Strain gradient elasticity theory, which incorporates intrinsic material length parameters into its constitutive relationships, is extensively utilized in modeling size-dependent mechanical behaviors of solids and structures in the engineering science. However, numerical challenges such as overflow phenomena are frequently encountered during solution procedures, whether through analytical solutions

Equilateral triangle lattices comprising zigzag beams are a typical kind of periodic structures with chiral unit cells. The in-plane deformation of these materials was believed to exhibit chiral effect, but the out-of-plane bending has never been explored. Here, we develop a continuum model to describe the overall bending behavior of such lattices by homogenizing them as micropolar plates. The governing

Shear wave elastography (SWE) is a promising imaging modality for mechanical characterization of tissues, offering biomarkers with potential for early and precise diagnosis. While various methods have been developed to extract mechanical parameters from shear wave characteristics, their relationships in viscoelastic materials under prestress remain poorly understood. Here, we present a generalized

Employing both analytical and numerical methodologies, we investigate the propagation of high-frequency, finite-amplitude, acoustic wave-forms in non-dissipative bubbly liquids under a (1D) PDE model, which we term the Crighton–Westervelt–Klein–Gordon (CWKG) equation. Exact traveling wave solutions (TWS)s for the pressure field are derived and analyzed. It is shown that the CWKG equation can admit

This paper examines various ways of improving the impact resilience of protective structures. Such structures’ purpose is to dissipate an impact’s energy while avoiding cracking and failure. We have tested the reaction of plane elastic-brittle lattices to an impulse. Four topologies are compared: periodic triangular, square, and hexagonal topologies, and aperiodic Penrose topology. Then, structures

Although nonlinear elastodynamics has been widely studied since the second half of the last century, still nowadays, some aspects of this theory need a more systematic analysis. Based on the classical theory of simple materials of differential type and the results on the analytical form of constitutive models consistent with the laws of thermodynamics, we here analyze the wave propagation in compressible

This study investigates the state of stress in slender elastic cylinders with variable cross-sections and axially graded material properties. In contrast to prismatic homogeneous cylinders, the continuous variation of cross-sectional dimensions and material properties along the axis of the cylinder produces additional shear stress distributions within the cross-sections. This work sheds the light on

Surface Green’s functions for a pre-deformed compressible soft magnetoactive (SMA) half-space are derived in this study. Two typical magnetic conditions are considered, one accounting for the effect of the external magnetic field, while the other does not. These Green’s functions are obtained for the first time using the principles of magneto-elastic continuum mechanics. By employing a generalized

This study presents a novel statistical-thermodynamic framework to model the finite deformation of the eukaryotic cell cytoskeleton, emphasizing the roles of actin filament orientation and bundle sliding. By introducing internal variables, such as an orientation order parameter and a microshear strain, the model captures the nonlinear mechanical response of the cytoskeleton under shear stress, including

This study extends classical elasticity to gradient elasticity by investigating the analytical solutions for inhomogeneous and anisotropic curvilinear nano-beams with axial symmetry. For this purpose, we consider two variations for the elastic material coefficients along the thickness of the curvilinear beam. First, the coefficients are assumed to be proportional to the radial coordinate as sij(r)=sijr

A thin dielectric elastomeric (DE) plate with thickness gradients deforms and wrinkles under applied voltages. Such wrinkling, with regular periodic patterns in thin functionally graded DEs, occurs to relax in-plane compressive stresses through out-of-plane deformations. These functionally graded DE-based soft actuators, primarily used in soft robotic applications, exhibit highly localized point loads

We consider the elastic unidirectional composite composed of n transversely-isotropic components, all of which are distributed statistically-isotropic in the transverse plane. Based on the minimum energy or complementary energy principles, the polarization (extended Hashin–Shtrikman-type) strain and stress trial fields are constructed to derive new direct upper or lower polarization estimates for some

This paper is devoted to the exploration of rectangular finite elements’ ability to model the stress-strain state of isotropic and orthotropic materials with a negative Poisson’s ratio, known as auxetic materials. By employing linear elasticity in the plane stress formulation, the research evaluates the linear compatible and the quadratic incompatible shape functions in describing the mechanical behavior

In this paper, we study the elastic response of 2D materials that are subjected to simultaneous in-plane strains and flexural deformations. A nonlinear elastic constitutive model is proposed for the in-plane and flexural deformations of 2D materials of arbitrary symmetries. The constitutive model consists of a series expansion of the strain energy density in terms of the strain and curvature components

In the contribution at hand, the quadratic Hill yield function is extended to a finite strain, multiplicative kinematic framework. Furthermore, it is expanded by a novel combination of linear and exponential hardening. The formulation is derived in a consistent manner. Subsequently, the capabilities to model Ti-6Al-4V in a realistic manner are demonstrated, considering the anisotropy in plastic material

The electrokinetic energy conversion (EKEC) of pressure driven flow in carbon nanotubes (CNTs) is of great interest due to its potential high conversion efficiency. The existing EKEC theories had made many simplified assumptions for this problem, such as the surface charge is fixed on the surface and can not move, the slip length is independent of pipe diameter and the surface charge density is decoupled

To address the needs of engineering applications, researchers often wish that the shapes of samples can be precisely controlled. The current work aims to propose a promising approach, i.e., through stress-free differential growth, to realize general shape transformations of thin hyperelastic shells. First, within the finite-strain regime, we formulate the 3D governing equations system for modeling

Dielectric elastomer actuators (DEAs) based on the dielectric elastomer minimum energy structure (DEMES) exhibit excellent dynamic shape deformation and fast response characteristics, making them widely applicable in flexible actuators, smart grippers, and biomimetic devices. While existing studies have explored the fundamental mechanisms of DEMES, most focus on simple structural types or single application

The constitutive behaviors of materials are often modeled using a network of different rheological elements. These rheological models are mostly developed within a one-dimensional small strain framework. One of the key impediments of extending these models to a three-dimensional finite deformation setting is to determine how the different types of connections, i.e., a series and a parallel connection

In contrast to the conventional strain sensors under the small-deformation condition, the large-deformation analysis on the flexible nanocomposite-reinforced stretch sensors remains to be investigated. In this research, an extended multi-field coupled homogenization model has been developed to illustrate the nonlinear stretch sensing capacities of flexible nanoparticle-reinforced composite sensors

This paper presents a theory and finite element formulation for the plane strain problem of hyperelastic bodies undergoing cylindrical bending using one-dimensional C0 elements called ROD. The paper addresses several aspects characteristic of thick shells experiencing finite elastic deformations, which are not typically encountered in the analysis of classical thin shells. These include significant

Unlike classical theories, which rely on local interactions and differential equations, peridynamic theory employs integro-differential equations to describe the mechanics of materials and structures. This distinctive approach allows peridynamics to naturally incorporate long-range forces and discontinuities, such as cracks, which are challenging to handle using classical partial differential equations

The present work describes the development of symmetry analysis for a rarefied polyatomic gas with a focus on the Extended Thermodynamics six independent fields (ET6) model. Rarefied polyatomic gas phenomena in Extended Thermodynamics derive mechanisms for several engineering fields, such as aerospace and mechanical engineering. In this work, symmetry analysis is developed by utilizing the one-dimensional

We employ data-driven models to predict the tensile strength of steel coils using information on their chemical composition and process parameters. The dataset contains extensive chemical analyses, diverse process parameters, and the characterized tensile strength as target property. We compare prediction quality and traceability of the predictions of pure machine learning models and physics-informed

Novel layered soft electroactive materials/structures have various special functions and features which can be uniquely applied to different modern science and engineering fields. In this paper, three-dimensional full-field solutions for the indentation characterization of layered soft electroactive media are presented by using a newly established semi-analytical approach. This approach is based on

Dielectric relaxation is a widespread physical phenomenon that results in the dielectric coefficient taking on complex values, with both the real and imaginary parts changing in response to variations in frequency and temperature. It is evident that dielectric relaxation affects the dynamic performance of piezoelectric acoustic devices. However, research on this topic remains limited. In this paper

This paper investigates the nonlinear forced vibration of doubly curved sandwich nanoshells with auxetic honeycomb core having negative Poisson's ratio and nanocomposite-reinforced coatings. It is assumed that the nanoshell structure rests on Winkler-Pasternak foundation. The dynamic response is analyzed under various periodic and impulsive pressure excitations. The basic governing, compatibility,

The virtual power principle for materials with microstructure modeled in the framework of micromorphic effective media is written from a micromechanical perspective, considering recent contributions of (Alavi et al., 2021, 2023) however restricting to statics. In the present work, we extend the micromorphic framework to dynamics by deriving the macroscopic kinetic energy from the upscaling of microscopic

We present experiments and analytic modeling of different states of finite torsion of soft cylinders. The problems of free torsion and restrained torsion are investigated. In free torsion, the cylinder is twisted and left free to elongate, thus exhibiting the Poynting elongation. In restrained torsion, the elongation of the cylinder is inhibited, so a reactive axial force arises (Poynting force). The

The analytical self-consistent model of a polycrystalline solid with isotropic grains and a general imperfect interface has been developed. The grain-to-grain bonding conditions assume a jump of both the displacement and normal traction vectors across the interface. The model is consistent with the general theory of curved deformable interfaces in solids with nanometre-scale microstructure (Gurtin

Magneto-active polymer composites (MAPCs) can change their mechanical properties (i.e., stiffness) and/or mechanical deformation upon an external magnetic stimulus. The mechanical response of MAPCs is primarily determined by the interaction between the polymer matrix and magnetic particles, alongside the performance of the constituent materials. When a directional dynamic magnetic field is applied

A multiscale simulation was carried out using a two-stage homogenization process to improve the performance of flexible, printable magnetoelectric (ME) polymer matrix composites. A periodically-poled checkerboard structure discovered in the multiscale optimum design of ceramic composites was applied to particle-dispersed polymer matrix composites, targeting a composite of piezomagnetic (PM) cobalt

This study, for the first time, investigates the bulk waves in mechanical metamaterial thickness- and shear-deformable doubly-curved shells; it considers spherical, elliptical, hyperbolic, and cylindrical shell structures. A third-order shear deformable model, involving thickness deformation, is employed to capture in-surface and out-of-surface, rotational, and stretching motions within a curvilinear

This paper explores the influence of microstructures on the effective thermal expansion coefficient of thermal metamaterials, highlighting the surface-induced size-dependent effects. These effects stem from the unique porous microstructural characteristics, influenced by volume fraction and geometric configuration. Unlike nanoscale phonon-driven surface effects, comprehensive finite element numerical

A plane strain problem for a partially electrically conducting and partially insulated crack in a homogeneous piezoelectric material is considered. The electrically conducting zone is located either on both crack faces or on one of them. Remote mechanical tensile stresses orthogonal to the crack and the electric field orthogonal or parallel to the crack are applied. The appearance of contact zones

We investigate the wave dispersion relations of an infinite elastic bar within the framework of linear bond-based peridynamics. This nonlocal integral-type model accounts for long-range interactions, which become significant at small scales and in cases of damage and fracture. Since a key element of this material model is the kernel function, we derive dispersion curves for several kernel choices.

Silicone elastomers play a critical role in the construction of soft robotics and foldable devices, owing to their exceptional versatility and mobility. This necessitates the development of innovative approaches in constitutive modeling to accurately simulate their behavior and optimize the design of such devices. Samples from five elastomers namely Smooth Sil 936, Clearflex 30, Dragon Skin 10 SLOW

In this paper, the thermodynamics of granular material is developed to get constitutive relations for unified modelling of undrained viscoplastic flow behavior with complex combined effects of state, rate, time, and path. The proposed formulations of energy storages and dissipations lead to the state-dependent hyperelasticity with an elastic instable region and the viscoplasticity with considerations

The two-dimensional thermoelectric coupling conduction problem of an inhomogeneity, which is characterized by a Laurent polynomial and embedded in a thermoelectric material subjected to uniform electric current density or uniform energy flux at infinity, is studied under the conditions of the electrical insulation and thermal conduction continuity. While the complex potential denoting the electric

This paper investigates hydraulic fracture in a medium with periodic heterogeneous toughness. Results for the plane-strain (KGD) model are analysed. The energy distribution as the fracture propagates is examined, along with the evolution of the crack geometry. It is shown that the solid layer acts as an elastic battery, discharging to promote rapid propagation through weaker material layers. The limiting

In this paper, three-dimensional (3D) dynamic analysis of a rotational smart piezomagnetic-flexomagnetic (PFM) multi-functional micro-disk has been investigated. In the mathematical modeling, an attempt has been made to develop a wide range of factors influencing the analyzed structure, which is intended to be used as a micro-sensor/actuator. The investigated smart micro-disk could have many sensitive

Partial contacts between faces are common in cracks. They produce strong stiffening effect, even if they are small. The cross-property connection implies that they produce a similar effect on the crack resistivity contributions. These effects lead to a substantial reduction of the “effective” crack density that controls the overall properties. The present work analyzes these issues in a systematic

Critical remarks on the paper “Analytical Solutions and Case Studies on Stress-Dependent Corrosion in Pressurized Spherical Vessels” published in Metals, 2023, vol. 13, are given. They concern serious errors in treating the problem, as well as incorrect treatment of works of other authors – in particular, article published in the International Journal of Engineering Science. Due to practical importance

For the first time, an analytical solution is derived for the boundary-value problem in the theory of elasticity for a straight edge dislocation axially piercing an elastic sphere. The solution is given by the sum of the well-known stress fields of the dislocation placed in an infinite elastic medium and the image stress fields caused by the presence of the sphere free surface. To get the second term

Under complex stress-states, mixed-mode fracture is critical to the crack propagation. Additionally, in quasi-brittle materials, the toughness and strength can differ across fracture modes. Therefore, to analyze mixed-mode fracture behaviors under different stress conditions, we developed a new phase-field cohesive zone model (PF-CZM). A directional strain energy decomposition scheme with anisotropic

For linear physical problems of equilibrium or steady-state phenomena in uncoupled and coupled cases, their fundamental equations are essentially similar so they can be treated on an equal footing. This work provides a unified formulation of the field solution in heterogeneous materials for linear multi-physical problems. Based on a modified Eshelby's equivalent inclusion model, the fields in the whole

This work delves into modelling and analysis of Love-type (LT) wave propagation in imperfectly bonded piezomagnetic stratum to a piezoelectric substrate under the influence of mass loading (ML) by developing three distinct models, viz. spring interface model (SIM), membrane interface model (MIM) and spring-membrane interface model (SMIM). Each of these models accounts to the presence of interfacial

Fosdick and Fried (2021) proposed a generalized Navier–Stokes theory for studying the dynamics of incompressible fluids which, under certain flow conditions, may support incompatible distortion rates. Herein, we complete the development of a comprehensive boundary condition, at a fixed wall, for the incompatibility tensor G of that theory; we clarify the physical conditions which express the presence

Existing nonlocal models cannot accurately capture the size-dependent mechanical behavior of functionally graded lattices because they assume constant intrinsic length, which oversimplifies the nonlocal effects of varying lattice topology microstructures. In this paper, we unveil that the intrinsic length obeys a gradient law determined by the configuration of the functionally graded lattices. Based

Forced vibrations of a thin elastic coating are considered. A long wave, multimode approximation is derived from the original 3D setup. It is governed by a 2D equation with the coefficients depending on trigonometric functions of the frequency parameter. The related explicit dispersion relations appear to be of general interest as well. Although the developed asymptotic formulation is oriented to the

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

Trabecular bone is a living material that adapts its spatial organisation and mechanical properties when subjected to loading. There were efforts to describe adaptation in trabecular bone with mathematical models regulating resorption and formation activities as a function of mechanical stimuli. In this paper, an approach to optimise parameters of a bone-adaptation model is proposed and investigated

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