The mechanical balance equations for a body with microstructure are derived from an expansion of the general Noll’s axiom of frame-indifference that takes into account the behavior of measures of microstructural interactions. Next, we introduce perfect internal constraints and adopt an extended determinism principle to analyze the consequences of their presence. Finally, we define the class of continua

In the paper, we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinite system of stochastic ordinary differential equations

A method is proposed to identify the fully anisotropic elasticity tensor by applying the impulse excitation technique. A specially designed batch of several differently oriented bar-shaped specimens with rectangular cross section is analyzed with respect to the eigenfrequencies of their fundamental flexural and torsional modes. Estimations based on the equations for the calculation of the isotropic

This work aims to analyze the effect of a new deformation measure in the response of 2D plates subjected to in-plane loads. The proposed formulation allows to clearly distinguish the energetic contribution of every involved deformation mechanism. The action functional is supposed to depend on a strain, a wryness and a new relative rotation tensor in the nonlinear hypothesis; therefore, the suggested

Thermites are powerful energetic materials able to release large amounts of energy in a self-propagating reaction. They have been widely applied in rail welding, pyrotechnics, and material synthesis, as they are highly exothermic. In recent years, there has been an increased interest on applying a thermite reaction in the plug and abandonment of wells due to the possibility of reducing the high cost

A stress-affected chemical reaction front propagation is considered using the concept of a chemical affinity tensor. A reaction between an elastic solid constituent and a diffusing constituent, localized at the reaction front, is considered. As a result of the reaction, the elastic constituent transforms into viscoelastic one. The reaction is accompanied by volume expansion that in turn may result

A fully second-order continuum theory of fluids is developed. The conventional balance equations of mass, linear momentum, energy and entropy are used. Constitutive equations are assumed to depend on density, temperature and velocity, and their derivatives up to second order. The principle of equipresence is used along with the Coleman–Noll procedure to derive restrictions on the constitutive equations

An Eulerian, hyperbolic, multiphase-flow model for dynamic and irreversible compaction of porous materials is constructed. A reversible model for elastic, compressible, porous material is derived. Classical homogenization results are obtained. The irreversible model is then derived in accordance with the following basic principles. First, the entropy inequality is satisfied by the model. Second, the

In this work, a mathematical modeling of the elastic properties of cubic crystals with centrosymmetry at small scales by means of the Toupin–Mindlin anisotropic first strain gradient elasticity theory is presented. In this framework, two constitutive tensors are involved, a constitutive tensor of fourth-rank of the elastic constants and a constitutive tensor of sixth-rank of the gradient-elastic constants

First, different porous media theories are presented. Some approaches are based on the classical mixture theory for fluids introduced in the 1960s by Truesdell and Coworkers. One of the first researchers who extended the theory to porous media (thus mixtures containing at least one solid constituent) and also accounting for chemical reactions was Bowen. Another important branch of porous media theory

The equilibrium equations and the traction boundary conditions are evaluated on the basis of the condition of the stationarity of the Lagrangian for coupled strain gradient elasticity. The quadratic form of strain energy can be written as a function of the strain and the second gradient of displacement and contains a fourth-, a fifth- and a sixth-order stiffness tensor \({\mathbb {C}}_4\), \({\mathbb

We employ a free energy density for Mg–Al alloys that is dependent on concentration, strain, and temperature, and derived from quantum mechanical calculations by Ghosh & Bhattacharya (Acta Mater 193:28–39, 2020) , to model the dynamic precipitation of the Mg\(_{17}\)Al\(_{12}\) phase during creep experiments in Mg–Al alloys. Our calculations show that the overall volume fraction of the dynamically

Devised towards geophysical applications for various processes in the lithosphere or the crust, a model of poro-elastodynamics with inelastic strains and other internal variables like damage (aging) and porosity as well as with diffusion of water is formulated fully in the Eulerian setting. Concepts of gradient of the total strain rate as well as the additive splitting of the total strain rate are

At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to describe the coarsening kinetics of the exsolution microstructure, we derive a thermodynamically consistent continuum theory for the multicomponent Cahn–Hilliard equations

In the present paper, we propose a mechanistic mathematical model describing the process of drug release from a drug delivery system. This model takes various aspects of drug release into account, namely gradual penetration of the surrounding solution into the system, dissolution of solid drug particles embedded within, diffusion of the dissolved drug, dissolution of the carrier and its collapse. Modeling

The thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly

We use the sixth-order linear parabolic equation $$\begin{aligned} \frac{\partial y}{\partial t}=B\left( \alpha \frac{\partial ^{6}y}{\partial x^{6}}-\frac{\partial ^{4}y}{\partial x^{4}}\right) ,\ x\in {\mathbb {R}}_{+},\ t>0, \end{aligned}$$ proposed by Rabkin and describing the evolution of a solid surface covered with a thin, inert and fully elastic passivation layer, to analyze the grain boundary

In this paper, the coupled phase field and local/nonlocal integral elasticity theories are used for stress-induced martensitic phase transformations (MPTs) at the nanoscale to investigate the limitations and contradictions of the nonlocal integral elasticity, which are due to the fact that the support of the nonlocal kernel exceeds the integration domain, i.e., the boundary effect. Different functions

Recent studies on metamorphic petrology as well as microstructural observations suggest the influence of mechanical effects upon chemically active metamorphic minerals. Thus, the understanding of such a coupling is crucial to describe the dynamics of geomaterials. In this effort, we derive a thermodynamically consistent framework to characterize the evolution of chemically active minerals. We model

Galerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate

Non-equilibrium processes in Schottky systems generate by projection onto the equilibrium subspace reversible accompanying processes for which the non-equilibrium variables are functions of the equilibrium ones. The embedding theorem which guarantees the compatibility of the accompanying processes with the non-equilibrium entropy is proved. The non-equilibrium entropy is defined as a state function

We study the linear theory of thermo-electro-viscoelasticity of Green–Naghdi type for the case of a one-dimensional body. For the corresponding mathematical model, we prove a uniqueness theorem of the solution to the mixed boundary-initial-value problem by means of the Laplace transform after rewriting the constitutive equations in an appropriate form. Moreover, we derive a result of continuous dependence

In this work, a 3D semi-analytical finite element method (SAFEM) is developed to calculate the effective properties of piezoelectric fiber-reinforced composites (PFRC). Here, the calculations are implemented in one-eighth of the unit cell to simplify the method. The prediction of the effective properties for periodic PFRC made of piezoceramic unidirectional fibers (PZT) with square and hexagonal space

This research work performs the first time exploring and addressing the flexomagnetic property in a shear deformable piezomagnetic structure. The strain gradient reveals flexomagneticity in a magnetization phenomenon of structures regardless of their atomic lattice is symmetrical or asymmetrical. It is assumed that a synchronous converse magnetization couples both piezomagnetic and flexomagnetic features

We apply the Stroh octet formalism to derive the electroelastic field for an anisotropic piezoelectric solid weakened by a blunt crack. The blunt crack itself is represented by a parabolic cavity with traction-free and charge-free boundary. Using identities developed in the Stroh octet formalism, we obtain explicit and full-field expressions for stresses, electric displacements, displacements and electric

In this article, several thermoelastic benchmark cases are studied within the framework of ordinary state based peridynamic theory (OSPD). By using OSPD, the limitations of geometrical discontinuity in fracture analysis can be overcome. Meanwhile, double nodes can also be avoided during crack definition. A domain integral method with thermal effect is applied in calculating the thermal stress intensity

This paper presents exact elasticity solutions for nano-plane structures subjected to any distribution of inplane body forces. In deriving the plane stress solutions, three different models are used. They are a lattice elasticity model called the Hencky bar-grid model (eHBM), the continualised nonlocal plane model (CNM) and Eringen’s nonlocal plane model (ENM). eHBM is a physical structural model comprising

A model to a coupled thermal-viscoelastic finite deformation problem is presented. The nonlinearities are solved using the successive linear approximation method. This method uses the relative Lagrangian formulation and the idea of the superposed large deformation by small deformations. Furthermore, the constitutive equations are calculated at each state, with the reference configuration updated for

The concept of porothermoelasticity has been developed to investigate the thermal and mechanical behavior of elastic materials with porosity. This approach combines the theory of heat conduction with poroelastic constitutive equations and by incorporating the coupling of temperature field with the stresses and pore pressure. The mathematical modeling of the porothermoelastic material to various practical

The Asymptotic Expansion Load Decomposition higher-order beam model is based on the classical two-scale asymptotic expansion in the linear elasticity framework.It was successively extended to eigenstrains and to plasticity in small deformations in different papers. The present paper offers a comprehensive and consistent presentation of our approach applied to civil engineering applications.

With the goal of ensuring the security of passengers for automotive industry, the present work addresses the temperature and impact speed envelope allowing ductile failure of plasticized PVC to be obtained. A database of about 250 test results has been constructed for various conditions at ten test temperatures, four impact speeds and two specimen geometries (with or without scoring). The desired ductile

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential

The influence of a microstructure on heat conduction in solids is studied using the internal variable approach. Two variants of the internal variable treatment are compared by means of the numerical simulation of two-dimensional heat conduction in a plate under a localised thermal pulse loading. Computation of the same problem by the different internal variable descriptions produces qualitatively dissimilar

This paper is concerned to study quasi-static boundary value problems of coupled linear theory of elasticity for porous circle and for plane with a circular hole. The Dirichlet type boundary value problem for a circle and the Neumann boundary value problem for a plane with a circular hole are solved explicitly. All the formulas are presented in explicit ready-to-use form. The solutions are represented

The phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy

A previous bone remodelling model was presented elsewhere [30], and in the present paper, the same model was tested with new conditions; an interaction between bone tissue, bone substitute material and a dental implant was considered. The bone substitute material was assumed to be dead tissue, which does not synthesizes neither absorbs bone tissue, and it was considered, as well, resolvable. A moving

The present study approaches the theory of Moore–Gibson–Thompson thermoelasticity in the context of the materials with double porosity structure. The main results of the present study are based on a reciprocity theorem for the thermoelastic materials with double porosity that leads us in determining of the uniqueness theorems for the solution of mixed problems for the materials with double porosity

The behavior of third gradient materials is analyzed. They possess stress tensor fields of second, third and fourth order. Starting from the principle of virtual power, we derive the admissible boundary conditions. Those on free surfaces can only be obtained by the application of the divergence theorem of surfaces. On the other hand, such an application to fictitious internal cuts makes no sense although

This paper is devoted to the development of a continuum theory for materials having granular microstructure and accounting for some dissipative phenomena like damage and plasticity. The continuum description is constructed by means of purely mechanical concepts, assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle, without incorporating any additional

Polyamide exhibits hygroscopic nature and can absorb up to 10% of moisture relative to its dry weight. The absorbed moisture increases the mobility of the molecular chains and causes a reduction in the glass transition temperature. Thus, depending on the moisture distribution, a polyamide component can show different stiffness and relaxation times. Moreover, the moisture distribution also depends on

The dynamic thermomechanical analysis on composite sandwich plates with damage is investigated in this paper. A thermomechanical extended layerwise/soild-element (TELW/SE) method is developed for sandwich plates. In the TELW/SE method, the thermomechanical extended layerwise theory is used to model the behavior of the laminated composite facesheets, while the thermomechanical eight-node solid element

In this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young’s

A second strain gradient theory-based continuum model is presented for the mechanics of an elastic solid reinforced with extensible fibers in plane elastostatics. The extension and bending kinematics of fibers are formulated via the second and the third gradient of the continuum deformation. The Euler equations arising in the third gradient of virtual displacement are then formulated by means of iterated

We discuss some aspects of using the spatial description and the finite volume method as applied to the solid mechanics problems. The main objective is to study the differential equation relating the strain measure to the velocity gradient. We show that this equation can be reduced to an integral form and the obtained equation has the structure of the balance equation without a source term. On the

Starting from the three-dimensional theory of linear elasticity, we arrive at the exact plate problem by the use of Taylor series expansions. Applying the consistent-approximation approach to this problem leads to hierarchic generic plate theories. Mathematically, these plate theories are systems of partial-differential equations (PDEs), which contain the coefficients of the series expansions of the

Starting from a Cosserat-type model for curved rods, we derive analytical expressions for the effective stiffness coefficients of multilayered composite beams with an arbitrary number of layers. For this purpose, we employ the comparison with analytical solutions of some bending, torsion, and extension problems for three-dimensional beams and rods. The layers of the composite beam consist of different

The pure titanium, as a biomaterial destined for production of load-demanding prostheses, requires thermo-mechanical processing to increase its strength. The most common way to achieve this is the method of grain fragmentation. Thermo-mechanical deformation of titanium is a complex process, which makes it very difficult to describe it by means of constitutive equations. Such constitutive relations

Anisotropic materials are those that the value of a property depends on the direction of analysis. This article addresses both analytical and numerical stress computation for orthotropic beams under normal and shear loads. The analytical solution is based on potential polynomial functions and the present work establishes general strategies which allow systematic evaluation of the polynomial coefficients

In this paper we investigate the influence of rotational viscosity on the plane shear-rotational wave propagation in the linear isotropic reduced Cosserat medium. In such a continuum body points possess independent rotational and translational degrees of freedom, but the material does not resist to the gradient of microrotation. Stress tensor is asymmetric, but the couple stress is zero. For the elastic

Iron and steels are allotropes, meaning they exhibit different crystal configurations. The martensitic transformation is crucial for a variety of processes, such as hardening. It is induced by a combination of undercooling and mechanical deformation. Due to the changing material properties within the phases, and due to topological changes that might occur during the transformation, a phase field approach

Foamed rubber with a mixed cellular microstructure is a compressible material used for various sealing applications in the automotive industry. For technical optimization, a sufficiently precise material model is required. Here a material description for the porous elastic and viscoelastic response of low density foamed rubber is proposed and adapted to ethylene propylene diene monomer (EPDM)-based

In this paper, we discuss a theoretical approach to morphological instability analysis of the coherent interphase boundaries in strained heterostructures. Taking into account the fact that, under certain conditions, the atomic arrangement of solid–solid interfaces is thermodynamically unstable, the evolution equation describing the kinetics of the relief formation is obtained. The considered process

The paper presents experimental analysis of relation between friction coefficient and contact pressure of \(\hbox {MoS}_2\) film deposited on \(\hbox {Ti}_6\hbox {Al}_4\hbox {V}\) substrate in contact with sapphire ball during reciprocating sliding motion. It is shown that the value of friction coefficient decreases with increasing contact pressure. A microscale modeling approach is next developed

An extension of Boley’s continuum mechanics-based successive approximation method is presented for rectangular beams composed of two isotropic linear elastic layers. The solution is cast into the form of tables, in complete analogy to the tables originally presented by Boley and Tolins for single-layer strips. The first column in these tables corresponds to the classical Bernoulli–Euler theory of beams

The friction stir welding (FSW) process generally induces a gradient of properties and a softer behaviour along the welded joint. To design aeronautical structures welded by FSW in fatigue, it is necessary to study the impact of this localized soft behaviour on the overall structure. In this study, the 2198-T8 hardening structural aluminium alloy is considered. Monotonic and cyclic mechanical tests

The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two- and three-neighbour interactions

This paper studies weak solutions of the axial oscillations of the carbon nanotube modeled as an elastic nanobeam surrounded by an elastic medium. The model used combines Eringen’s theory of non-local elasticity and the equations of axial oscillations proposed by Aydogdu. Based on the Sturm–Liouville problem associated with this case, the weak solutions of the longitudinal waves in the carbon nanotube

Within the general approach to the modified Kirsch problem incorporating surface elasticity and residual surface stress (surface tension) by the original Gurtin–Murdoch model, the proper boundary conditions at an arbitrary cylindrical surface are derived in terms of complex variables for the plane strain and plane stress. In the case of the plane stress, the properties are allowed for not only of the

In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced