Eleni Agiasofitou

Technical University of Darmstadt | TU · Institute for Mechanics

In this work we propose the elastodynamic model of wave-telegraph type for the description of dynamics of quasicrystals. Phonons are represented by waves, and phasons by waves damped in time and propagating with finite velocity. Therefore, the equations of motion for the phonon fields are of wave type and for the phason fields are of telegraph type...

The aim of the present work is the unification of incompatible elasticity theory of dislocations and Eshelbian mechanics leading naturally to Eshelbian dislocation mechanics. In such a unified framework, we explore the utility of the $J$-, $M$-, and $L$-integrals. We give the physical interpretation of the $M$-, and $L$-integrals for dislocations,...

In this work, based on Eringen's theory of nonlocal anisotropic elasticity, the three-dimensional nonlocal anisotropic elasticity of generalized Helmholtz type is developed. The derivation of a new three-dimensional nonlocal anisotropic kernel, which is the Green function of the three-dimensional anisotropic Helmholtz equation, enables to capture a...

In this paper, dislocations in piezoelectric materials are studied in the framework of linear incompatible theory of piezoelectricity with eigendistortion and eigenelectric field. We consider that both field variables, the displacement vector u and the electrostatic potential ϕ, possess a jump discontinuity at the dislocation surface. This leads to...

A nonlocal elasticity theory with nonlocality in space and time is developed by considering nonlocal constitutive equations with a dynamical scalar nonlocal kernel function. The proposed theory is specified to isotropic nonlocal elasticity of Klein–Gordon type, which is an extension of nonlocal elasticity of Helmholtz type, and it possesses one cha...

In this work, the elastic 4×4 Green tensor of one-dimensional quasicrystals is given and has phonon, phason and phonon–phason coupling components. Using the residue method, a closed-form expression of the elastic 4×4 Green tensor for one-dimensional hexagonal quasicrystals of Laue class 10, which possess 10 independent material constants, is derive...

In this work, within the framework of the linear piezoelectricity theory of quasicrystals, the three-dimensional and two-dimensional Green tensors for arbitrary piezoelectric quasicrystals are derived. In the piezoelectricity of quasicrystals, where phonon, phason and electric fields exist, we introduce the corresponding multifields by developing a...

Quasicrystals endowed with piezoelectric properties belong nowadays to novel piezoelectric materials. In this work, the basic framework of generalized piezoelectricity theory of quasicrystals is investigated by providing an improvement of the existing constitutive modelling. It is shown, for the first time, that the tensor of phason piezoelectric m...

The Toupin-Mindlin anisotropic first strain-gradient elasticity is a generalized continuum field theory valid at small scales. The field theoretical framework, the constitutive tensors, and the material parameters are given for anisotropic, cubic, and isotropic materials in first strain gradient elasticity. Since the characteristic lengths are in t...

In this work, a nonlocal elasticity theory with nonlocality in space and time is presented by considering nonlocal constitutive equations with a dynamical scalar nonlocal kernel. Based on the proposed theory, we consider the isotropic nonlocal elasticity of Klein-Gordon type including a characteristic internal time scale parameter in addition to th...

In this work, the J-, M- and L-integrals of two line charges and two line forces in generalized plane strain are derived in the framework of three-dimensional (3D) electrostatics and three-dimensional compatible linear elasticity, respectively, in order to study the interaction between them. The key point in this derivation is achieved by expressin...

In this work, based on the theory of linear incompatible piezoelectricity with eigendistortion and eigenelectric field, the concept of electro‐elastic dislocations is presented. Both field variables, the displacement vector u and the electrostatic potential φ, possess a jump discontinuity at the dislocation surface. Electro‐elastic dislocations are...

This Special Issue of Crystals is devoted to the "Recent Advances in Quasicrystals". The aim of the Special Issue is to bring together researchers spanning the wide spectrum of quasicrystals, providing a current depiction of the research in this field, offering a venue for a deeper understanding and embracing new technologies and applications, in w...

In this work, a mathematical modeling of the elastic properties of cubic crystals with centrosymmetry at small scales by means of the Toupin–Mindlin anisotropic first strain gradient elasticity theory is presented. In this framework, two constitutive tensors are involved, a constitutive tensor of fourth-rank of the elastic constants and a constitut...

In this work, dislocations in piezoelectric materials are studied in the framework of linear incompatible theory of piezoelectricity with eigendistortion and eigenelectric field. We introduce for the first time the concept of the electric dislocation density vector as additional defect measure necessary for the description of the jump of the electr...

This special issue on "Advances in Micromechanics of Defects" is devoted to the coverage of recent advancements and developments achieved in the emerging research field of micromechanics of defects in this interdisciplinary research area that lies at the intersection of engineering science, materials science and applied mathematics. Several aspects...

In this work, we derive the J-, M- and L-integrals of body charges and point charges in electrostatics, and the J-, M- and L-integrals of body forces and point forces in elasticity and we investigate their physical interpretation. Electrostatics is considered as field theory of an electrostatic scalar potential φ (scalar field theory) and elasticit...

The explicit formulas of the J‐, M‐, and L‐integrals of straight (screw and edge) dislocations in isotropic materials are presented. The obtained results reveal the physical interpretation and significance of the M‐, and L‐integrals for straight dislocations. The M‐integral between two straight dislocations (per unit length) is equal to half the in...

In this work, using the framework of (three-dimensional) Eshelbian dislocation mechanics, we derive the J-, M-, and L-integrals of a single (edge and screw) dislocation in isotropic elasticity as a limit of the J-, M-, and L-integrals between two straight dislocations as they have recently been derived by Agiasofitou and Lazar [Int. J. Eng. Sci. 11...

In this work, the so-called Eshelbian or configurational mechanics of quasicrystals is presented. Quasicrystals are considered as a prototype of novel materials. Material balance laws for quasicrystalline materials with dislocations are derived in the framework of generalized incompatible elasticity theory of quasicrystals. Translations, scaling tr...

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory...

Phason dynamics constitutes a challenging and interesting subject in the study of quasicrystals, since there is not a unique model in the literature for the description of the dynamics of the phason fields. Here, we introduce the elastodynamic model of wave-telegraph type for the description of dynamics of quasicrystals [1, 2]. Phonons are represen...

Based on Eringen’s model of nonlocal anisotropic elasticity, new solutions for the stress fields of screw dislocations in anisotropic materials are derived. In the theory of nonlocal anisotropic elasticity the anisotropy is twofold. The anisotropic material behavior is not only included in the anisotropy of the elastic stiffness properties, but als...

A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation density tensors and introducing the dislocation current tensors for the phonon and phason fields, including the Bi...

A nonlinear continuum theory of material bodies with continuously distributed dislocations is presented, based on a gauge theoretical approach. Firstly, we derive the canonical conservation laws that correspond to the group of translations and rotations in the material space using Noether’s theorem. These equations give us the canonical Eshelby str...

In the present paper we investigate conservation and balance laws in the framework of linear elastodynamics considering the strain energy density depending on the gradients of the displacement up to the third order, as originally proposed by Mindlin (Int.J. Solids Struct. 1, 417–438, 1965). The conservation and balance laws that correspond to the s...

In this work we derive conservation and balance laws in the context of linear, anisotropic elasticity of grade three including cohesive forces. More particularly, for a homogeneous medium without external forces we derive the conservation laws of translation and addition of solutions as well as the balance laws that stem from the rotation and scali...

The paper presents a new procedure to construct micro-mechanical damage models able to describe size effects in solids. The new approach is illustrated in the case of brittle materials. We use homogenization based on two-scale asymptotic developments to describe the overall behavior of a damaged elastic body starting from an explicit description of...

In the present work, we study the overall behavior of a microfractured elastic body within the configurational mechanics framework. Micro and macro scales are considered and scale changes are carried out by asymptotic developments homogenization. The homogenized equations of material momentum and scalar moment of material momentum are obtained. In...

In this work, an asymptotic homogenization technique is used to describe the overall behavior of a damaged elastic body with a locally periodic distribution of growing microcracks. The microstructural deterioration is represented, at the macroscopic level, by a local internal variable related to the microcracks lengths. An evolution damage law is d...

In this work, the derivation of the configurational equations for a cracked elastic body by postulating balance laws, is studied. To this end, a proper kinematics is proposed, according to which the evolution of the crack in the material configuration and the physical motion (deformation) are separated. A rigorous localization procedure provides th...

In this work, an asymptotic expansion homogenization is used to study the overall behaviour of a damaged elastic body with a locally periodic distribution of growing microcracks. The microstructure evolution is represented, at the macroscopic level, by a local internal variable related to the microcracks lengths. An evolution damage law is deduced,...

The concept of a balance law for an elastic fractured body, in Euclidean and material space, is used to investigate the propagation of a circular crack in an elastic body. In the spirit of modern continuum mechanics, a rigorous localization process results in the local equations in the smooth parts of the body and, in addition, in the relations hol...

This work aims at the study of the dynamic fracture of an elastic material in the framework of configurational mechanics. The analysis is based on global balances for physical and configurational fields. Thus, the concept of balance law for an elastic fractured body, in Euclidean and material space, is treated in detail. In the spirit of modern con...

The concern of this work is the derivation of material conservation and balance laws for second gradient electroelasticity. The conservation laws of material momentum, material angular momentum and scalar moment of momentum on the material manifold are derived using Noether's theorem and the exact conditions under which they hold are rigorously stu...

In the spirit of modern continuum mechanics, global balance laws for momentum, angular momentum, energy and pseudomomentum are formulated for an elastic body in the presence of a moving crack. Upon localization, the corresponding balance equations in the bulk and at the crack tip are simultaneously obtained. The proposed framework is convenient for...