Mahmoud Mousavi

• Associate Professor in Solid Mechanics
• Professor (Associate) at Uppsala University

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...

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 w...

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 nonlo...

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...

In this paper, we provide detailed variational formulations for the reduced micromorphic model in rectangular and cylindrical coordinates. In these formulations, the material is modeled as consisting of deformable particles that exhibit microstrain and macroscopic strain fields. This microstrain field is independent of the macroscopic strain field...

The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being the inclusion) with complex cell topologies. For that, a computational homogenization scheme based on Mindlin (type II) strain gradient elastic...

Highly anisotropic materials like wood and unidirectional polymer composite structures are sensitive to shear deformations, in particular close to fixed joints. Large wooden structures in buildings and, e.g. wind-turbine blades, are designed to last for decades, and hence are susceptible to unwanted creep deformations. For improved structural desig...

Mechanical coupling in architectured materials has been traditionally investigated in the context of generalized continuum mechanics and is often assumed to be non-existent in the framework of classical continuum mechanics. In this paper, we challenge this misconception and study an anisotropic architectured material exhibiting shear-shear and shea...

Hydrogen embrittlement is a classical problem in bulk materials while it is rather untouched for advanced materials such as micro-architectured materials. This can be a barrier to industrial adoption of these materials where hydrogen is present as a popular source of energy. In this study, we developed a numerical scheme to assess the hydrogen degr...

Mechanical behavior of additively manufactured lattice materials has been mainly investigated under uniaxial compression, while their performance under uniaxial and multiaxial tension are yet to be understood. To address this gap, a generic elastoplastic homogenization scheme with continuum damage model is developed, and three different lattice mat...

A novel numerical framework for low cycle fatigue analysis of lattice materials is presented. The framework is based on computational elastoplastic homogenization equipped with the theory of critical distance to address the fatigue phenomenon. Explicit description of representative volume element and periodic boundary conditions are combined for co...

A plane within reduced micromorphic model subjected to external static load is studied using the finite element method. The reduced micromorphic model is a generalized continuum theory which can be used to capture the interaction of the microstructure. In this approach, the microstructure is homogenized and replaced by a reduced micromorphic materi...

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...

Computational first-order homogenization theory is used for the elastic analysis of generally anisotropic lattice materials within classical continuum mechanics. The computational model is tailored for structural one-dimensional (1D) elements, which considerably reduces the computational cost comparing to previously developed models based on solid...

We present singularity-free solution for cracks within polar media in which material points possess both position and orientation. The plane strain problem is addressed in this study for which the generalized continua including micropolar, nonlocal micropolar, and gradient micropolar elasticity theories are employed. For the first time, the variati...

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...

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 ten...

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....

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 pred...

In this paper, the dynamic behavior of an orthotropic substrate weakened by moving cracks and reinforced by a non-homogenous coating is studied. First, the solution to the screw dislocation in an orthotropic strip with imperfect orthotropic functionally graded coating is obtained. Then, for the anti-plane analysis of cracks, the screw dislocations...

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 w...

In this paper, the dynamic behavior of an orthotropic substrate weakened by moving cracks and reinforced by a non-homogenous coating is studied. First, the solution to the screw dislocation in an orthotropic strip with imperfect orthotropic functionally graded coating is obtained. Then, for the anti-plane analysis of cracks, the screw dislocations...

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 defor...

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 o...

In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the...

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 ar...

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. D...

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 Part II paper, the inplane analysis is carried out to study cracks of Mode I and II. Generalized continua including nonlocal elasticity of bi-Helmholtz type and g...

Dislocation-based analysis of cracked magnetoelectroelastic solid under remotely uniform anti-plane mechanical with in-plane electromagnetic loading is presented. The solution to the generalized dislocation including screw dislocation and electric and magnetic jumps within an incompatible framework are reviewed from the literature. In order to mode...

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 surf...

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, th...

This paper investigates the linear steady state problem of several moving cracks in a functionally graded magneto-electro-elastic strip subjected to anti-plane mechanical and in-plane electric and magnetic loading. For simplicity, it is assumed that the properties of the strip vary continuously according to exponential functions along the thickness...

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...

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. T...

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. T...

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...

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 circula...

The mode III fracture analysis of a cracked graded plane in the framework of classical, first strain gradient, and second strain gradient elasticity is presented in this paper. Solutions to the problem of screw dislocation in graded materials are available in the literature. These solutions include various frameworks such as classical elasticity, a...

The bending analysis of a thin rectangular plate is carried out in the framework of the second gradient elasticity. In contrast to the classical plate theory, the gradient elasticity can capture the size effects by introducing internal length. In second gradient elasticity model, two internal lengths are present, and the potential energy function i...

The governing differential equation for the free vibration of a rod undergoing finite strain is obtained by means of Hamilton's principle. The equation contains quadratic as well as cubic nonlinear terms. For the low-frequency analysis of rods, the two harmonics solution is considered for the equation. The Galerkin method is employed to convert the...

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 displ...

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 s...

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 probl...

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 interact...

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 probl...

The effect of steady-state thermal loading on a cracked layer is investigated. A Volterra type thermo-elastic dislocation is introduced in a layer which is free of traction on the boundaries. The assumptions of quasi-static, steady-state condition are employing and the uncoupled theory of thermo-elasticity is considered. The Fourier transformation...

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 bending analysis of laminated shells of revolution, such as spherical, conical and cylindrical panels, is carried out utilizing the differential cubature method (DCM). To do so, a general software based on the DCM is developed which can tackle shells of revolution with symmetric and unsymmetric lamination sequence. Analysis of shells with gener...

This paper deals with the application of the differential cubature method (DCM) to the bending analysis of laminated cylindrical panels. Symmetric and unsymmetric laminate, with various combinations of clamped, simply supported and free boundary conditions, are considered, with either uniform or sinusoidal transversely distributed loads. Using firs...