We establish the uniformity of stresses inside both a non-parabolic open inhomogeneity and a non-elliptical closed inhomogeneity interacting with a nearby circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. Our procedure involves the introduction of a conformal mapping function for the doubly connected

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical

We study the phase-field model with the elasticity energy arising from the coherency stress across the two-phase interface for lithium-ion batteries by using olivine LiFePO4 as a model system. The existence of global solutions about this model which is a coupled system of elliptic and parabolic equations with the singular points in the case of a logarithmic nonlinear term p(c) is proved. We demonstrate

Shotguns have increasingly used case-hardened steel pellets, as opposed to “classical” lead, owing to food safety and environmental concerns. Correspondingly, there is increasing concern about unintended ricochet of pellets and subsequent bodily harm, such as eye damage. Correspondingly, this paper focuses on the impact of pellets with a surface and the post-impact ricochet range. Equations for general

We investigate the buckling and post-buckling properties of a hyperelastic half-space coated by two hyperelastic layers when the composite structure is subjected to a uniaxial compression. In the case of a half-space coated with a single layer, it is known that when the shear modulus μf of the layer is larger than the shear modulus μs of the half-space, a linear analysis predicts the existence of a

In this article, we explore the possibility of modeling the interaction of a 2d elastic body with a thin 2d elastic body of possibly higher thickness using a 1d model for the thin body. We use the asymptotic analysis with respect to the small thickness of the 2d interaction model and formulate five different limit models depending on the order of stiffness of the thin body with respect to the thickness

A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically

This paper provides a numerical solution for the degenerate scale for a rigid curve in antiplane elasticity. The degenerate scale problem for the rigid curve is formulated on the usage of the logarithmic potential. After assuming the displacement to be a vanishing value along the rigid curve, the boundary integral equation (BIE) is formulated. The problem can be first formulated in the degenerate scale

Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional

This note discusses the Timoshenko–Ehrenfest beam theory and the Griffith fracture theory. Both were annunciated in the West in 1921, exactly a century ago. Much progress has been made in these fields. Discussing the deficiencies of the theories might pave way ahead.

In this note, we study the response of a viscoelastic body whose stress relaxation modulus and creep compliance depend on the density of the body in such a manner that the stress and strain appear linearly in the constitutive equation. Such models would be useful to study the response of porous viscoelastic bodies undergoing small deformations, as the moduli depend on the porosity, and hence the density

With the development of advanced manufacturing technologies, the importance of functionally graded materials is growing as they are advantageous over widely used traditional composites. In this paper, we present a novel peridynamic model for higher order functional graded plates for various thicknesses. Moreover, the formulation eliminates the usage of shear correction factors. Euler–Lagrange equations

This paper is concerned with the deformation of beams in the framework of the linear theory of micromorphic elastic solids. First, the plane strain of anisotropic and homogeneous elastic cylinders is investigated. Existence and uniqueness results are presented. Then, Saint-Venant’s problem for micromorphic beams is formulated. A method is established to reduce the extension, bending and torsion to

Biological membranes undergo noticeable thermal fluctuations at physiological temperatures. When two membranes approach each other, they hinder the out-of-plane fluctuations of the other. This hindrance leads to an entropic repulsive force between membranes which, in an interplay with attractive and repulsive forces owing to other sources, affects a range of biological functions: cell adhesion, membrane

Traditional equivalent inclusion method provides unreliable predictions of the stress concentrations of two spherical inhomogeneities with small separation distance. This paper determines the stress and strain fields of multiple ellipsoidal/elliptical inhomogeneities by equivalent inhomogeneous inclusion method. Equivalent inhomogeneous inclusion method is an inverse of equivalent inclusion method

This paper describes a small-strain poroelasticity model to examine the interstitial fluid pressure and matrix deformation in a non-homogeneous solid tumor consisting of an inner core with a reduced specific microvascular area encapsulated in an outer tissue shell with a regular specific microvascular area. A singular perturbation technique is employed to capture the transitional behavior at the interface

We consider a 2D problem of a circular cylinder that is infinitely long and whose external surface is free from outside effects and acted upon by an asymmetrical temperature distribution that is harmonic in time. The problem is within the context of the theory of thermoelasticity without energy dissipation. The exact solution is obtained by a direct approach. The results are represented graphically

In constitutive modelling of rubber-like materials, the strain-hardening effect at large deformations has traditionally been captured successfully by non-Gaussian statistical molecular-based models involving the inverse Langevin function, as well as the phenomenological limiting chain extensibility models. A new model proposed by Anssari-Benam and Bucchi (Int. J. Non Linear Mech. 2021; 128; 103626

We present a growth model for special Cosserat rods that allows for induced rotation of cross-sections. The growth law considers two controls, one for lengthwise growth and another for rotations. This is explored in greater detail for straight rods with helical and hemitropic material symmetries by introduction of symmetry-preserving growth to account for the microstructure. The example of a guided-guided

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy

The Kröner solution is used to determine the shear modulus of any polycrystalline aggregate composed of cubic crystals. This solution from the self-consistent method takes the form of a cubic equation specified by the three elastic properties of the crystal. The ductile/brittle transition for homogeneous and isotropic materials in uniaxial tension is specified by terms of the shear modulus and the

This work presents the development of a 2D nonlinear magnetoelastic framework for a thin membrane undergoing large deformations. An asymptotic O(h) theory is obtained, starting from the 3D variational magnetostatic and force balance equations for a weakly magnetizable material, using the approach described by Steigmann. The model is subsequently specialized to axisymmetry and applied to a pre-stretched

This paper makes a rigorous case for considering the continuum derived by the homogenization of extensive quantities as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance

The fractional derivative models with time-varying viscosity have been used in characterizing creep or relaxation properties of different viscoelastic material, and many combination models were presented using the Boltzmann superposition principle. However, those models defined as initial ones in this manuscript usually ignored the initial loading ramp, and the ideal-loading condition is commonly assumed

The flexural wave propagation in a microbeam is studied based upon the nonlocal strain gradient model with the spatial and time fractional order differentials in the present work. To capture the dispersive behaviour induced by the inherent nanoscale heterogeneity, the stress gradient elasticity and the strain gradient elasticity are often used to model the mechanical behaviour. The present model incorporates

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions

The experimental and numerical analyses of the linear time-invariant dynamical behavior of the clamping region of a 2D pantographic material are presented. The experimental observations of the clamping area, obtained by means of a specialized stereo microscope, are compared with the results of a second gradient linear model enforcing the same symmetries as the system microstructure.

In this paper, we consider the Moore–Gibson–Thompson thermoelastic theory. We restrict our attention to radially symmetric solutions and we prove the exponential decay with respect to the time variable. We demonstrate this fact with the help of energy arguments. Later, we give some numerical simulations to illustrate this behaviour.

The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary

Maxwellian-type rheological models of inelastic effects of creep type at large strains are revisited in relation to inelastic strain gradient theories. In particular, we observe that a dependence of the stored energy density on inelastic strain gradients may lead to spurious hardening effects, preventing the model from accommodating large inelastic slips. The main result of this paper is an alternative

This article presents a new higher-order beam model. The present beam model is governed by differential equations that are similar to those present in some existing higher-order beam models; however, the present beam model makes use of a novel method of calculating the transverse shear stiffness, which facilitates the calculation of a shear-warping stiffness without the need for an assumed warping

In the past few decades, numerous studies have attempted to address the various phenomena that take place simultaneously during bone remodeling. Drawing from Frost’s “mechanostat theory,” multiple phenomenological models of varying complexity have been developed to describe bone remodeling in terms of evolution of bone porosity, tissue properties, and mineralization. The main goal of this paper is

A magnetoactive porous solid comprises a porous polymer matrix with embedded magnetizable particles. The connected porous space of the polymer matrix is filled with a fluid. Under externally applied magnetic fields, the magnetoactive porous solid can undergo large deformations in the elastic regime, triggering diffusive flow in the interconnected pores. The coupled hydromagnetomechanical behavior of

Under given prestress conditions, solitary waves in fluid-filled elastic tubes are confined to a rather narrow set of combinations of the background fluid velocity and the wave speed. This set, which we call the domain of existence, is bounded by several curves that represent various physical and mathematical restrictions. Remarkably, these restrictions can be cast as purely algebraic conditions to

A three-dimensional (3D) electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal (QC) circular plates with simply supported or clamped boundary conditions is presented through a state vector approach. Both perfect and imperfect bonds between the layers are considered by adjusting the parameter sets in the model. Governing equations for the plates subjected to electric or elastic

In the present work, the effect of a thermodynamically consistent inelastic interface stress on nanovoid evolution in NiAl is studied. Such interface stress is introduced for the solid–gas interface of nanovoids within the concept of the phase field approach. The Cahn–Hilliard (CH) equation using the Helmholtz free energy describes the evolution of nanovoid concentration. The interface stress changes

The availability and evolution of chemical agents play an important role in the growth of a tumour and, therefore, the mathematical description of their consumption is of special interest. Usually, Fick’s law of diffusion is adopted for describing the local character of the evolution of chemicals. However, in a highly complex, heterogeneous medium, as is a tumour, the progression of chemical species

A new non-classical model for first-order shear deformation circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. Through a variational formulation based on Hamilton’s principle, the equations of motion and boundary conditions are simultaneously obtained, and the microstructure and surface energy effects are treated in a unified manner

The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of

A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first involves experimentally acquiring the deformed shape that a given microcapsule takes

In this review paper, some relevant models, algorithms, and approaches conceived to describe the bone tissue mechanics and the remodeling process are showcased. Specifically, we briefly describe the hierarchical structure of the bone at different levels and underline the geometrical substructure characterizing the bone itself. The mechanical models adopted to describe the bone tissue at different levels

Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static analysis is accurate enough, as the rocking motion is the dominant mode of their interaction with the surrounding soil (i.e. soil–structure interaction problem). In this study, the soil–structure interaction

By using the couple-stress elasticity theory, this article firstly analyzes the size-dependent elastohydrodynamic lubrication (EHL) line contact between a deformable half-plane and a rigid cylindrical punch. The size effect that emerged from the material microstructures is described by the characteristic material length. It is assumed that the viscosity and density of the lubricant vary with the fluid

We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo certain boundary integrals or constant integrals, between these formulations using the Legendre transform and properties of Maxwell’s equations. Bifurcation equations

We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity

We describe multiscale geometrical changes via structured deformations (g,G) and the non-local energetic response at a point x via a function Ψ of the weighted averages of the jumps [un](y) of microlevel deformations un at points y within a distance r of x. The deformations un are chosen so that limn→∞un=g and limn→∞∇un=G. We provide conditions on Ψ under which the upscaling “n→∞” results in a macroscale

A simplified metaelastic model is presented to study long-wavelength dynamics of random composites filled with coated rigid spheres under the condition that the characteristic wavelength of the displacement field is much larger than the average distance between adjacent coated rigid spheres. The model is characterized by a simple differential relation between the displacement field of the composite

A novel high-order three-scale (HOTS) computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales is developed in this paper. The multiple heterogeneities of axisymmetric composite structures we investigated are taken into account by periodic distributions of representative unit cells on the mesoscale and microscale. First

This paper is devoted to the investigation of three-dimensional models of thermo-electro-magneto-elastic solids made of a multidomain inhomogeneous anisotropic material. General boundary and initial boundary value problems corresponding to the static and dynamic models are studied where, on certain parts of the boundary, mechanical displacement, electric and magnetic potentials and temperature vanish

The governing equation of linear peridynamics is developed for the most general anisotropic materials (triclinic materials). As a departure from the standard peridynamic theory, the linear constitutive equation in the form of a micromodulus is determined by directly requiring the resulting peridynamic equation to converge to a comparable classical elastodynamic equation for a triclinic material as

Adhesively bonded joints have widely been used in a number of engineering applications, owing to their improved mechanical performance as compared with other mechanical joining techniques, such as rivets or bolts. In this study, a theoretical solution of double-lap joints is established, with functionally graded adhesive and isotopic adherends, under harmonic loads. Assuming a parabolic distribution

In this paper, an integral transformation of the displacement is employed to determine the solution of the elastodynamics problem of two collinear Griffith cracks with constant velocity situated in a mid-plane of an infinite orthotropic strip where the boundaries are assumed to be stress-free. By use of the integral transformation of the displacement, the problem is reduced to a solution of the triple

In this paper, the static behavior of an elastic beam resting on a rigid substrate is investigated. The structure lies on a rigid substrate and exchanges with it tangential forces, in correspondence with a finite number of contact points. These actions entail extension of the beam in the longitudinal direction together with a negligible bending, owing to the small eccentricity between the beam’s axis

The optimized design of composite adaptive structures puts forward higher requirements and challenges to the actual configuration of the structural section. In this paper, a trapezoidal laminate model of composite materials is established. Based on the classical laminates theory, the bending problem of trapezoidal laminates is solved by using the Kantorovich method and the principle of minimum potential

In this paper, we review classical and recent results on the Lagrangian description of dissipative systems. After having recalled Rayleigh extension of Lagrangian formalism to equations of motion with dissipative forces, we describe Helmholtz conditions, which represent necessary and sufficient conditions for the existence of a Lagrangian function for a system of differential equations. These conditions

We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic

Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology

This work considers a rubber cylinder under zero axial force that elongates in response to the normal stresses produced during torsion (the Poynting effect). The combined elongation and twisting deformation occurs at an elevated temperature at which the rubber undergoes time-dependent scission and re-crosslinking of its macromolecular network junctions. A constitutive theory accounting for this microstructural

A hemi-variational formulation for a damaged non-homogeneous Timoshenko beam is proposed here for the purpose of fast simulation of the properties of a dam. The dam is therefore modeled as a damaged non-homogeneous Timoshenko beam embedded in 2D space. The damage evolution and the mechanics of the beam are governed both by the hemi-variational principle and by the assumption on the form of the deformation

In this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for