Showing papers in "Mathematics and Mechanics of Solids in 2019"
TL;DR: A review of the state of the art in the study of mechanical metamaterials is given in this article, where the very attractive property of having a microstructure capable of determining exotic and specific properties is discussed.
Abstract: In this paper, we give a review of the state of the art in the study of mechanical metamaterials. The very attractive property of having a microstructure capable of determining exotic and specifica...
266 citations
TL;DR: In this article, a relaxation of the Moore-Gibson-Thompson equation has been proposed for a thermo-elastic model where the heat conduction is described by a relaxation.
Abstract: We consider a thermoelastic theory where the heat conduction is described by the Moore–Gibson–Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parame...
128 citations
TL;DR: In this paper, variational formulations and governing equations with boundary conditions are derived for a pair of Euler-Bernoulli beam bending models following a simplified version of Mindlin's...
Abstract: As a first step, variational formulations and governing equations with boundary conditions are derived for a pair of Euler–Bernoulli beam bending models following a simplified version of Mindlin’s ...
94 citations
TL;DR: In this paper, the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin-Murdoch surface elasticity and Toupin...
Abstract: Here we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin...
54 citations
TL;DR: In this article, a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities, is presented.
Abstract: In this paper, we give a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities. The main scope of this...
52 citations
TL;DR: In this article, a nonlocal differential model has been used to predict the size effect in nanostructures, but this model often gives rise to paradoxes, such as the cantilever.
Abstract: Eringen’s nonlocal differential model has been widely used in the literature to predict the size effect in nanostructures. However, this model often gives rise to paradoxes, such as the cantilever ...
49 citations
TL;DR: In this paper, it is shown that every object in the world has a three-dimensional geometrical shape and it is usually possible to model structures in a 3D fashion, although this approach can be computationally expe...
Abstract: Every object in the world has a three-dimensional geometrical shape and it is usually possible to model structures in a three-dimensional fashion, although this approach can be computationally expe...
47 citations
TL;DR: In this paper, the authors demonstrate augmented properties derived from their engineered structure using metamaterials and 3D printing technologies, which have enabled the fabrication of complex metamolecular structures.
Abstract: Mechanical metamaterials demonstrate augmented properties derived from their engineered structure. Advances in three-dimensional (3D) printing technologies have enabled the fabrication of complex m...
39 citations
TL;DR: In this paper, Apalara considered a one-dimensional porous elasticity system with memory and established a general decay of energy for the system in the case of equal-speed wave propagations.
Abstract: In previous work, Apalara considered a one-dimensional porous elasticity system with memory and established a general decay of energy for the system in the case of equal-speed wave propagations. In...
39 citations
TL;DR: In this article, the homogenized behavior of three-dimensional periodic structures made of welded elastic bars was determined in the framework of static linear elasticity, and it has been shown that such structures can b
Abstract: We determine in the framework of static linear elasticity the homogenized behavior of three-dimensional periodic structures made of welded elastic bars It has been shown that such structures can b
38 citations
TL;DR: In this paper, the theoretical foundations for tuning the properties of metamaterials are presented, and the theoretical foundation for tuning metamur-materials is discussed. But the theoretical framework is not defined yet.
Abstract: Mechanical metamaterials are designed to exhibit enhanced properties not found in natural materials or to bolster the properties of existing materials. The theoretical foundations for tuning the me...
TL;DR: Similarity theory is a branch of engineering science that deals with establishing conditions of similarity among phenomena and is applied to various fields, such as structural engineering problems as discussed by the authors, and it has been applied to many engineering problems.
Abstract: Similarity theory is a branch of engineering science that deals with establishing conditions of similarity among phenomena and is applied to various fields, such as structural engineering problems,...
TL;DR: Eringen's model is one of the most popular theories in non-local elasticity as discussed by the authors, and has been applied to many practical situations with the objective of removing anomalous stress concentrations around g...
Abstract: Eringen’s model is one of the most popular theories in non-local elasticity. It has been applied to many practical situations with the objective of removing anomalous stress concentrations around g...
TL;DR: By means of variational asymptotic homogenization, using Piola's meso-macro ansatz, this article derived the linear Timoshenko beam as the macro-scale limit of a beam-like periodic planar square.
Abstract: By means of variational asymptotic homogenization, using Piola’s meso-macro ansatz, we derive the linear Timoshenko beam as the macro-scale limit of a meso-scale beam-like periodic planar square la...
TL;DR: In this article, the axisymmetric adhesive contact problem was studied in the framework of the Johnson-Kendall-Roberts (JKR) theory for a thin compressible elastic layer attached to a rigid support.
Abstract: Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius.
TL;DR: The properties of multiscale composites are of great interest in engineering and biology as mentioned in this paper, particularly, hierarchical composite structures can be found in nature and in engineering. Duri...
Abstract: The study of the properties of multiscale composites is of great interest in engineering and biology. Particularly, hierarchical composite structures can be found in nature and in engineering. Duri...
TL;DR: A set of “bone like” microstructures with variety of distributions has been created to study pseudo “patient variabilities” and could be used to develop precise predictive numerical models while developing parametric studies on an infinite number of virtual samples and correlating patient dependency with more precise mechanobiological numerical models.
Abstract: The development of a predictive model for bone remodeling is becoming increasingly important for medical applications such as bone surgery or bone substitutes like prostheses. However, as bone remo...
TL;DR: In this paper, the possible justification of nonlocal beam models (at the macroscopic scale) from an asymptotic derivation based on nonlocal two-dimensional elasticity was discussed.
Abstract: The paper is focused on the possible justification of nonlocal beam models (at the macroscopic scale) from an asymptotic derivation based on nonlocal two-dimensional elasticity (at the material sca...
TL;DR: In this paper, the construction of reliable dynamic models of nanostructures is an important task for design procedures of different nanoresonator devices, which allow as to perform different numeri...
Abstract: Construction of reliable dynamic models of nanostructures is an important task for design procedures of different nanoresonator devices. Such theoretical models allow as to perform different numeri...
TL;DR: In this paper, the authors identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the poi...
Abstract: Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the poi...
TL;DR: In this paper, exact solutions for the static bending response of simply supported isotropic micro-and nano-beams were derived for the same static bending problem of a single beam.
Abstract: This paper presents the exact solutions derived for the static bending response of simply supported isotropic micro- and nano-beams. The governing differential equations of equilibrium and the asso...
TL;DR: In this article, the propagation and decay of waves in a one-dimensional, viscoelastic peridynamic medium is investigated. And the effect of spatial nonlocality on the decay of a wave in a dissipative material was investigated.
Abstract: The effect of spatial nonlocality on the decay of waves in a dissipative material is investigated. The propagation and decay of waves in a one-dimensional, viscoelastic peridynamic medium is analyz...
TL;DR: The development of linear elastodynamics in pure stress-based formulation began over half a century ago as an alternative to the classical displacement-based treatment that came into existence two decades ago as discussed by the authors.
Abstract: The development of linear elastodynamics in pure stress-based formulation began over half-a-century ago as an alternative to the classical displacement-based treatment that came into existence two ...
TL;DR: This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage, using the finite-element method.
Abstract: Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide a...
TL;DR: In this article, the authors analyzed the thermoelastic interactions inside an infinitely extended thick plate due to axis-symmetric temperature distribution applied at the lower and upper surfaces of the plate under memory-dependent generalized thermo-elasticity.
Abstract: The present work is carried out under generalized thermoelasticity theory with memory-dependent derivatives. The main purpose of this work is to analyze the thermoelastic interactions inside an infinitely extended thick plate due to axis-symmetric temperature distribution applied at the lower and upper surfaces of the plate under memory-dependent generalized thermoelasticity. The formulation of the problem is done in the context of the theory of thermoelasticity under memory-dependent derivatives with inclusion of time delay parameter τ and kernel functions that are defined in a slipping interval [t−τ,t). The potential function concept along with Laplace and Hankel transform techniques is used to solve the problem. Furthermore, inversion of the Hankel transform technique is used to find the solution in the Laplace transform domain. The final solution in the space–time domain is obtained by employing a numerical method of Laplace inversion. We have also compared the present findings with work which has bee...
TL;DR: In this paper, a model of elastic solids reinforced with fibers resistant to extension and bending is formulated in finite-plane elastostatics and the linear theory of the proposed model is also derived through a linear theory.
Abstract: A model of elastic solids reinforced with fibers resistant to extension and bending is formulated in finite-plane elastostatics. The linear theory of the proposed model is also derived through whic...
TL;DR: In this article, it was shown that for nanostructures under transverse bending, the effective Young modulus is appreciably greater (in magnitude) than that of the same elements under axial loads.
Abstract: Previous studies demonstrate that, for nanostructures under transverse bending, the effective Young modulus is appreciably greater (in magnitude) than that of the same elements under axial loads. T...
TL;DR: In this paper, a tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities was derived.
Abstract: We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the fourth...
TL;DR: Based on the generalized thermoelastic diffusion theory with memory-dependent derivative in both the generalized heat conduction law and the generalized diffusion law, the transient response is introduced in this article.
Abstract: Based on the generalized thermoelastic diffusion theory with memory-dependent derivative in both the generalized heat conduction law and the generalized diffusion law, the transient response is inv
TL;DR: In this article, a full phase-field model for a fluid-driven fracture in a nonlinear poroelastic medium is presented, where the nonlinearity arises in the Biot equations when the permeability depends on poro...
Abstract: In this paper, we present a full phase-field model for a fluid-driven fracture in a nonlinear poroelastic medium. The nonlinearity arises in the Biot equations when the permeability depends on poro...