We construct a one-dimensional first-order theory for functionally graded elastic beams using the variational-asymptotic method. This approach ensures an asymptotically exact one-dimensional equations, allowing for the precise determination of effective stiffnesses in extension, bending, and torsion via numerical solutions of the dual variational problems on the cross-section. Our theory distinguishes

This paper provides an algorithm for the 3D printing technology, decomposing the entire surface into subdomains of different curvature, to be covered by distance holding reinforcing substructures in each subdomain. The domain decomposition is based on a draping simulation and a membrane stress analysis. The choice of printed substructures is based on our previous mathematical analysis using dimensional

A hierarchical asymptotic modeling approach is applied to solve unilateral contact problems for vibroadhesive micropatterned elastic interfaces. The deformation model for individual micropillars accounts for contributions from both local (Hertzian contact) and global (elastic rod with variable cross-section) deformations. The deformation model of substrate (elastic half-space), on top of which the

Most plate models in use are hypothesis-based, which struggle to resolve the internal stress distribution resulted from plate microstructural heterogeneities, making the strength prediction of such plates still a challenging issue nowadays. To this end, exemplified by fibre-reinforced laminates, the asymptotic behaviour of three-dimensional full-resolution models of microstructural plates is studied

Adhesion and deadhesion processes at the interface between an object and a substrate are well-established phenomena in the realm of materials science and biophysics. These processes can be profoundly influenced by thermal fluctuations, a phenomenon empirically validated through numerous experimental observations. While discrete models have traditionally served as a foundation for understanding this

A phenomenological pseudo-elastic model for isotropically elastic, incompressible materials exhibiting Mullins-type dissipation has been developed using a complementary energy-based approach. The work-conjugate constitutive variables in the inverse stress–strain relations are the Hencky logarithmic strain tensor and the Cauchy stress tensor. The thermo-mechanically consistent pseudo-elastic model is

In this work, synthetic waveforms generated by a point source of acoustic oscillations in a cylindrical cavity filled with a fluid are calculated using Biot's theory. The calculations are performed for the case when the pores and the cavity are filled with different immiscible fluids. The influence of surface tension on the parameters of elastic waves is investigated. It is shown that the influence

This work describes a thermo-poroelasticity model for a porous medium filled by two immiscible fluids in the framework of the Biot theory of poroelasticity. Local thermal equilibrium is assumed, i.e., the solid, the wetting fluid and the nonwetting fluid experience the same temperature variation in a continuum material particle. The constitutive relations in the present model include the thermally

Viscoelastic (VE) pads, commonly employed as passive damping components in damping devices to absorb and dissipate energy, present challenges in predicting the mechanical behavior under large deformation due to significant nonlinearity. This study introduces a novel nonlinear time-domain model to accurately characterize the response of VE pads subjected to cyclic loading across small, moderate, and

This paper presents a continuum theory for flexoelectric semiconductors and analyzes the interaction between electric currents and inhomogeneous deformations, which provides an opportunity for strain gradient engineering. Basic principles for continuum physics, including mass conservation, charge conservation, balance of linear momentum, balance of angular momentum, electrostatics, and thermodynamic

This paper deals with the investigation of the elastic stability of double tapered microbeams embedded in Winkler elastic foundation. It is considered that the microbeam is embedded in a continuous elastic constraint and its cross-section changes linearly along the longitudinal direction. Nonlocal couple stress theory and Bernoulli-Euler beam theory are used to obtain the size-dependent constitutive

The system of non-interacting electrically charged core-massless spring-shell mechanical units, demonstrating negative effective mass, is considered, seen as a Drude–Lorentz gas. When such an ideal gas is exposed to the external harmonic field, it demonstrates as the certain conditions the negative frequency-dependent electrical conductivity. The negative value of the electrical conductivity σ implies

Continuum mechanical models for growth and remodelling of biological tissue are well suited for the description of physiological and pathological processes, such as bone remodelling, muscle adaption or the progression of a tumour. An overview of four selected growth models from the literature is given and fundamental kinematic and multiphasic approaches for open and closed systems are outlined. Beyond

This study presents an investigation into the elastic wave propagation of graphene origami (GO)-enabled auxetic metamaterial plates, using a quasi-three-dimensional (3D) model for the first time. It introduces an eight-parameter quasi-3D theory for the governing equations of motion of the metamaterial plates, including axial, transverse, rotational, and stretching motions through variational algebra

This study aims to integrate micromechanics-based analytical models with machine learning (ML) models to predict the effective properties of two-phase composites. A novel approach grounded in Maxwell’s effective field method (EFM) is proposed to address the accuracy limitations inherent in micromechanics-based models while minimizing the amount of data needed to fit ML models. Notably, this new approach

The novelty here comes from not only the perfect nonlinear three-dimensional (3D) electro-elasticity investigation but also the mixed material itself. The literature widely showed mechanical assessments on the piezoelectric structures; however, a lack of nonlinear three-dimensional elasticity studies has been witnessed on these kinds of smart materials. Therefore, a nonlinear 3D elasticity-piezoelectricity

Analysing scale phenomena in nanostructures is crucial for modelling and optimizing modern nanotechnological devices. Notably, soft nanostructures can be effectively designed as basic components of smart electro-mechanical systems that require geometrically nonlinear analyses as their structural parts undergo large deflection. Adoption of non-conventional approaches for accurate assessment of size

An active composite material is assumed to be composed of a passive isotropic elastic matrix with spherical voids containing active rod-like elements, each of which being in diametrical contact with the void’s surface. A ball-bearing fixation between the rod and the contact pads is assumed, and thereby the normal contact becomes a primary mode through which the rod-like elements transfer active loading

The recent advances of solid mechanics of polymer networks are that they can be well-modelled by a physically-based size-dependent constitutive relation via a simplified strain gradient elasticity theory. However, boundary value problems of plate models composed of polymer networks have not been reported, which limit wide applications of the models in the engineering science. In this paper, we systematically

Eshelby's inhomogeneity problem is solved within the second form of Mindlin's first strain gradient elasticity theory for the prediction of the effective elastic properties of composites. Considering Green's function technique, an integral equation is established for an ellipsoidal inhomogeneity embedded in a homogeneous elastic medium and subjected to non-uniform boundary conditions. Within isotropic

The present study provides closed-form expressions of propagation (kinking) angles by generalizing maximum energy release rate criterion in linear elastic fracture mechanics (LEFM) within micropolar theory of elasticity to address the in-plane, brittle crack propagation phenomenon in size-dependent materials with the presence of particle rotations.

In this paper, we propose a self-consistent scheme for the calculation of the components of the effective electrical conductivity tensor. The calculations were fulfilled for a microinhomogeneous material, the components of which have the Hall effect. The presence of the Hall effect leads to appearance of asymmetry of the components of the conductivity tensor and to dependence of these components on

For the first time, strict analytical solutions for the elastic fields and the strain energies of an infinitely thin dilatational disk (DD) and a dilatational cylindrical inclusion (CyI) of finite length coaxially embedded in an infinite elastically isotropic cylinder with free surface are given and analyzed in detail. The solutions are represented in an integral form that is suitable for further analytical

The main objective of this study is to implement extended finite element method (XFEM) to two-dimensional (2D) micropolar structures in order to extract basic fracture parameters required in linear elastic fracture mechanics (LEFM) in a computationally efficient manner, and thus to provide basis to explore the crack propagation phenomenon within this framework. The stress and couple-stress intensity

Estimating model parameters from experimental data is a common practice across various research fields. For nonlinear models, the parameters are estimated using an optimization algorithm that minimizes an objective function. Assessing the certainty of these parameter estimates is crucial to address questions such as “what is the probability the estimation error is smaller than 5%?”, “is our experiment

Engineering interleaves of composite laminates with carbon nanotubes (CNTs) improves interlaminar fracture toughness, creating also conductivity, which can be employed for damage identification. The paper explores machine learning (ML) solution of the inverse problem of the defect identification for interleaves with anisotropic conductivity (aligned CNTs). The electrical and geometrical properties

Unlike ordinary solid materials, underground nano-materials such as kerogen, have relatively small dimensions and suffer from unavoidable in-situ stresses. The coexistence of size effects and initial stresses poses a great challenge to the constitutive modeling of deeply buried nano-inclusions. Despite the theories of strain gradient elasticity (SGE) and initially stressed elasticity (ISE) have been

Indentation of the coated piezoelectric transversely isotropic half-space by a conical conductive punch is modeled. The coating is assumed to be functionally-graded (continuously inhomogeneous in depth) with all group of electromechanical properties varying independently in depth according to arbitrary continuous functions or piecewise homogeneous. The problem is described mathematically in terms of

The effective elastic and conductive properties of matrix composites depend on two geometric factors – inhomogeneity shapes and orientation distribution – and on the property contrast between the matrix and inhomogeneities. The roles of the two geometric factors are strongly coupled; both are also coupled with the role of the property contrast. These issues are examined, with particular attention paid

The effects of oven temperature during printing on nonlinear vibration for fractional-order PET films are considered in this paper. The effect of temperature, fractional order modelling and some other parameters are analysed with respect to the response of the resonance. Fractional order kelvin-Voigt ontological relationship is used to describe the characteristics of viscoelastic materials. The differential

A mechanical heart valve, an essential prosthetic for managing valvular heart disease, consists of a metal frame housing two or three leaflets (depending on the design) that control blood flow within the heart. However, leaflet dysfunction can impede their movement, leading to valve defects. This study extensively investigates the hemodynamics of such a bileaflet mechanical heart valve with dysfunctions

Coupling of piezoelectric and semiconducting properties can stimulate a field-particle coupling wave (FPCW) between electric field and charge carriers on an elastic wave-front (EWF) propagating in a piezoelectric semiconductor. The wave velocity of a FPCW is usually greater than the EWF as vibration frequency rises such that carrier behavior on and in front of the EWF will be disturbed in advance.

This work deals with finding the analytical displacements and stresses in thermoelasticity problems involving solid isotropic cylinders and spheres with an emphasis on stress-focusing phenomena relevant to the nuclear industry and high-temperature engineering. The study considers solid spheres and infinitely long solid cylinders with three different types of thermal loading: prescribed outer surface

In this paper, we apply mesoscale numerical modeling to predict the effective elastic properties of conductive carbon-black/ultra-high-molecular-weight-polyethylene nanocomposites. The models are based on X-ray microcomputed tomography images. The images show that for the considered range of carbon additive weight fractions, the conductive carbon black (CB) particles are distributed around the ult

We study the anti-plane shear waves in a domain consisting of an elastic layer (plate) with a coating attached to an elastic half-space (substrate). We assume an imperfect contact between the layer and the half-space, allowing some sliding. We also assume some elastic bonds between the layer and the substrate. On the free top surface we apply the compatibility conditions within the Gurtin–Murdoch surface

The derivation of the boundary conditions is the most challenging part of the asymptotic techniques underlying low-dimensional models for thin elastic structures. At the moment, these techniques do not take into consideration the effect of the environment, e.g., a Winkler foundation, when tackling boundary conditions, and have to be amended. In this paper as an example we consider an antiplane problem

Understanding many micro-vascular diseases is aided by examining the dynamical behavior of blood cells. For instance, micro-vascular stenosis significantly influences the dynamics of red blood cells and hence causes several micro-vascular disorders. Thus, the objective of the current study is to numerically simulate cellular blood flow in stenosed micro-vessels with different stenosis severities and

We detail the energy balance of a propagating hydraulic fracture. Using the linear hydraulic fracture model which combines lubrication flow and linear elastic fracture mechanics, we demonstrate how different propagation regimes are related to the dominance of a given term of the power balance of a growing hydraulic fracture. Taking an energy point of view allows us to offer a physical explanation of

The classic phenomenological models fail to describe the physical landscape of creep deformation for amorphous solids. In this paper, creep behavior of typical metallic glasses with chemical compositions La62Al14Ag2.34Ni10.83Co10.83, Pd20Pt20Cu20Ni20P20 and Cu46Zr39Hf8Al7 were studied. Instead, we attempt to use a modified hierarchically correlated model informed by physics to realize the creep behaviors

This work is related to modeling of metal surface modification process by combined particles beam. On the basis of thermodynamics of irreversible processes, including equations of state in differential form, a nonlinear model is formulated. The model takes into account the interaction of thermal, diffusion and mechanical waves and finiteness of relaxation times of thermal and diffusion processes. For

The manuscript investigates the buckling behaviour of Bernoulli-Euler nanobeams composed of Functionally-Graded (FG) materials with different cross-sectional shapes. This analysis is conducted using the surface stress-driven model of elasticity. The nonlocal governing equations for the elastostatic buckling problem are derived employing the principle of virtual work. The study also includes a parametric

A new method for assimilating a frequency-dependent drag coefficient into time-domain acoustic simulations is presented. The method combines structural (wave propagation) simulations together with acoustic attenuation of the individual frequencies through a model for the frequency-dependent drag coefficient. An incident pressure pulse is obtained experimentally or from a preliminary finite element

The paper develops a new integral micromorphic elastic continuum model, which can describe dispersion properties of band-gap metamaterials, i.e., metamaterials that inhibit propagation of waves in a certain frequency range. The enrichment consists in nonlocal treatment of three terms in the expression for the potential energy density of the standard micromorphic continuum. After proper calibration

The incorporation of ceramics into polymers, forming solid composite electrolytes (SCEs) leads to enhanced electrical performance of all-solid-state lithium metal batteries. This is because the dispersed ceramics particles increase the ionic conductivity, while the polymer matrix leads to better contact performance between the electrolyte and the electrode. In this study, we present a model, based

The determination of surface elastic moduli is discussed in the context of a recently proposed strongly anisotropic surface elasticity model. The aim of the model was to describe deformations of solids with thin elastic coatings associated with so-called hyperbolic metasurfaces. These metasurfaces can exhibit a quite unusual behaviour and concurrently a very promising wave propagation behaviour. In

Polylactic acid (PLA) nanofibrous networks have gained substantial interest across various engineering and scientific disciplines, such as tissue engineering, drug delivery, and filtration, due to their unique and multifunctional attributes, including biodegradability, tuneable mechanical properties, and surface functionality. However, predicting their mechanical behaviour remains challenging due to

The macroscopic behaviors of materials are determined by interactions that occur at multiple lengths and time scales. Depending on the application, describing, predicting, and understanding these behaviors may require models that rely on insights from atomic and electronic scales. In such cases, classical simplified approximations at those scales are insufficient, and quantum-based modeling is required

Structural schemes of applicative interests in Engineering Science frequently encounter the intricate phenomenon of discontinuity. The present study intends to address the discontinuity in the flexure of elastic nanobeam by adopting an abstract variational scheme. The mixture unified gradient theory of elasticity is invoked to realize the size-effects at the ultra-small scale. The consistent form of

Nanocomposites can show different properties according to the type of reinforcements they have. In this article, a model for the study of nanocomposites is examined, which is able to examine all nanocomposites with elliptical, cylindrical, spherical and rectangular reinforcements. Also, in this model, unlike some other models, the effects of interphase section are included. The results obtained from

There has been tremendous recent interest in Direct Air Capture (DAC) systems. A key part of any DAC system are the multiple air intake units. In particular, the arrangement of such units for optimal capture and sequestration is critical. Accordingly, this work develops an easy to use model for a modular unit system, where an approximate flow field is computed for each unit and the aggregate flow field

The drying phenomenon in soils involves complex interactions between thermal, hydrological, and mechanical effects within a multiphase system. While several researches (both mechanics and mixture theory approach) has been applied to study various thermo-hydro-mechanical (THM) coupled processes in porous media, incorporating both multiphase flow and phase change in soil drying remains limited. This

The paper proposes a transparent and compact form of constitutive and equilibrium relations for the plane thermoelasticity of quasicrystal solids. The symmetry and positive definiteness of the obtained extended tensors of material constants are studied. An extension of the Stroh formalism is proposed for solving plane problems of thermoelasticity for quasicrystals. It is proved that the eigenvalues

Estimation of macroscopic properties of heterogeneous materials has always posed significant problems. Procedures based on numerical homogenization, although very flexible, consume a lot of time and computing power. Thus, many attempts have been made to develop analytical models that could provide robust and computationally efficient tools for this purpose. The goal of this paper is to develop a reliable

A new scaling theory called finite similitude has appeared in the open literature for the scaling of physical systems. The theory is founded on the metaphysical concept of and consequently can in principle be applied to all physics. With regard to the application of the theory to multi-physics however, an obstacle is dissimilar mathematical formulations, that are preferred and applied in practice.

Micromechanical modelling of particulate composites with non-ellipsoidal particle shapes presents significant challenges because analytical approaches based on the fundamental results of Eshelby cannot be used. On the other side, direct numerical evaluations by finite element analysis can involve high computational cost in the case when particle features have small radius of curvature, sharp edges

Although auxetic metamaterials exhibit unique and unusual mechanical properties, such as a negative Poisson's ratio, their mechanics remains poorly understood. In this study, we model a graded beam fabricated from graphene origami-enabled auxetic metamaterials and investigate its dynamics from the perspective of different shear deformation theories. The auxetic metamaterial beam is composed of multiple

A three-dimensional rate-independent framework consistent with thermodynamics is presented to study the dissipative response of metals. The entropy inequality is transformed into equality by introducing a non-negative, continuous rate of dissipation function. The constitutive relation that relates the Hencky strain and Cauchy stress is parametrized by replacement stress, instead of the plastic strain

We propose a weak form of the transient heat equations for solid bodies, as a time-dependent spatial variation of the heat displacement vector field, whose time derivative is the heat flux. This develops the variational principle originally proposed by Biot, inasmuch Fourier’s law is embedded as a holonomic constraint, while energy conservation results from the variation (the vice-versa from Biot)

Hard-magnetic soft (HMS) beams made of soft polymer matrix embedded with hard-magnetic particles can generate large and fast deformation under magnetic stimulation. Dynamic modeling and simulation of HMS beams interacting with complex environment are challenging in terms of computational accuracy and efficiency. This paper presents a method for high-order modeling and efficient computation of HMS beams