We develop a linear theory of the Cosserat continuum of a special type. This continuum possesses only rotational degrees of freedom. The constitutive equation for the moment stress tensor is the same as for the elastic continuum. The main feature of our model is that the differential equation relating the wryness tensor to the angular velocity vector contains a source term. Thanks to a special choice

Our study is a generalization of some results obtained by Synge in the classical theory of elasticity. By this extension, we wish to cover the theory of micropolar elastic bodies. More precisely, we approach the electroacoustic energy flux in the case of plane waves of harmonic type which propagate in piezoelectric crystals which are supposed to be prepolarized and prestressed.

A Correction to this paper has been published: 10.1007/s00161-022-01098-4

After the wide premise of Part I, where the equations for Cauchy’s continuum were retrieved through the energy minimization and some differential geometric perspectives were specified, the present paper as Part II outlines the variational derivation of the equilibrium equations for second gradient materials and their transformation from the Eulerian to the Lagrangian form. Volume, face and edge contributions

In the original publication of the article, a typo error has been introduced in the appendix section

The present work is devoted to a study of the generalized poro-thermoelasticity theory and aims to derive the variational principle and continuous dependence results in the context of this theory. The basic field equations are considered for an isotropic and homogeneous fluid-saturated poro-thermoelastic medium. With the concept of incorporating initial conditions into the field equations, an alternative

In material modeling, when dealing with diffusion at large deformations, there are usually two different variants for the diffusion flux: an isotropic law in the current placement and an isotropic law in the reference placement. The first one causes diffusion behavior, which is independent from the initial shape of the body, i.e., it causes a deformation-independent behavior. The second one relates

The principal goal of the present paper is to study rarefied relativistic polyatomic gases in both Minkowski spacetime and Robertson–Walker spacetime. The field equations are determined from a recently developed generalized relativistic BGK-type model for polyatomic gases. This model is applied to both Minkowski spacetime and flat and non- flat Robertson–Walker spacetimes. The equation of state for

The generalized Reissner-type operator of three-dimensional micropolar mechanics of solids is presented, on the basis of which the generalized Reissner-type operator of three-dimensional micropolar mechanics of thin solids with one small size is obtained under the new parameterization of the domains of these bodies. From the last Reissner-type operator, in turn, the generalized Reissner-type variational

The effective parametrization of a multilayer thin domain, called a new parametrization, is considered and consists in using, in contrast to the classical approaches, several base surfaces. In addition, the new parameterization is characterized by the fact that it is experimentally more accessible than other parameterizations used in the scientific literature, since the front surfaces are used as basic

The chemical structure, polymer mobility and mechanical properties are studied for a cross-linked amorphous poly(ether urethane) (PU) from glass transition to rubber elasticity for juvenile dry samples and for water-saturated states after exposure to humid air (r.h. = 29, 67, 95, 100%) at \(60~^\circ \hbox {C}\) during 1 y of ageing. For saturated samples, network chain cleavage is the chemical ageing

In this study, the time-dependent mechanics of multilayered thick hyperelastic beams are investigated for the first time using five different types of shear deformation models for modelling the beam (i.e. the Euler–Bernoulli, Timoshenko, third-order, trigonometric and exponential shear deformable models), together with the von Kármán geometrical nonlinearity and Mooney–Rivlin hyperelastic strain energy

The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pileup against, absorption by, and transfer through the grain boundary, is developed for non-uniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i)

Numerical analyses and acoustic experiments were performed to investigate the effects of geometric parameters on the hydro-acoustic characteristics of flow over cylinders with circular, square and rectangular cross sections, respectively. A hybrid method which combines RANS and FWH equations was applied for the numerical analyses. The hydro-acoustic characteristics were obtained for circular cylinders

Toward directly simulating pseudo-elastic effects of shape memory alloys, new elastoplastic equations of von Mises type are proposed by correlating the yield surface radius with the yield surface center, thus establishing a new elastoplasticity model characterized by three coupled quantities for isotropic and anisotropic hardening. Within the framework of conventional macroscopic elastoplasticity,

A modified form of BGK source terms is proposed for modeling two-phase flows with thermodynamical disequilibrium. The novelty is that three independent time-scales allow to manage the return to the thermodynamical equilibrium while remaining in agreement with the second law of thermodynamics. This is achieved thanks to the definition of a “local-in-time” equilibrium state which tends toward the asymptotic

In this study, we consider the final boundary value problem for a thermoelastic Cosserat material. With the help of a simple translation, our final problem is transformed in a usual mixed problem with boundary relations and initial data. For this new problem, we obtain some theorems of uniqueness of solutions. For this, we do not use any law of conservation of energy, as is usually done to obtain a

Natural rubber (NR) blends were filled with soya protein isolate (SPI) in various amounts: 0; 10; 20; 30; 40 phr. To improve interfacial adhesion, calcium sulfate dihydrate (CSD) in amounts of 0 and 2.5 phr was added. Hardness, tensile strength, and elongation at break before and after thermooxidation aging (TOA), morphology of blends and thermal stability were studied for prepared blends. Amount of

The notion of dynamic inclusion can be utilized to represent phenomena in micromechanics of solids such as phase transformations, in particular when subjected to dynamic loading. If the size of a dynamic inclusion is comparable to the inherent length parameters of its constituent material, then the size effect manifests its significance. The present paper is, hence, dedicated to the employment of the

As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar

In this paper, we introduce the interval-valued KT-pseudoinvex variational control problems involving multiple integral objective functionals. Specifically, a new condition of generalized convexity is defined for the functionals involved in the new class of interval-valued variational control problems. Moreover, it is proved that an interval-valued KT-pseudoinvex variational control problem is described

Some errors exist in the above paper.

Presented herein is a numerical variational approach to the two-dimensional (2D) incompressible nonlinear elasticity. The governing equations are derived based upon the minimum total energy principle by considering the displacement and a pressure-like field as the two independent unknowns. The tensor equations are replaced by equations in a novel matrix-vector form. The proposed solution method is

The multiple delaminations at different interfaces and their interactions should be described simultaneously in an accurate analysis approach of composite laminates under the multi-physics loading, but it is not studied thoroughly in the existing research works. A thermo-mechanical cohesive zone model is proposed to investigate the thermo-mechanical progressive growth of multiple delaminations in composite

In this article, on the basis of the stochastic theory of turbulence and the regularity of equivalence of measures, the calculation of the friction coefficient is presented for the laminar–turbulent transition on the flat plate. As a result, the formula for the friction coefficient depending on the turbulence intensity, the scale of turbulence, the velocity-profile index, and the Reynolds number for

We consider a linear theory of a viscoelastic Cosserat continuum of a special type. In doing so, we associate the main variables characterizing the stress–strain state of the continuum with quantities characterizing the electrodynamic and thermal processes. Taking into account the suggested analogues, we interpret equations describing the continuum as equations of thermodynamics and electrodynamics

In this study, some pioneering contributions, envisaged in the works of Gabrio Piola, were developed through tools of the modern differential geometry and applied to the second gradient continua. Part I introduced the variational approach for the equilibrium problem according to the first gradient theory and exploited differential geometric perspectives for the present scenario. By prescribing the