Materials based on pantographic unit cells have very interesting mechanical peculiarities. For these reasons they are largely studied from a theoretical, experimental, and numerical point of view. Numerical simulations furnish an important contribution for the the design and optimization of such materials and, more generally, for metamaterials. Here, we consider the influence of inertial forces, removing

We analysed the problem of determining the exponents in the asymptotic solution of the isotropic theory of elasticity problem at the top of the wedge-shaped region where its sides (or one of them) are supported by a thin coating and lean without friction on the rigid bases. On the other side of the wedge-shaped region, it is assumed that there are various boundary conditions, including when there is

A model for the mechanics of lipid membranes with non-uniform (coordinate-dependent) properties is discussed. The coordinate-dependent responses of the membranes are incorporated via the augmented non-uniform energy function and material parameters, which are dependent explicitly on the surface coordinates. We formulate the associated normal and tangential Euler equilibrium equations through which

We consider the Neumann problem in a theory of plane micropolar elasticity incorporating micropolar surface effects. The incorporation of surface elasticity utilizes the Eremeyev–Lebedev–Altenbach shell model, leading to a set of second-order boundary conditions describing the separate micropolar elasticity of the surface. The Neumann problem is of particular interest, since the question of solvability

Problems of interface cracks starting from the common corner points of pairs of perfectly glued wedges of different isotropic elastic materials are addressed. It is demonstrated that for a few particular configurations and a restrictive condition imposed on values of elastic constants (corresponding to vanishing of the second Dundurs parameter), the problem of elastic equilibrium may be solved by Khrapkov’s

The central theme of this study is to investigate a remarkable capability of a second-gradient continuum model developed for pantographic structures. The model is applied to a particular type of this metamaterial, namely the wide-knit pantograph. As this type of structure has low fiber density, the applicability of such a continuum model may be questionable. To address this uncertainty, numerical simulations

Static condensation is widely used as a model order reduction technique to reduce the computational effort and complexity of classical continuum-based computational models, such as finite-element models. Peridynamic theory is a nonlocal theory developed primarily to overcome the shortcoming of classical continuum-based models in handling discontinuous system responses. In this study, a model order

Over the last two decades, there have been tremendous advances in the computation of diffusion and today many key properties of materials can be accurately predicted by modelling and simulations. In this paper, we present, for the first time, comprehensive studies of interdiffusion in three dimensions, a model, simulations and experiment. The model follows from the local mass conservation with Vegard’s

Using the non-standard geometric structure proposed by Loos, we present a coordinate-free formulation of the theory for time-dependent finite-dimensional mechanical systems with n degrees of freedom. The state space containing the system’s information on time, position and velocity is defined as a (2n+1)-dimensional affine bundle over an (n+1)-dimensional generalized space-time. The main goal is to

Implicit rate-type constitutive relations utilising discontinuous functions provide a novel approach to the purely phenomenological description of the inelastic response of solids undergoing finite deformation. However, this type of constitutive relation has so far been considered only in the purely mechanical setting, and the complete thermodynamic basis is largely missing. We address this issue,

There are a number of plate-type piezoelectric devices in engineering, hence it is crucial to search for a method that can accurately acquire the electro-mechanical coupled field of a piezoelectric plate. A method for calculating the coupled field of an orthotropic piezoelectric plate with arbitrary thickness under an arbitrary electro-mechanical load is put forward in this article. First, the Green’s

In the paper the axisymmetric problem of elasticity theory is studied for the radially inhomogeneous sphere of small thickness that does not contain any of the poles 0 and π. Here the case is considered when the elasticity modules vary linearly with respect to the radius. It is assumed that the lateral surface of the sphere is free of stresses, and at the ends of the sphere (at the conical sections)

In this research paper, an analytical solution with numerical illustration is presented for elastoplastic analysis in a functionally graded thick-walled rotating transversely isotropic cylinder under a radial temperature gradient and uniform pressure using the transition theory of Seth and generalized strain measure theory. The theory of Seth requires no assumptions, such as infinitesimally small deformation

In this paper, we discuss the mechanics of anelastic bodies with respect to a Riemannian and a Euclidean geometric structure on the material manifold. These two structures provide two equivalent sets of governing equations that correspond to the geometrical and classical approaches to non-linear anelasticity. This paper provides a parallelism between the two approaches and explains how to go from one

A hybrid quantum–classical model is proposed whereby a micro-structured (Cosserat-type) continuum is construed as a principal Hilbert bundle. A numerical example demonstrates the possible applicability of the theory.

We investigate the numerical reconstruction of the missing thermal boundary conditions on an inaccessible part of the boundary in the case of steady-state heat conduction in anisotropic solids from the knowledge of over-prescribed noisy data on the remaining accessible boundary. This inverse problem is tackled by employing a variational formulation that transforms it into an equivalent control problem;

A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three-dimensional, polar, and nonpolar continua are obtained. Next, these kinematics and conservation laws are connected to their corresponding counterparts for surface continua, based

In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of order n≥1. These conditions are effective and of degree n (the tensor’s order) in the components of the normal to the plane (or the direction of the axial symmetry). These results are then extended to obtain necessary and

In this paper, we consider a one-dimensional laminated beam with structural damping and an infinite memory acting on the effective rotation angle. Under appropriate assumptions imposed on the relaxation function, we show that the system is well-posed by using the Hille–Yosida theorem, and then we establish general decay results, from which exponential and polynomial decays are only special cases, in

The goal of this article is to study the feedback control for non-stationary three-dimensional Navier–Stokes–Voigt equations. Based on the existence, uniqueness, and boundedness result of the weak solutions to the equations, we obtain the existence of solutions to the feedback control system. An existence result for an optimal control problem is also given. We illustrate our main result with an evolutionary

Harmonic Cartesian polynomial and rational functions are shown to provide a simple way of obtaining a semi-analytical solution to the uncoupled, two-dimensional problem of thermomagnetoelasticity for a long, transversely isotropic, elastic cylinder carrying an axial, steady electric current. The proposed method involves the solution of a difficult inhomogeneous biharmonic equation for the stress function

Strain-stiffening behavior of materials such as rubberlike materials and biological soft tissues is an important phenomenon. In this paper, we proposed a surface Green’s function tensor to describe the strain-stiffening behavior of the stretchable elastomer based on the Gent constitutive model. The surface Green’s function tensor of the Gent constitutive model can be recovered to that of neo-Hookean

In this study, the frictional moving contact problem for an orthotropic layer bonded to an isotropic half plane under the action of a sliding rigid cylindrical punch is considered. Boundary conditions of the problem include the normal and tangential forces applied to the layer with a cylindrical punch moving on the surface of the layer in the lateral direction at a constant velocity V. It is assumed

The existence of the so-called ‘dark’ issues of mechanics implies that our present accounting for mass and energy is incorrect in terms of applicability on a cosmological scale, and the question arises as to where the difficulty might lie. The phenomenon of quantum entanglement indicates that systems of particles exist that individually display certain characteristics, while collectively the same characteristic

We present in this study a new approach for predicting the plastic and shakedown limits of structures composed of orthotropic materials. In this approach, the Hill yield criterion is introduced to Melan’s theorem. By formulating the problem by means of the finite element method and solving the resulting large-scale nonlinear optimization problem we successfully predict the plastic and shakedown limits

A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that includes only one material length scale parameter, while the Gurtin–Murdoch surface elasticity theory containing three surface elasticity constants is employed to approximate the nature of surface energy effects

Since Eshelby’s (1957) result (Eshelby, JD. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc R Soc London A 1957; 421: 379–396) that ellipsoids in an infinite matrix have uniform localization tensors, all attempts to find other finite domain shapes sharing that same property have failed and valuable proofs were provided that none could exist. Since that

For a solid surface or interface that is subjected to transverse loading, the influence of its flexural resistibility to bending deformation becomes significant. A spherical inhomogeneity or void embedded in an infinite elastic medium under the application of nonhydrostatic loads represents a typical example. In this work, we consider the most fundamental loading of a far-field unidirectional tension

The equilibrium forms of pantographic blocks in a three-point bending test are investigated via both experiments and numerical simulations. In the computational part, the corresponding minimization problem is solved with a deformation energy derived by homogenization within a class of admissible solutions. To evaluate the numerical simulations, series of measurements have been carried out with a suitable

For monodomain nematic elastomers, we construct generalised elastic–nematic constitutive models combining purely elastic and neoclassical-type strain energy densities. Inspired by recent developments in stochastic elasticity, we extend these models to stochastic–elastic–nematic forms, where the model parameters are defined by spatially independent probability density functions at a continuum level

We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character – considering either the electric field E, the electric displacement D or the electric polarization P. The first variation of the energy functional results in the set of Euler–Lagrange partial

In linear elasticity, a fourth-order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties elastic constants of a material. The main goal of the current work is to derive a compact matrix representation of the elasticity tensor that correlates with its intrinsic algebraic properties. Such representation can be useful in design of artificial materials

The viscoelastic Kelvin-Voigt model is considered within the context of quasi-static deformations and generalized with respect to a nonlinear constitutive response within the framework of limiting small strain. We consider a solid possessing a crack subject to stress-free faces. The corresponding class of problems for strain-limiting nonlinear viscoelastic bodies with cracks is considered within a

A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a

Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen fibril network. The microstructural properties of the collagen network contribute to continuum mechanical tissue properties that are strongly anisotropic with tensile-compressive asymmetry. In this study, a novel approach based on a continuous distribution