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  • 1.
    Bergström, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Chemical Engineering.
    Hossain, Shakhawath
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Chemical Engineering.
    Uesaka, Tetsu
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Chemical Engineering.
    Scaling Behaviour of Strength of 3D-, Semi-flexible-, Cross-linked Fibre Network2019In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 166, no July 2019, p. 68-74Article in journal (Refereed)
    Abstract [en]

    Anisotropic, semi-flexible, cross-linked, random fibre networks are ubiquitous both in nature and in a wide variety of industrial materials. Modelling mechanical properties of such networks have been done extensively in terms of criticality, mechanical stability, and scaling of network stiffnesses with structural parameters, such as density. However, strength of the network has received much less attention. In this work we have constructed 3D-planar fibre networks where fibres are, more or less, oriented in the in-plane direction, and we have investigated the scaling of network strength with density. Instead of modelling fibres as 1D element (e.g., a beam element with stretching, bending and/or shear stiffnesses), we have treated fibres as a 3D-entity by considering the features like twisting stiffness, transverse stiffness, and finite cross-link (or bond) strength in different deformation modes. We have reconfirmed the previous results of elastic modulus in the literature that, with increasing density, the network modulus indeed undergoes a transition from bending-dominated deformation to stretching-dominated with continuously varying scaling exponent. Network strength, on the other hand, scales with density with a constant exponent, i.e., showing no obvious transition phenomena. Using material parameters for wood fibres, we have found that the predicted results for stiffness and strength agree very well with experimental data of fibre networks of varying densities reported in the literature.

  • 2.
    Edvardsson, Sverker
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Gradin, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Isaksson, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    On dissipative effects of paper web adhesion strength2011In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 48, no 1, p. 24-30Article in journal (Refereed)
    Abstract [en]

    This work is concerned with the adhesion strength between a paper web and a metal roll surface, which is a common situation in paper machines world-wide. It is shown that the classic expression relating the work of adhesion to the peeling angle and web tension is, in general, insufficient. An improved model is suggested to take into account the energy dissipation due to elastic-plastic deformation behavior of wet paper materials. To judge the model, an industrially relevant example of wet newsprint and a mild steel surface is studied. It is found that the agreement between theory and experimental observations is excellent. A key result is that elastic-plastic material behavior must always be included for wet paper materials in peeling processes.

  • 3. Hägglund, R.
    et al.
    Isaksson, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Analysis of localized failure in low-basis weight paper2006In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 43, no 18-19, p. 5581-5592Article in journal (Refereed)
    Abstract [en]

    Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code.

  • 4. Hägglund, R
    et al.
    Isaksson, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    On the coupling between macroscopic material degradation and interfiber bond fracture in an idealized fiber network2008In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 45, no 3-4, p. 868-878Article in journal (Refereed)
    Abstract [en]

    The numerical analysis performed here, using a finite element network model, provides a number of important results regarding the evolution of micro fractures in planar random fiber networks where the only active microscopic fracture mechanism is bond fracture. The fibers are randomly distributed in the network meaning that the network is considered having in-plane isotropic properties on the macroscopic scale. The network is loaded so that, in an average sense, homogenous macroscopic stress and strain fields are present. Several conclusions are drawn. It is found that the development of macroscopic material degradation follows an exponential two-parameter law, consisting of an onset parameter and a fracture rate parameter, justifying a previous theory derived by the authors. The fracture rate parameter is linearly related to the inverse of the bond density above a certain density limit (percolation) and increases with increasing slenderness ratio of the fibers when keeping the bond density at a constant level. The strain energies stored in interfiber bonds are exponentially distributed over the whole network. The numerical analysis reveals that there is a linear relation between the ratio of fractured and initial number of loaded bonds, and the network's macroscopic material stiffness normalized with its pristine stiffness, confirming earlier findings based on experimental observations. At localization the analyzed theory looses its validity because the fracture process is no longer randomly distributed over the whole network. Localization coincides with location of peak load in force-displacement tensile tests.

  • 5.
    Isaksson, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Hägglund, R.
    Analysis of the strain field in the vicinity of a crack tip in an in-plane isotropic paper material2007In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 44, no 2, p. 659-671Article in journal (Refereed)
    Abstract [en]

    Strains, computed by the finite element method, are evaluated and compared to an experimentally determined strain field. The analyzed low-density paper has been designed to ensure bond-breakage as the dominating damage mechanism and the paper material is approximately in-plane isotropic. An optical non-contact displacement measuring system has been used in fracture tests to determine the strain field in the crack-tip region of a pre-fabricated crack. Additionally, acoustic emission monitored tensile tests have been conducted to determine onset and evolution of damage processes and thereby enabling calibration of required constitutive parameters. The results suggest that the investigated paper material can tolerate significantly higher strains than what is predicted by a classic elastic-plastic J2-flow theory. Immediately before onset of the final fracture (i.e., localization), the experimental measured normal strain in the near-tip region is around 60% higher than the computed strain when using exclusively an elastic-plastic theory for the corresponding load while the strain computed utilizing a non-local damage theory is of the same order of magnitude as the experimentally measured strain. Hence, it seems essential to include a non-local continuum theory to describe strains in the near-tip region quantitatively correct for paper materials. It is demonstrated that path independence of the well-known J-integral does not prevail for this class of material models. Only for the special situation of a homogenous damage field in the crack-tip region may the stress and strain fields be described by the well-known HRR-solutions.

  • 6.
    Isaksson, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Hägglund, R.
    Evolution of bond fractures in a randomly distributed fiber network2007In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 44, no 18-19, p. 6135-6147Article in journal (Refereed)
    Abstract [en]

    Fracture in a planar randomly ordered fiber network subjected to approximately homogenous macroscopic stress and strain field is considered. A theory describing material degradation on a macroscopic scale is derived via Griffith's energy balance for an internal fractured area in the network assuming the active fracture process on the microscopic level is fiber-fiber bond breakage. Attention is confined to a purely mechanical theory assuming isothermal processes and the theory relies on equations commonly used in theories of statistical physics. In the theory, a bond breaking driving force is stated to be equal to the elastic strain energy density of a non-fractured network. A debond fraction can be coupled to a linearly decrease of the network's macroscopic stiffness. The rate of the fracture processes is determined by the network's inherent properties (bond and fiber density, bond strength, etc.). During the loading process, until onset of localization, the bond breaks occur at randomly distributed locations spread over the fiber network and the theory estimate material degradation on a macroscopic level. When localization takes place, the fracture process changes from a two-dimensional randomly distributed process to a one-dimensional process and other theories have to be included to describe post-localization behavior. An approximately in-plane isotropic low-density paper is used in tensile experiments while monitoring acoustic emission activity to evaluate the theory. The experimentally obtained results support the theory surprisingly well.

  • 7.
    Isaksson, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Hägglund, R
    Gradin, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Continuum damage mechanics applied to paper2004In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 41, no 16-17, p. 4731-4755Article in journal (Refereed)
    Abstract [en]

    The mechanical behavior of two packaging paper materials subjected to tensile loading up to complete breakage has been investigated. A model for isotropic strain hardening elastic anisotropic plasticity, coupled to anisotropic damage, is discussed. The constitutive relations, including a gradient enhanced damage model, are developed within a thermodynamical framework. The Helmholtz free energy in the continuum is assumed to depend not only on the strain and stress components but also on the damage in the material.The model has been analyzed in a non-linear finite element procedure. The capability of the model to properly capture and simulate the failure of a paper material subjected to tensile loading is demonstrated by means of several numerical examples that are compared to, and verified with, experiments on packaging paper specimens of varying geometry.

  • 8.
    Isaksson, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Hägglund, Rickard
    SCA R&D Centre.
    Structural effects on deformation and fracture of random fiber networks and consequences on continuum models2009In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 46, no 11-12, p. 2320-2329Article in journal (Refereed)
    Abstract [en]

    The mechanical behavior of fibrous networks is governed by complex multiple mechanisms. This study examines the effect of microstructure on the macroscopic deformation and fracture of two-dimensional random fiber networks and its practical implications for understanding the material failure in paper materials by using finite element models. Remote load is a pure mode I opening field, applied via a boundary layer. Characteristic networks, consisting of the union of solutions of several unique networks, are interpolated on a rectangular grid covering the whole problem domain. The interpolated solutions are interpreted as network-equivalent continuums representing the mechanical behavior, on average, for a specific set of structural properties. A regularization routine is included in a variational procedure in order to minimize potential energy in the body and produce continuous strains at cell borders in the grid. It is shown that using a classical continuum linear elastic fracture mechanics (LEFM) approach to describe macroscopic singular-dominated fields in fiber networks, can lead to erroneous results especially in networks having a low degree of bonds per fiber. The classical continuum description is too simple to capture the essential mechanical behavior for this class of material since a structural effect, that alters the displacement field, becomes pronounced. It is necessary to include a nonlocal theory to describe the mechanical behavior at a continuum level. By using an appropriate characteristic length in a nonlocal continuum formulation, strain energies, in the neighborhood of a dominant macroscopic singularity, are calculated that agree well with characteristic network models and hence produce fairly good agreements between the networks and the nonlocal continuum models. A key conclusion found is that, only for networks with a high degree of bonding, can the mechanical behavior around a macroscopic singularity be captured by the classical local continuum theory. In networks with a low degree of bonds per fiber, there are regions far away from the macroscopic singularity that have relatively higher magnitudes of strain energy than predicted by the classical theory. A relation between an internal length scale parameter, used in the nonlocal continuum model, and the structural properties of the network is approximated by a simple function.

  • 9.
    Isaksson, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Ståhle, P
    Mode II crack paths under compression in brittle solids: A theory and experimental comparison2002In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 39, no 8, p. 2281-2297Article in journal (Refereed)
    Abstract [en]

    A study of crack propagation paths in the situation where the crack is suppressed to open during growth due to high compressive forces has been performed. This problem was analyzed theoretically very recently by the authors and is here extended to involve a limited number of illustrative experimental results reported elsewhere in the literature. By analyzing the experimental crack growth patterns, the conclusion is that the model cannot describe the more realistic microscopic failure in detail. Since shear crack growth on the microscale strongly depend on inhomogenities in the material, like cavities, grains or inclusions; the closed crack growth patterns observed are not smooth or free of kinks. Nevertheless, the model show good agreement with the reported experimental observations of the paths of closed macroscopic mode II cracks on samples in brittle materials, induced under overall compression. Failure patterns experimentally observed supports the theory that the growth of mode II cracks under compression in brittle materials follow a propagation path described by a function y ¼ kxb, where b ¼ 3=2. This is strongly supported by the measured values obtained from various experiments. In all the studied experiments, the exponent b was found in the interval [1.43–1.58]. Further, an investigation of the curvature parameter k has been performed and the conclusion is that k does also agree with the simplified model, even though not as good as the exponent b. However, k differs in general <15% from the theoretical value predicted by the model. The process of crack growth is in the simplified model assumed to be controlled by the mode II stress intensity factor KII of the main crack and the difference between the compressive remote normal stress parallel with the crack plane (r111) and the compressive remote normal stress perpendicular to the crack plane (r122).

  • 10.
    Isaksson, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Ståhle, Per
    Directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions2003In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 40, no 13-14, p. 3523-3536Article in journal (Refereed)
    Abstract [en]

    A directional crack growth criterion in a compressed elastic perfectly plastic material is considered. The conditions at the crack-tip are evaluated for a straight stationary crack with a small incipient kink. Remote load is a combined hydrostatic pressure and pure shear applied via a boundary layer. Crack surfaces in contact are assumed to develop homogenous Coulomb friction. The crack opening displacement of an extended kink is examined in a finite element analysis to judge the risk of opening mode failure. It has been found that the direction that maximizes the crack opening displacement of an extended kink tip coincides very well with a prediction of the crack growth direction obtained by using a criterion for continued crack growth direction discussed by the authors elsewhere [Int. J. Fract. 108 (2001) 351]. Moreover, the by the model predicted incipient crack growth directions are qualitatively comparable with reported crack paths obtained in ductile materials in a limited number of experiments performed under a combined load of inplane shear and compression.

  • 11.
    Persson, Johan
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Isaksson, Per
    Applied Mechanics, Ångström Laboratory, Uppsala University, Box 534, SE-75121 Uppsala, Sweden.
    A mechanical particle model for analyzing rapid deformations and fracture in 3D fiber materials with ability to handle length effects2014In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 11-12, p. 2244-2251Article in journal (Refereed)
    Abstract [en]

    A mechanical model for analyses of rapid deformation and fracture in three-dimensional fiber materials is derived. Large deformations and fractures are handled in a computationally efficient and robust way. The model is truly dynamic and computational time and memory demand scales linearly to the number of structural components, which make the model well suited for parallel computing. The specific advantages, compared to traditional continuous grid-based methods, are summarized as: (1) Nucleated cracks have no idealized continuous surfaces. (2) Specific macroscopic crack growth or path criteria are not needed. (3) The model explicitly considers failure processes at fiber scale and the influence on structural integrity is seamlessly considered. (4) No time consuming adaptive re-meshing is needed. The model is applied to simulate and analyze crack growth in random fiber networks with varying density of fibers. The results obtained in fracture zone analyses show that for sufficiently sparse networks, it is not possible to make predictions based on continuous material assumptions on a macroscopic scale. The limit lies near the connectivity l(c)/L = 0.1, where is the ratio between the average fiber segment length and the total fiber length. At ratios l(c)/L < 0.1 the network become denser and at the limit l(c)/L -> 0, a continuous continuum is approached on the macroscopic level. (C) 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.

  • 12. Semb, G.
    et al.
    Gradin, Per A.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Stresses and Strains in a Race Track Strap with a radical clearance2002In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 39, no 3, p. 699-708Article in journal (Refereed)
    Abstract [en]

    In certain situations it is desirable to transfer only tensile loads between two points in a structure whilst minimising any stress concentrations. In such circumstances a so-called race track starp can be utilised. The strap consists of two semi-circular elements that transfer the load, from bolts at each end, to two parallel flexible elements joining the whole together. The strap is loaded in tension by means of these bolts. This paper considers the situation where there is clearance between the bolts and the semi-circular elements of the strap. To develop an analytical model, it is assumed that engineering beam theory is applicable, that the influence of the membrane strains can be ignored and that the clearance is small as compared with the bolt and strap radii. It was found that the simple analytical model compared well with both finite element calculations and experiments.

  • 13.
    Åslund, Pär
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Hägglund, Rickard
    SCA R and D Centre, Box 716, SE-851 21 Sundsvall, Sweden.
    Carlsson, Leif
    Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA .
    Isaksson, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences. Applied Mechanics, The Ångström Laboratory, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden .
    An analysis of strain localization and formation of face wrinkles in edge-wise loaded corrugated sandwich panels using a continuum damage model2015In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 56-57, p. 248-257Article in journal (Refereed)
    Abstract [en]

    This paper examines the compressive failure mechanism in edge-to-edge loaded corrugated sandwich panels. The formation of face wrinkles is specifically considered. A detailed finite element model of face sheets and web core of a sandwich panel was developed to provide insight on the failure mechanism. A gradient enhanced continuum damage theory was implemented to capture length effects caused by the material microstructure including formation of damage in the face sheets and core. Distributions of strains in the face sheets determined from finite element analysis (FEA) are compared to experimentally measured strains. The predicted location and orientation of the face wrinkle, as indicated by high values of the second principal strain, agrees well with experimental observations.Load vs. out-of-plane deflection curves obtained from FEA with the gradient enhanced damage material model are compared to those obtained from a linear-elastic material model and experimentally determined curves. The gradient enhanced solution gives qualitatively better agreement with experimental results, although the magnitudes of strains are less than those determined experimentally.

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