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

This study is based on continuum damage mechanics and constructs an improved macro–micro-two-scale model to predict the fatigue life of engineering metallic materials subjected to variable amplitude loading. To account quantitatively for the fatigue damage retarding effect of higher load on lower ones in a loading sequence, the cyclic plastic response curve of microscopic weak inclusion is independently

Closed-form analytical representations of the rigid body orientation quaternion, angular velocity vector and the external moment vector satisfying kinematic equations and equations of motion are derived. In order to analyze errors of orientation algorithms for strapdown inertial navigation systems, reference models for specific rigid body rotation cases are formulated. Based on solutions, analytical

A thermodynamically consistent concept to model the strain-induced crystallisation phenomenon using a multiphase approach is discussed in Loos et al. (CMAT 32(2):501–526,2020). In this follow-up contribution, the same mechanical framework is used to construct a second model that sets the same three phases in a serial connection, demonstrating an alternative to the former parallel connection of phases

A six-equation Baer–Nunziato model at pressure equilibrium for two ideal gases is derived from a full non-equilibrium model by applying an asymptotic pressure expansion. Conditions on the interfacial pressure are provided that ensure hyperbolicity of the reduced model. Closure conditions for the relaxation terms are given that ensure consistency of the model with the second law of thermodynamics.

The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is not obtained by an affine assumption but by minimizing

The purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is

The main goal of the present paper was to obtain some new uniqueness results for the anisotropic thermoelastic bodies with double porosity structure. There are obtained some auxiliary results based on the Betti reciprocity relation that involve some thermoelastic processes.

The linear theory of coupled gradient elasticity has been considered for hemitropic second gradient materials, specifically the positive definiteness of the strain and strain gradient energy density, which is assumed to be a quadratic form of the strain and of the second gradient of the displacement. The existence of the mixed, fifth-rank coupling term significantly complicates the problem. To obtain

A nonlinear elastic model for nets made up of two families of curved fibers is proposed. The net is planar prior to the deformation, but the equilibrium configuration that minimizes the total potential energy can be a surface in the three-dimensional space. This elastic surface accounts for the stretching, bending, and torsion of the constituent fibers regarded as a continuous distribution of Kirchhoff

The present paper develops a version of a compound hierarchical model of materials, which implements a possibility of representing a complex process of the development of interrelated deformation effects in the form of a succession of formally independent elementary acts described by the related particular models of irradiation-induced swelling, plasticity, thermal and irradiation creep. In describing

This paper is concerned with a mechanical explanation of a highly inhomogeneous distribution of hydrogen within metal specimens, based on the micropolar continuum approach. The primary focus is on the modeling of the nonuniform stress–strain state of a cylindrical metal specimen that rapidly fades away from the border and changes the inner structure of the material near the lateral surface. The boundary

We present an analytical study of the problem associated with an edge dislocation near a completely coated finite anticrack (or rigid line inhomogeneity). The two foci of the elliptical coating-matrix interface are located at the two tips of the anticrack. In addition, the coating and the matrix have identical shear moduli but distinct Poisson’s ratios. By means of conformal mapping and analytic continuation

New finite strain elastoplastic \(J_2\)-flow equations with no reference to the yield condition are proposed for the purpose of simultaneously simulating low-to-ultrahigh cycle failure effects of metals. As inherent response features of such new equations, the entire responses up to eventual failure under cyclic and non-cyclic loadings of constant and variable amplitudes are automatically predicted

Residual stresses introduced into components in the course of manufacturing processes may considerably impair fatigue life and therefore the operational reliability and safety of the final product. Particularly in critical applications in the aerospace industry, where peripheral milling is a common surface finishing operation for components made from the titanium alloy Ti–6Al–4V, it is desirable to

An electrochemical–thermomechanical model for the description of charging and discharging processes in lithium electrodes is presented. Multi-physics coupling is achieved through the constitutive relations, obtained within a consistent thermodynamic framework based on the definition of the free energy density, sum of distinct contributions from different physics. The system is characterized by finite

The paper deals with the effect of different stress-state-dependent damage mechanisms on the onset of fracture in ductile metals. A continuum damage model is discussed using a strain tensor as an appropriate damage variable. It takes into account the influence of stress state on the damage condition and on the evolution equations of damage strains. A fracture condition based on critical damage parameters

Unfortunately, the original version of the article contained error in the below equation terms.

As thermoset polymers find frequent implementation in engineering design, their application in structural engineering is rather limited. One key reason relies on the ongoing curing process in typical applications such as post-installed adhesive anchors, joints by structural elements or surface-mounted laminates glued by adhesive polymers. Mechanochemistry including curing and aging under thermal as

Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level, a material possessing a substructure at a microscopic length scale calls for introducing

The manuscript aims to investigate the static behavior of laminated nanoplates in hygro-thermal environment. The theoretical framework is based on the Kirchhoff hypothesis for thin structures including the effect of material length scales, which is described by a nonlocal model. For this purpose, the plane stress constitutive laws for laminates are enriched by a size-dependent parameter according to

We present two multifield and one single-field variational principles for the initial boundary value problem of diffusion. Chemical potential and concentration appear as conjugate variables in the multifield formulations. The main importance of the proposed formulations is the approach used to generate the variational principles, where the framework of Generalized Standard Materials is used for constitutive

The present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod, respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads

Modern developments of biomedical applications demand a better understanding of mechanical behaviour of soft biological tissues. As human soft tissues demonstrate a significant structural and functional diversity, characterisation of their mechanical behaviour still remains a challenge. Limitations related with implementation of mechanical experiments on human participants lead to a use of finite-element

Thin linearly elastic Kirchhoff–Love-type circular cylindrical shells of periodically micro-inhomogeneous structure in circumferential and axial directions (biperiodic shells) are investigated. The aim of this contribution is to formulate and discuss a new averaged nonasymptotic model for the analysis of selected stability problems for these shells. This, so-called, general nonasymptotic tolerance

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