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  • 1.
    Bagheri, R.
    et al.
    University of Zanjan, Iran.
    Ayatollahi, M.
    University of Zanjan, Iran.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating2015In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 93, p. 93-101Article in journal (Refereed)
    Abstract [en]

    Abstract The fracture problem for a medium composed of a cracked piezoelectric strip with functionally graded orthotropic coating is studied. The layer is subjected to anti-plane mechanical and in-plane electrical loading. In this paper, we first address, the problem of a screw dislocation located in a substrate which is imperfectly bonded to the coating. Then, in order to model the cracked piezoelectric layer, by means of the dislocation solution, we construct integral equations for the layer, in which the unknown variables are dislocation densities. These unknowns are determined through satisfaction of the boundary conditions on the crack faces. By use of the dislocation densities, the field intensity factors are determined. Several examples are presented to demonstrate the applicability of the proposed solution. ", keywords = Piezoelectric strip; Functionally graded layer; Imperfect bonding; Multiple cracks; Stress intensity factors, isbn = 0020-7403, doi=https://doi.org/10.1016/j.ijmecsci.2014.11.025

  • 2.
    Bagheri, R.
    et al.
    University of Zanjan, Iran.
    Ayatollahi, M.
    University of Zanjan, Iran.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Analytical solution of multiple moving cracks in functionally graded piezoelectric strip2015In: Applied mathematics and mechanics, ISSN 0253-4827, E-ISSN 1573-2754, Vol. 36, no 6, p. 777-792Article in journal (Refereed)
    Abstract [en]

    The dynamic behaviors of several moving cracks in a functionally graded piezoelectric (FGP) strip subjected to anti-plane mechanical loading and in-plane electrical loading are investigated. For the first time, the distributed dislocation technique is used to construct the integral equations for FGP materials, in which the unknown variables are the dislocation densities. With the dislocation densities, the field intensity factors are determined. Moreover, the effects of the speed of the crack propagation on the field intensity factors are studied. Several examples are solved, and the numerical results for the stress intensity factor and the electric displacement intensity factor are presented graphically finally.

  • 3.
    Fariborz, Shahriar
    Amirkabir University, Iran.
    Free vibration of a rod undergoing finite strain2012In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 382, no 1Article in journal (Refereed)
    Abstract [en]

    The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchhoff stress and Green strain tensors, the equation of motion is written in terms of displacement in reference configuration. Three different types of homogenous boundary conditions may be considered for the rod, leading to three nonlinear eigenvalue problems. The series solutions with three terms satisfying the boundary conditions are utilized and the relationships between amplitudes of vibration are obtained by means of the Galerkin method. The backbone curves are drawn and the internal resonance between different modes of vibration is analyzed.

  • 4.
    Fernandes, R
    et al.
    Texas A&M University.
    El-Borgi,
    Texas A&M University at Qatar.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Reddy, JN
    Texas A&M University.
    Mechmoum,
    Texas A&M University at Qatar.
    Nonlinear size-dependent longitudinal vibration of carbon nanotubesembedded in an elastic medium2017In: Physica E: Low-dimensional Systems and Nanostructures, ISSN 1386-9477, Vol. 88, p. 18-25Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbonnanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation isbased on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradientare included in the expression of the strain energy and the velocity and its gradient are taken into account in theexpression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies areintroduced to model size effects. The governing motion equation along with the boundary conditions are derivedusing Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNTrod are first obtained. Then, the nonlinear free vibration response is investigated for various values of lengthscales using the method of multiple scales.

  • 5.
    Fernandes, Ralston
    et al.
    Texas A&M University at Qatar.
    Mousavi, Mahmoud
    Aalto University, Finland.
    El-Borgi, Sami
    University of Carthage, Tunisia.
    Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory2016In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 227, no 9, p. 2657-2670Article in journal (Refereed)
    Abstract [en]

    A nonlinear finite strain and velocity gradient framework is formulated for the Euler-€Bernoulli beam theory. This formulation includes finite strain and the strain gradient within the strain energy generalization as well as velocity and its gradient within the kinetic energy generalization. Consequently, static and kinetic internal length scales are developed to capture size effects. The governing equation with initial and boundary conditions is obtained using the variational approach. Free and forced vibration of a simply supported nanobeam is studied for different values of static and kinetic length scales using the method of multiple scales.

  • 6.
    Korsunsky, Alexander M.
    et al.
    University of Oxford, UK .
    Guénolé, Julien
    FAU, Germany.
    Salvati, Enrico
    University of Oxford, UK .
    Sui, Tan
    University of Oxford, UK .
    Mousavi, Mahmoud
    University of Oxford, UK & Aalto University, Finland.
    Prakash, Arun
    FAU, Germany.
    Bitzek, Erik
    FAU, Germany.
    Quantifying eigenstrain distributions induced by focused ion beam damage in silicon2016In: Materials letters (General ed.), ISSN 0167-577X, E-ISSN 1873-4979, p. 47-49Article in journal (Refereed)
    Abstract [en]

    Abstract Eigenstrain offers a versatile generic framework for the description of inelastic deformation that acts as the source of residual stresses. Focused ion beam (FIB) milling used for nanoscale machining is accompanied by target material modification by ion beam damage having residual stress consequences that can be described in terms of eigenstrain. Due to the lack of direct means of experimental determination of residual stress or eigenstrain at the nanoscale we adopt a hybrid approach that consists of eigenstrain abstraction from molecular dynamics simulation, its application within a finite element simulation of a flexible silicon cantilever, and satisfactory comparison of the prediction with experimental observation. Directions for further enquiry are briefly discussed. ", keywords = Focused ion beam milling; Molecular dynamics; Eigenstrain; Residual stress, isbn = 0167-577X, doi=https://doi.org/10.1016/j.matlet.2016.08.111

  • 7.
    Li, Kaiyuan
    et al.
    Aalto university Finland.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Hostikka, Simo
    Aalto university Finland.
    Char cracking of medium density fibreboard due to thermal shock effect induced pyrolysis shrinkage2017In: Fire safety journal, ISSN 0379-7112, E-ISSN 1873-7226, Vol. 91, p. 165-173, article id SIArticle in journal (Refereed)
    Abstract [en]

    Pyrolysis experiments were conducted on medium density fibreboard (MDF) in inert atmosphere and different ambient pressures, to investigate the char shrinkage and cracking. It is found that the char cracking under uniform heat flux is a typical thermal shock process induced by unbalance shrinkage along the sample thickness during pyrolysis. To predict the number of char fissures, the critical stress criterion and energy conservation theory are used to develop mathematical models under plane constitutive stress state, which reveal that under the same surface degradation the number of char fissures (blisters) strongly relates to the pyrolysis depth at cracking time. Increasing external heat flux decreases the pyrolysis depth and increases the number of char fissures. Both experiments and numerical modelling are used to validate the models. The experimental results show that the horizontal shrinkage is 11% of original length and the micro-structure of char fissures of MDF is less uniform compared to the one of natural wood with a cellular pattern. The surface stresses after cracking are found similarly close to the tensile strength under different heat fluxes, while the surface stresses are very different assuming no crack, which indicates the cracking process reduces the surface stress to lower than the tensile strength. The modelled cracking times are different from the observed cracking time as the fissures are hard to identify at its initial stage and only when they have expanded to certain size the fissures are visually observed. Using the modelled cracking time, the number of char blisters can be well correlated with the pyrolysis depth.

  • 8.
    Monfared, M. M.
    et al.
    University of Zanjan, Iran.
    Ayatollahi, M.
    University of Zanjan, Iran.
    Mousavi, Mahmoud
    Aalto University, Finland.
    The mixed-mode analysis of a functionally graded orthotropic half-plane weakened by multiple curved cracks2016In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 86, no 4, p. 713-728Article in journal (Refereed)
    Abstract [en]

    The problem of functionally graded orthotropic half-plane with climb and glide edge dislocations is solved. Dislocations are used as the building blocks of defects to model cracks of modes I and II. Following a dislocation-based approach, the problem is reduced to a system of singular integral equations for dislocation density functions on the surfaces of smooth cracks. These integral equations enforce the crack-face boundary conditions and are solved numerically for the dislocation density. The numerical results include the stress intensity factors for several different cases of crack configurations and arrangements.

  • 9.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Dislocation-based fracture analysis of functionally graded magnetoelectroelastic solids2015In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 95, no 12, p. 1501-1513Article in journal (Refereed)
  • 10.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Dislocation-based fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type - Part II: Inplane analysis2016In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, p. 105-120Article in journal (Refereed)
    Abstract [en]

    Abstract This paper is the sequel of a companion Part I paper devoted to dislocation-based antiplane fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type. In the present paper, the inplane analysis is carried out to study cracks of Modes I and II. Generalized continua including nonlocal elasticity of bi-Helmholtz type and gradient elasticity of bi-Helmholtz type (second strain gradient elasticity) offer nonsingular frameworks for the discrete dislocations. Consequently, the dislocation-based fracture mechanics within these frameworks is expected to result in a regularized fracture theory. By distributing the (climb and glide) edge dislocations, (Modes I and II) cracks are modeled. Distinctive features are captured for crack solutions within second-grade theories (nonlocal and gradient elasticity of bi-Helmholtz type) comparing with solutions within first-grade theories (nonlocal and gradient elasticity of Helmholtz type) as well as classical elasticity. Other than the total stress tensor, all of the field quantities are regularized within second-grade theories, while first-grade theories give singular double stress and dislocation density and classical elasticity leads to singularity in the stress field and dislocation density. Similar to gradient elasticity of Helmholtz type (first strain gradient elasticity), crack tip plasticity is captured in gradient elasticity of bi-Helmholtz type without any assumption of the cohesive zone. ", keywords = Crack; Inplane; Dislocation; Nonlocal elasticity of bi-Helmholtz type; Gradient elasticity of bi-Helmholtz type; Nonsingular, isbn = 0020-7683, doi=https://doi.org/10.1016/j.ijsolstr.2016.03.025

  • 11.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Dislocation-based fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type Part I: Antiplane analysis2016In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, p. 222-235Article in journal (Refereed)
    Abstract [en]

    Abstract In the present paper, the dislocation-based antiplane fracture mechanics is employed for the analysis of Mode III crack within nonlocal and (strain) gradient elasticity of bi-Helmholtz type. These frameworks are appropriate candidates of generalized continua for regularization of classical singularities of defects such as dislocations. Within nonlocal elasticity of bi-Helmholtz type, nonlocal stress is regularized, while the strain field remain singular. Interestingly, gradient elasticity of bi-Helmholtz type (second strain gradient elasticity) eliminates all physical singularities of discrete dislocation including stress and strain fields and dislocation density while the so-called total stress tensor still contains singularity at the dislocation core. Based on the distribution of dislocations, a fracture theory with nonsingular stress field is formulated in these nonlocal and gradient theories. Strain and displacement fields within nonlocal fracture theory are identical to the classical ones. In contrast, gradient elasticity of bi-Helmholtz type leads to a full nonsingular fracture theory in which stress, strain and dislocation density are regularized. However, the singular total stress of a discrete dislocation results in singular total stress of the plane weakened by a crack. Within classical fracture mechanics, Barenblatt’s cohesive fracture theory assumes that cohesive forces is distributed ahead of the crack tip to model crack tip plasticity and remove the stress singularity. Here, considering the dislocations as the carriers of plasticity, the crack tip plasticity is captured without any assumption. Once the crack is modeled by distributing the dislocations along its surface, due to the gradient theory, the distribution function gives rise to a non-zero plastic distortion ahead of the crack. Consequently, regularized solutions of crack are developed incorporating crack tip plasticity. ", keywords = Crack; Antiplane; Dislocation; Nonlocal elasticity of bi-Helmholtz type; Gradient elasticity of bi-Helmholtz type; Nonsingular, isbn = 0020-7683, doi=https://doi.org/10.1016/j.ijsolstr.2015.10.033

  • 12.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland & Aristotle University, Greece.
    Aifantis, E. C.
    Aristotle University, Greece.
    A note on dislocation-based mode III gradient elastic fracture mechanics2015In: Journal of the Mechanical Behavior of materials, ISSN 2191-0243, Vol. 24, no 3-4, p. 125-129Article in journal (Other academic)
  • 13.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Aifantis, Elias C.
    Aristotle University, Greece; St Petersburg, Russia.
    Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks2016In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 202, no 1, p. 93-110Article in journal (Refereed)
    Abstract [en]

    The in-plane classical dislocation-based linear elastic fracture mechanics analysis is extended to the case of strain gradient elasticity. Nonsingular stress and smooth-closure crack profiles are derived. As in the classical treatment, the crack is represented by a distribution of climb edge dislocations (for Mode I) or glide edge dislocations (for mode II). These distributions are determined through the solution of corresponding integral equations based on variationally consistent boundary conditions. An incompatible framework is used and the nonsingular full-field plastic distortion tensor components are calculated. Numerical results and related graphs are provided illustrating the nonsingular behaviour of the stress/strain components and the smooth cusp-like closure of the crack faces at the crack tip. The work provides an alternative approach to celebrated “Barenblatt’s treatment” of cracks, without the introduction of a cohesive zone and related to intermolecular forces ahead of the physical crack tip. It also supplements a recent paper by the authors in which the mode III crack, represented by an array of screw dislocations, was solved within the present gradient elasticity framework.

  • 14.
    Mousavi, Mahmoud
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013). Tehran Polytechnic, Iran.
    Fariborz, Shahriar
    Tehran Polytechnic, Iran.
    Anti-plane elastodynamic analysis of cracked graded orthotropic layers with viscous damping2012In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 36, no 4, p. 1626-1638Article in journal (Refereed)
    Abstract [en]

    Stress analysis is carried out in a graded orthotropic layer containing a screw dislocation undergoing time-harmonic deformation. Energy dissipation in the layer is modeled by viscous damping. The stress fields are Cauchy singular at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks with any location and orientation in the layer. These equations are solved numerically thereby obtaining the dislocation density function on the crack surfaces and stress intensity factors of cracks. The dependencies of stress intensity factors of cracks on the excitation frequency of applied traction and material properties of the layer are investigated. The analysis allows the determination of natural frequencies of a cracked layer. Furthermore, the interactions of two cracks having various configurations are studied.

  • 15.
    Mousavi, Mahmoud
    et al.
    Tehran Polytechnic, Iran.
    Fariborz, Shahriar
    Tehran Polytechnic, Iran.
    Propagation of Anti-plane Shear Waves in a Cracked Graded Strip with Viscous Damping2011In: 11TH INTERNATIONAL CONFERENCE ON THE MECHANICAL BEHAVIOR OF MATERIALS (ICM11) / [ed] Guagliano, M; Vergani, L, Elsevier, 2011, Vol. 10, no 0, p. 792-797Conference paper (Refereed)
    Abstract [en]

    The dislocation-distributed technique is utilized to study the elastodynamic fracture behavior of a graded isotropic layer with viscous damping. By investigation of the stress components due to the dislocation, the familiar Cauchy singularity is detected at the location of dislocation. Then the dislocation is utilized for the formation of cracks in the strip. The stress components of dislocation and time-harmonic antiplane point force leads to the integral equations. These equations results in the stress intensity factors (SIF) for the crack configuration in the strip.

  • 16.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Juha, Paavola
    Aalto University, Finland.
    Djebar, Baroudi
    Aalto University, Finland.
    Distributed non-singular dislocation technique for cracks in strain gradient elasticity2014In: Journal of the Mechanical Behavior of Materials, ISSN 2191-0243Article in journal (Refereed)
  • 17.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Korsunsky, Alexander M.
    University of Oxford.
    Non-singular antiplane fracture theory within nonlocal anisotropic elasticity2015In: Materials & design, ISSN 0264-1275, E-ISSN 1873-4197, p. 854-861Article in journal (Refereed)
    Abstract [en]

    Abstract In the present paper, the distributed dislocation technique is applied for the analysis of anisotropic materials weakened by cracks. Eringen’s theory of nonlocal elasticity of Helmholtz type is employed. The non-singular screw dislocation within anisotropic elasticity is distributed to model cracks of mode III. The corresponding dislocation density functions are evaluated using the proper crack-face boundary conditions. The nonlocal stress field within a plane weakened by cracks is determined. The crack opening displacement is also discussed within the framework of nonlocal elasticity. The stress singularity of the classical linear elasticity is removed by the introduction of the nonlocal theory of elasticity. The general anisotropic case and the special case of orthotropic material are studied. The effect of material orthotropy is presented for a crack which is not necessarily aligned with the principal orthotropy direction. ", keywords = Cracks; Anisotropy; Fracture mechanics; Dislocations; Nonlocal elasticity; Integral equations, isbn = 0264-1275, doi=https://doi.org/10.1016/j.matdes.2015.09.068

  • 18.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Lazar, Markus
    Darmstadt University of Technology, Germany.
    Distributed dislocation technique for cracks based on non-singular dislocations in nonlocal elasticity of Helmholtz type2015In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 136, no 0, p. 79-95Article in journal (Refereed)
    Abstract [en]

    Abstract In the present paper, the distributed dislocation technique is extended for crack problems within Eringen’s theory of nonlocal elasticity of Helmholtz type. Employing distributed dislocation technique, non-singular stresses of cracks of modes I, II and III are obtained using the non-singular stresses of climb edge, glide edge and screw dislocations and dislocation density functions which are solutions of the non-singular integral equations of distributed dislocation technique. The cracks are modeled by a continuous distribution of straight dislocations. The nonlocal elasticity solutions of crack problems do not contain a stress singularity. We found that the non-singular crack stresses are zero at the crack tip or near the crack tip.

  • 19.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Analysis of a cracked concrete containing an inclusion with inhomogeneously imperfect interface2015In: Mechanics research communications, ISSN 0093-6413, E-ISSN 1873-3972, Vol. 63, p. 1-5Article in journal (Refereed)
    Abstract [en]

    Abstract The distributed dislocation technique is applied to determine the behavior of a cracked concrete matrix containing an inclusion. The analysis of cracked concrete in the presence of inclusions such as steel expansions is a practical problem that needs special attention. The solution to the problem of interaction of an edge dislocation with a circular inclusion having circumferentially inhomogeneously imperfect interface is available in the literature. This analytical solution is used in the distributed dislocation technique to obtain the stress intensity factor for the cracked concrete in the presence of inclusion. The interface of the matrix and the inclusion is assumed inhomogeneously imperfect and the stress intensity factor is determined for the cracked concrete for a case of two identical cracks on diametrically opposite sides of the inclusion. Consideration of this general inhomogeneously imperfect interface is the contribution of this paper. The variation of the inhomogeneity parameters is studied and presented. Additionally, the general assumption for the interface is simplified to the special case of perfectly bonded interface. The observations for the perfect interface are coincident with the previously reported results.

  • 20.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Analysis of cracked functionally graded piezoelectric strip2013In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 50, no 14-15, p. 2449-2456Article in journal (Refereed)
    Abstract [en]

    Abstract The fracture behavior of a cracked strip under antiplane mechanical and inplane electrical loading is studied. A functionally graded piezoelectric strip with exponential material gradation is under consideration. The mechanical and electrical loading is combined via loading coupling factor. The problem of a graded piezoelectric strip containing a screw dislocation is solved. This solution results in stress and electric displacement components with Cauchy singularity. Based on the solution achieved for the dislocation, the distributed dislocation technique (DDT) is utilized to form any geometry of multiple cracks and analyze the behavior of a cracked strip under antiplane mechanical and inplane electrical loading. This technique is capable of the analysis of a strip with a system of interacting cracks. Several examples including strips with single crack, two straight cracks and two curved cracks are presented.

  • 21.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Analysis of functionally graded magneto-electro-elastic layer with multiple cracks2013In: Theoretical and applied fracture mechanics (Print), ISSN 0167-8442, E-ISSN 1872-7638, Vol. 66, p. 1-8Article in journal (Refereed)
    Abstract [en]

    Abstract In this paper, the distributed dislocation technique (DDT) is developed to be utilized for the analysis of a cracked functionally graded piezoelectric-€“piezomagnetic (FGPP) layer under anti-plane mechanical and in-plane electric and magnetic fields. By using the Fourier transformation, the closed-form expressions for the shear stress, electric displacement and magnetic displacement components are obtained for a generalized Volterra-type screw dislocation. The generalized dislocation in FGPP layer contains dislocation in the displacement component and jump in the electric and magnetic potentials. The expressions of generalized stress intensity factor are derived in the DDT. The solution of the dislocation problem is utilized in the DDT to solve the problem of arbitrary configurations of multiple embedded and edge cracks. The generalized intensity factors of the cracked layer are obtained. Numerical results for generalized intensity factors of straight and curved cracks are presented. The DDT is proved to be useful in the analysis of the interaction of the embedded and edge cracks in an FGPP layer.

  • 22.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Analysis of plate in second strain gradient elasticity2014In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 84, no 8, p. 1135-1143Article in journal (Refereed)
  • 23.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Baroudi, Djebar
    Aalto University, Finland.
    Cracks in strain gradient elasticity-distributed dislocation technique2014In: 20TH EUROPEAN CONFERENCE ON FRACTURE / [ed] Zhang, Z Skallerud, B Thaulow, C Ostby, E He, J, Elsevier, 2014, p. 77-82Conference paper (Refereed)
    Abstract [en]

    The mode III fracture analysis of graded cracked plane in the framework of classical and strain gradient elasticity is presented in this work. Solutions to the problem of screw dislocation in plane are available for classical and strain gradient elasticity theories. Different approaches for the formulation of the strain gradient theory, especially considering the boundary conditions, result in singular and nonsingular stress fields at the crack tip. One of the applications of the dislocation is the analysis of cracked medium via the Distributed Dislocation Technique (DDT). The DDT has been applied extensively in the framework of the classical elasticity. In this article, this technique is generalized for the nonsingular strain gradient elasticity formulation available in the literature. For a system of interacting cracks in classical elasticity, DDT results in a system of Cauchy singular integral equations. In the framework of the gradient elasticity, due to the regularization of the classical singularity, a system of nonsingular integral equations is obtained. Plane with one crack is studied and the singular stress distribution in the classical elasticity is compared with the nonsingular stress components in gradient elasticity theories. (C) 2014 Elsevier Ltd.

  • 24.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Reddy, J. N.
    Texas A&M University, USA.
    Variational approach to dynamic analysis of third-order shear deformable plates within gradient elasticity2015In: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648, Vol. 50, no 6, p. 1537-1550Article in journal (Refereed)
    Abstract [en]

    A variational approach based on Hamilton’s principle is used to develop the governing equations for the dynamic analysis of plates using the Reddy third-order shear deformable plate theory with strain gradient and velocity gradient. The plate is made of homogeneous and isotropic elastic material. The stain energy, kinetic energy, and the external work are generalized to capture the gradient elasticity (i.e., size effect) in plates modeled using the third-order shear deformation theory. In this framework, both strain and velocity gradients are included in the strain energy and kinetic energy expressions, respectively. The equations of motion are derived, along with the consistent boundary equations. Finally, the resulting third-order shear deformation (strain and velocity) gradient plate theory is specialized to the first-order and classical strain gradient plate theories.

  • 25.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Reddy, J. N.
    Texas A&M University, USA.
    Romanoff, Jani
    Aalto University, Finland.
    Analysis of anisotropic gradient elastic shear deformable plates2016In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 227, no 12, p. 3639-3656Article in journal (Refereed)
    Abstract [en]

    In this paper, Reddy’s third-order shear deformable plate theory is employed for the analysis of centrosymmetric anisotropic plate structures within strain gradient elasticity. The general three-dimensional anisotropic gradient theory is reduced to a two-dimensional formulation for the analysis of thick plate structures. The third-order shear deformation theory (TSDT) takes into account quadratic variation of the transverse shear strains of the plate and does not require shear correction factors. In order to investigate the case of small strains but moderate rotations, the von Kármán strains are considered. The TSDT is also simplified to anisotropic Kirchhoff plate theory within gradient elasticity. To study specific material properties in more detail, the (Kirchhoff and TSDT) gradient plate theory of general anisotropy is simplified to the more practical case of orthotropic plates. It is observed that the gradient theory provides the capability to capture the size effects in anisotropic plate structures. As case studies, the bending and buckling behaviors of the simply supported orthotropic (Kirchhoff and TSDT) plates are studied. Variationally consistent boundary conditions are also discussed. Finally, analytical solutions are presented for the bending and buckling of simply supported orthotropic Kirchhoff plates. The effects of internal length scales on deflections and buckling loads are presented.

  • 26.
    Ouakad, Hassen M.
    et al.
    King Fahd University of Petroleum and Minerals, Saudi Arabia.
    El-Borgi, Sami
    Texas A&M University, Qatar.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Friswell, Michael I.
    Swansea University, UK.
    Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory2018In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 62, p. 207-222Article in journal (Refereed)
    Abstract [en]

    This paper examines the length-scale effect on the nonlinear response of an electrically actuated Carbon Nanotube (CNT) based nano-actuator using a nonlocal strain and velocity gradient (NSVG) theory. The nano-actuator is modeled within the framework of a doubly-clamped Euler–Bernoulli beam which accounts for the nonlinear von-Karman strain and the electric actuating forcing. The NSVG theory includes three length-scale parameters which describe two completely different size-dependent phenomena, namely, the inter-atomic long-range force and the nano-structure deformation mechanisms. Hamilton's principle is employed to obtain the equation of motion of the nonlinear nanobeam in addition to its respective classical and non-classical boundary conditions. The differential quadrature method (DQM) is used to discretize the governing equations. The key aim of this research is to numerically investigate the influence of the nonlocal parameter and the strain and velocity gradient parameters on the nonlinear structural behavior of the carbon nanotube based nanobeam. It is found that these three length-scale parameters can largely impact the performance of the CNT based nano-actuator and qualitatively alter its resultant response. The main goal of this investigation is to understand the highly nonlinear response of these miniature structures to improve their overall performance.

  • 27.
    Salvati, E.
    University of Oxford, Engineering Science Department.
    Papadaki, C.
    University of Oxford, Engineering Science Department.
    Zhang, H.
    University of Oxford, Engineering Science Department.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Wermeille, D.
    ESRF European Synchrotron Radiation Facility.
    Korsunsky, A.M.
    University of Oxford, Engineering Science Department.
    Nanoscale Structural Damage due to Focused Ion Beam Milling of Silicon with Ga ions2018In: Materials letters (General ed.), ISSN 0167-577X, E-ISSN 1873-4979, Vol. 13, p. 346-349Article in journal (Refereed)
  • 28.
    Salvati, E.
    et al.
    Oxford university, England.
    Brandt, L. R.
    Oxford university, England.
    Papadaki, C.
    Oxford university, England.
    Zhang, H.
    Oxford university, England.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Wermeille, D.
    ESRF, XMaS Beamline, Frankrike.
    Korsunsky, A. M.
    Oxford university, England.
    Nanoscale structural damage due to focused ion beam milling of silicon with Ga-ions2018In: Materials letters (General ed.), ISSN 0167-577X, E-ISSN 1873-4979, Vol. 213, p. 346-349Article in journal (Refereed)
    Abstract [en]

    The exposure of sample to Focused Ion Beam leads to Ga-ion implantation, damage, material amorphisation, and the introduction of sources of residual stress; namely eigenstrain. In this study we employ synchrotron X-ray Reflectivity technique to characterise the amorphous layer generated in a single crystal Silicon sample by exposure to Ga-ion beam. The thickness, density and interface roughness of the amorphous layer were extracted from the analysis of the reflectivity curve. The outcome is compared with the eigenstrain profile evaluated from residual stress analysis by Molecular Dynamics and TEM imaging reported in the literature. (c) 2017 Elsevier B.V. All rights reserved.

  • 29.
    Tahaei Yaghoubi, Saba
    et al.
    Aalto University, Finland.
    Balobanov, Viacheslav
    Aalto University, Finland.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Niiranen, Jarkko
    Aalto University, Finland.
    Variational formulations and isogeometric analysis for the dynamics ofanisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams2018In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 69, p. 113-123Article in journal (Refereed)
    Abstract [en]

    A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.

  • 30.
    Yaghoubi, Saba Tahaei
    et al.
    Aalto University, Finland.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013). Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Size effects on centrosymmetric anisotropic shear deformable beam structures2017In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 97, no 5, p. 586-601Article in journal (Refereed)
    Abstract [en]

    In this paper, the size effect on beam structures with centrosymmetric anisotropy is studied within strain gradient elasticity theory. Applying dimension reduction to the three dimensional anisotropic gradient elasticity, the third-order shear deformable (TSD) beam is analysed. A variational approach is used to determine the equilibrium equations of TSD beam together with consistent (classical and non-classical) boundary conditions. The TSD beam theory which is suitable for deep beam structures can be replaced by (less complicated) Euler-Bernoulli beam model for thin beam structures. The anisotropic Euler-Bernoulli beam model is also formulated within the framework of strain gradient theory. This anisotropic beam theory can be used to study size effects for any types of centrosymmetric anisotropy. To address the more practical cases of composite structures, the formulation is simplified for orthotropic and transversely isotropic materials. Finally, the analytical solutions are provided for bending of simply supported (TSD and Euler-Bernoulli) beams as well as clamped Euler-Bernoulli beams. The effect of the crystal orientation with respect to the beam geometry is investigated in these examples.

  • 31.
    Yaghoubi, Saba Tahaei
    et al.
    Aalto University, Finland.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Strain and velocity gradient theory for higher-order shear deformable beams2015In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 85, no 7, p. 877-892Article in journal (Refereed)
    Abstract [en]

    The strain and velocity gradient framework is formulated for the third-order shear deformable beam theory. A variational approach is applied to determine the governing equations together with initial and boundary conditions. Within the gradient framework, the strain energy is generalized to include strain as well as strain gradient. Furthermore, the kinetic energy is also generalized to include velocity and the velocity gradient. Such approach results in the introduction of the static and kinetic internal length scales. For dynamic analysis of beams, most of the gradient theories do not take the velocity gradient into account. The model developed in this paper depicts the influence of the velocity gradient on the governing equations and initial and boundary conditions of the third-order shear deformable theory. Through the assumption of the velocity gradients, kinematic quantities are distinguished on the microscale and on the macroscale. Finally, Timoshenko and Euler–Bernoulli beam theories are also presented by simplifying the third-order theory.

  • 32.
    Yaghoubi, SabaTahaei
    et al.
    Aalto university, Finland.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013). Aalto university, Finland.
    Paavola, Juha
    Aalto university, Finland.
    Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity2017In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 109, p. 84-92Article in journal (Refereed)
    Abstract [en]

    Buckling of centrosymmetric anisotropic beams is studied within strain gradient theory. First, the three dimensional anisotropic gradient elasticity theory is outlined. Then the dimension of the three dimensional theory is reduced, resulting in Timoshenko beam as well as Euler–Bernoulli beam theories. The governing differential equations together with the consistent (classical and non-classical) boundary conditions are derived for centrosymmetric anisotropic beams through a variational approach. By considering von Kármán nonlinear strains, the geometric nonlinearity is taken into account. The obtained nonlinear formulation can be used to study the postbuckling configuration. The analysis of size effect on anisotropic beam structures is missing in the literature so far, while the present model allows one to characterize the size effect on the buckling of the centrosymmetric anisotropic micro- and nano-scale beam structures such as micropillars. As a specific case, the governing buckling equation is obtained for the more practical case of orthotropic beams. Finally, the buckling loads for orthotropic simply supported Timoshenko and Euler–Bernoulli beams as well as a clamped Euler–Bernoulli beam are obtained analytically and the effect of the internal length scale parameters on the buckling load is depicted.

1 - 32 of 32
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