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  • 1.
    Hallbäck, Nils
    et al.
    Karlstad University, Faculty of Technology and Science.
    Girlanda, Orlando
    Karlstad University, Faculty of Technology and Science.
    Tryding, Johan
    Finite Element Analysis of Ink-tack Delamination of Paperboard2006In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 43, p. 899-912Article in journal (Refereed)
  • 2.
    Hallbäck, Nils
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
    Tofique, Muhammad Waqas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
    Development of a distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half-plane2014In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, p. 2878-2892Article in journal (Refereed)
    Abstract [en]

    A distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half plane has been developed. The dipole density distribution is represented with a weighted Jacobi polynomial expansion where the weight function captures the asymptotic behaviour at each end of the crack. To allow for opening and sliding at crack kinking and branching the dipole density representation contains conditional extra terms which fulfil the asymptotic behaviour at each endpoint. Several test cases involving straight, kinked and branched cracks have been analysed, and the results suggest that the accuracy of the method is within 1% provided that Jacobi polynomial expansions up to at least the sixth order are used. Adopting even higher order Jacobi polynomials yields improved accuracy. The method is compared to a simplified procedure suggested in the literature where stress singularities associated with corners at kinking or branching are neglected in the representation for the dipole density distribution. The comparison suggests that both procedures work, but that the current procedure is superior, in as much as the same accuracy is reached using substantially lower order polynomial expansions.

  • 3.
    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

  • 4.
    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

  • 5.
    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.

  • 6.
    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.

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