

The aim of this work is to propose a modification of the Jiang criterion (Jiang in Fatigue Fract Eng Mater Struct 23:19–32, 2000), developed for the general multiaxial loading on our own experimental data gained for the aluminium alloy 2124-T851, currently mostly used in the aviation industry, and the stainless steel 316L under combined loading states in low-cycle fatigue domain. Eight strain loading

We present an elastic damage constitutive model for polymeric foam based on thermodynamics framework to consider the effects of anisotropy and the growth and coalescence of cavities. The evolution equation of the proposed model describes the material behavior sustaining anisotropic and unilateral damage. To carry out finite element analysis, the material properties for various polymeric foams are applied

A fluid occupying a mechanically isolated vessel with walls kept at spatially non-uniform temperature is in the long run expected to reach the spatially inhomogeneous steady state. Irrespective of the initial conditions the velocity field is expected to vanish, and the temperature field is expected to be fully determined by the steady heat equation. This simple observation is however difficult to prove

A 2D-continuum model describing finite deformations in plane of discrete bi-pantographic fabrics has been recently obtained by applying an asymptotic procedure based on a set of local generalized coordinates. Rectangular bi-pantographic prototypes were additively manufactured by selective laser sintering using polyamide as raw material. Displacement-controlled bias extension tests were performed on

Void growth and morphology evolution are studied using a 3D representative volume element with a spherical void embedded in an FCC single crystal. The plastic flow contours are studied to determine the scenarios leading to fully plastic flow and plastic flow with elastic region. Further, the effect of anisotropy on void growth is studied through three initial crystallographic orientations (ICOs) [100]

In a preceding paper, we have showed as swarm robotics displacement can be related to the deformation of a continuum material, discretized by a lattice network representing the swarm. To reach this aim, it is fundamental to know the swarm configuration, i.e., its shape; this can be computed from the knowledge of the relative distances between its elements and it is studied as a geometry distances problem

This paper investigates the failure strain as a dependence of the stress triaxiality and the Lode angle parameter for polyurethane rigid foams (PUR) of two densities (100 and \(300\,\hbox {kg/m}^{3})\). Tests were carried out in tension for various configurations, resulting in different states of stress triaxiality at various Lode angles in the critical areas. The failure strain was determined for

The work is devoted to the description of unsteady thermal processes in low-dimensional structures. To obtain the relationship between the microscopic and macroscopic descriptions of solids, it is necessary to understand the heat transfer mechanism at the micro-level. At the latter, in contrast to the macro-level, analytical, numerical, and experimental studies demonstrate significant deviations from

General constitutive equations of heat transport with second sound and ballistic propagation in isotropic materials are given using non-equilibrium thermodynamics with internal variables. The consequences of Onsager reciprocity relations between thermodynamic fluxes and forces and positive definiteness of the entropy production are considered. The relation to theories of Extended Thermodynamics is

This work describes an approach for strain determination at the “in-plane” torsional test using digital image correlation (DIC) without brushing a statistical pattern on the specimen. It is well known that the in-plane torsion test represents a appropriate test method for material characterization of sheet metal in terms of yielding and kinematic hardening (Wagner et al. in Application of the in-plane

The classical theory for asymmetric lipid bilayer surfaces is revisited from the vantage point of three-dimensional liquid crystal theory. Independent tangential motions of the leaflets comprising the bilayer are accommodated in a framework that allows for distinct leaflet properties.

In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogenization techniques using the equivalence of energy at the macro- and microscales within a so-called representative

A coupled thermomechanical damage approach for dynamic shear failure in brittle solids is proposed in the present contribution. The model is constructed by asymptotic homogenization from microstructures with dynamically evolving microcracks, in mode II, with unilateral contact and friction conditions on their lips. Crack-tip and frictional heating effects assumed at the small scale give rise to distributed

In this paper, a nonlinear finite element procedure is developed to solve the coupled system of phase field and elasticity equations at large strains for martensitic phase transformations at the nanoscale. The transformation is defined based on an order parameter which varies between 0 for austenite to one for martensite. The phase field equation relates the rate of change of the order parameter to

Buckling of uniformly and not uniformly compressed tower buildings, resting on Winkler type soil, is investigated. An equivalent beam is introduced, able to capture the essential behavior of the building. It is a 3D Timoshenko beam, modeled in the framework of a direct approach, whose constitutive law is derived via a homogenization procedure, which includes the effect of the column prestress. The

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the

We analyze in this contribution the propagation of bulk and Rayleigh surface waves in periodic architectured materials undergoing internal damage. An elastic damageable continuum-based model is developed in the framework of the thermodynamics of irreversible processes, whereby the displacement experiences a jump across the faces of the propagating crack. The crack propagation involves an enhancement

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