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  • 1.
    Aidanpää, Jan-Olov
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Shen, H.H.
    Gupta, R.B.
    Babic, M.
    One-dimensional model for the transition from periodic to chaotic motions in granular shear flows1993In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 16, no 1-2, p. 153-161Article in journal (Refereed)
    Abstract [en]

    A simple one-dimensional mechanical model to simulate some aspects of the dynamics of granular flow is suggested. The model consists of a visco-elastic packet bouncing between two oscillating walls. The motion of the walls is prescribed to be harmonic. The amplitude and frequency of the wall motion are related to the concentration and shear rate, respectively. The dynamics of the system is studied for various parameter combinations and it is shown that periodic as well as chaotic motions are possible for different parameters and initial conditions. Results are presented in the form of time histories, power spectral densities, phase diagrams, Poincare plots and bifurcation diagrams. This simple one-dimensional model presents many features that are analogous to those observed in the two-dimensional simple shear flow of disks.

  • 2.
    Akshantala, Nagendra V.
    et al.
    School of Aerospace Engineering, Georgia Institute of Technology, Atlanta.
    Talreja, Ramesh
    A mechanistic model for fatigue damage evolution in composite laminates1998In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 29, no 2, p. 123-140Article in journal (Refereed)
    Abstract [en]

    We propose a mechanistic model which is capable of describing the evolution of transverse cracking in cross ply laminates subjected to cyclic tension in the longitudinal direction. The key feature of the model is that it incorporates delamination associated with transverse cracks in a manner that induces further formation of transverse cracks as delamination grows in fatigue. A variational approach is taken to estimate the stresses in the region between transverse cracks, and these are found to be accurate away from the crack planes when comparison is made with finite element computations. The evolution of transverse crack density and the associated overall elastic moduli changes predicted by the model are in agreement with experimental results

  • 3.
    Kumar, Rajesh Sai Santosh
    et al.
    School of Aerospace Engineering, Georgia Institute of Technology, Atlanta.
    Talreja, Ramesh
    A continuum damage model for linear viscoelastic composite materials2003In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 35, no 3-6, p. 463-480Article in journal (Refereed)
    Abstract [en]

    This paper presents a constitutive model for linear viscoelastic orthotropic solids containing a fixed level of distributed cracks. The model is formulated in a continuum damage mechanics framework using internal variables taken as second rank tensors. Use is made of the correspondence principle for linear viscoelastic solids to define a pseudo strain energy function in the Laplace domain. This function is then expressed as a polynomial in transformed strain and tensorial damage variables using the integrity bases restricted by the initial orthotropic symmetry of the material. The constitutive relationships derived in the Laplace domain are then converted to the time domain by using the inverse Laplace transform. The model is applied to the specific case of cross-ply laminates with transverse matrix cracks. The material coefficient functions appearing in the model are determined by a numerical (finite element) method for one cross-ply laminate configuration at one damage level. Predictions of the viscoelastic response are then made for the same laminate at other damage levels and for other cross-ply laminate configurations at different damage levels. These predictions agree well with independently determined time variations of properties by an analytic method (Kumar and Talreja, 2001, Linear viscoelastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials 33 (3), 139-154) as well as with the numerically calculated values. Extension of the model to incorporate effects of transient temperature, physical aging and moisture is outlined

  • 4.
    Kumar, Rajesh Sai Santosh
    et al.
    School of Aerospace Engineering, Georgia Institute of Technology, Atlanta.
    Talreja, Ramesh
    Linear viscoelastic behavior of matrix cracked cross-ply laminates2001In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 33, no 3, p. 139-154Article in journal (Refereed)
    Abstract [en]

    The linear viscoelastic behavior of matrix cracked symmetric cross-ply laminates is studied. A lower bound solution and an approximate 3D solution to the properties are obtained by using the elastic-viscoelastic correspondence principle. The accuracy of Schapery's approximate Laplace inversion technique in the solution procedure is discussed

  • 5.
    Lacy, Thomas E.
    et al.
    Department of Aerospace Engineering, Wichita State University.
    McDowell, David l.
    G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA.
    Talreja, Ramesh
    Gradient concepts for evolution of damage1999In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 31, no 12, p. 831-860Article in journal (Refereed)
    Abstract [en]

    While low-order measures of damage have sufficed to describe the stiffness of bodies with distributed voids or cracks, such as the void volume fraction or the crack density tensor of Vakulenko, A.A., Kachanov, M., 1971., addressing the growth of distributed defects demands a more comprehensive description of the details of defect configuration and size distribution. Moreover, interaction of defects over multiple length scales necessitates a methodology to sort out the change of internal structure associated with these scales. To extend the internal state variable approach to evolution, we introduce the notion of multiple scales at which first and second nearest-neighbor effects of nonlocal character are significant, similar to homogenization theory. Further, we introduce the concept of a cutoff radius for nonlocal action associated with a representative volume element (RVE), which exhibits statistical homogeneity of the evolution, and flux of damage gradients averaged over multiple subvolumes. In this way, we enable a local description at length scales below the RVE. The mean mesoscale gradient is introduced to reflect systematic differences in size distribution and position of damage entities in the evolution process. When such a RVE cannot be defined, the evolution is inherently statistically inhomogeneous at all scales of reasonable dimension, and the concept of macroscale gradients of internal variables is the only recourse besides micromechanics. Based on a series of finite element calculations involving evolution of 2D cracks in brittle elastica arranged in random periodic arrays, we examine the evolution of the mean mesoscale gradients and note some preliminary implications for the utility of such an approach.

  • 6.
    Li, Chunlin
    et al.
    Luleå University of Technology.
    Nordlund, Erling
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Deformation of brittle rocks under compression - with particular reference to microcracks1993In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 15, no 3, p. 223-239Article in journal (Refereed)
    Abstract [en]

    A constitutive model for brittle rocks has been developed based on the analysis of microcracks. The macroscopic deformation of a rock is decomposed into three components: response of the rock matrix, closure of open cracks and deformation due to the fracture of microcracks. The main contribution of this approach is the prediction of macroscopic deformation induced by microcracking. The basic model units are sliding cracks. Wing cracks are initiated at tips of sliding cracks and propagated in the major loading direction. The relationships between the compressive stress, the length of the growing crack and deformation due to the fracture of cracks are established. A deformation solution to an elliptic crack is employed to describe the closure effect of an open crack under compression. The total deformation caused by the closure and fracture of cracks is obtained by the sum of the components of individual cracks. In this model, the nonlinear behavior of deformation results either from the closure of open cracks at low stress levels, or from the fracture of microcracks at high stress levels. Hysteresis is captured under cyclic loading. Comparisons of the model simulations with experimental data are presented and show good agreement in the prefailure stage.

  • 7.
    Lindgren, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Domkin, K.
    Dalarna University.
    Hansson, Sofia
    Dislocations, vacancies and solute diffusion in physical based plasticity model for AISI 316L2008In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 40, no 11, p. 907-919Article in journal (Refereed)
    Abstract [en]

    A physical based model for the evolution of flow stress of AISI 316L from room temperature up to 1300 °C, strains up to 0.6 and strain rates from 0.0005 up to 10 s-1 is developed. One set of tests have been used for model calibration and another more complex set of tests for its validation. The model is based on a coupled set of evolution equations for dislocation density and (mono) vacancy concentration. Furthermore, it includes the effect of diffusing solutes in order to describe dynamic strain ageing (DSA). The model described the overall flow stress evolution well with exception of the details of the effect of the DSA phenomenon. Its numerical solution is implemented in a format suitable for large-scale finite element simulations.

  • 8.
    Lindgren, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Qin, Hao
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Wedberg, Dan
    AB Sandvik Coromant, Metal Cutting Modeling, 811 81 Sandviken.
    Improved and simplified dislocation density based plasticity model for AISI 316 L2017In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 108, p. 68-76Article in journal (Refereed)
    Abstract [en]

    A previously published dislocation density based flow stress model has been refined and made more consistent with underlying physical assumptions. The previous model included many temperature dependent parameters that are taken as constant in the current work. The model has also been simplified with respect to dynamic strain aging. Additional contributions to flow stress from the Hall-Petch effect and solute hardening have now been explicitly included in the model. Furthermore, the dynamic recovery part of the model has been improved.

  • 9.
    Liu, Hongyuan
    et al.
    Luleå University of Technology.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Numerical studies on the inter-particle breakage of a confined particle assembly in rock crushing2005In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 37, no 9, p. 935-954Article in journal (Refereed)
    Abstract [en]

    Understanding rock crushing mechanisms may provide an efficient key to better fragmentation efficiency. In this paper, firstly the fracture processes of a rock specimen under uniaxial and triaxial compressions are simulated using the rock and tool interaction (R–T2D) code and compared with the results from experimental observations in literatures. It is found that, with increasing confinement, the fracture process is more progressive and the failure mechanism gradually changes from axial splitting to shear fracture. Then the inter-particle breakage process in a particle bed under confined conditions is numerically investigated from a mechanics point of view. The results show that when the particle breaks depends on the strength criterion, how it is broken depends on the stress distribution and redistribution, and where it is broken depends on the heterogeneous distribution in the particle. It is found that, irrespective of the particle shape or particle bed arrangement, the fragmentation starts from the particles which are loaded in quasi-uniaxial compression. The resulting fragmentation is usually axial splitting between the two highest stressed loading points. After that, the particles which are loaded at first in quasi-triaxial compression, because of the confinement from the neighbouring particles, the loading plate or the container wall, fail progressively. Depending on the location of the loading points, small fragments are torn off at the loading points with a large piece preserved. In the final stage, the local crushing at the highest stressed contact points becomes an important failure mechanism. Through this study, it is concluded that the R–T2D code can capture the features of the inter-particle breakage process, and a better qualitative understanding of the physics and mechanics of deformation and breakage is gained.

  • 10.
    Singh, Chandra Veer
    et al.
    Department of Aerospace Engineering, Texas A&M University.
    Talreja, Ramesh
    A synergistic damage mechanics approach for composite laminates with matrix cracks in multiple orientations2009In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 41, no 8, p. 954-968Article in journal (Refereed)
    Abstract [en]

    This paper treats the problem of elastic response of composite laminates containing matrix cracks in plies of multiple orientations. The approach taken has been described as synergistic damage mechanics (SDM) and has been previously illustrated for [0 m / ± θ n / 0 m / 2] s laminates with cracks of equal density in + θ and - θ plies [Singh, C.V., Talreja, R., 2008. Int. J. Solids Struct. 45(16), 4574-4589]. The current work extends the approach to [0 m / ± θ n / 90 r] s and [0 m / 90 r / ± θ n] s laminates with cracks additionally in the 90°-plies. The interaction between the ± θ-cracks and the 90°-cracks is analyzed in terms of the crack surface displacements using a three-dimensional finite element (FE) model and found to be significant only for crack orientations close to 90°. The stiffness degradation of the laminate with all cracking modes simultaneously present is formulated by continuum damage mechanics using a second order tensor characterization of damage. The elastic moduli changes predicted by the SDM procedure are validated by independent three-dimensional FE calculations. For a particular case of quasi-isotropic [0 / 90 / ∓ 45] s laminate, the elastic moduli predictions are evaluated against experimental data. Finally, a parametric study is performed to examine the effects of ply thickness changes on stiffness properties.

  • 11.
    Sørensen, Bent F.
    et al.
    Materials Department, Risø National Laboratory.
    Talreja, Ramesh
    Effects of nonuniformity of fiber distribution on thermally-induced residual stresses and cracking in ceramic matrix composites1993In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 16, no 4, p. 351-363Article in journal (Refereed)
    Abstract [en]

    A three-dimensional finite element analysis is conducted to estimate stresses induced by thermal cooldown in unidirectionally fiber-reinforced ceramic matrix composites. Various configurations of nonuniform fiber distributions are considered. Both cases of thermal expansion mismatch between isotropic, linearly thermoelastic fibers and matrix are studied. Significant effects of nonuniformity of fiber distributions on the local stress states are found. The initiation of various possible cracking modes is discussed in the light of these results

  • 12. Talreja, Ramesh
    Continuum modelling of damage in ceramic matrix composites1991In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 12, no 2, p. 165-180Article in journal (Refereed)
    Abstract [en]

    A continuum model for determining mechanical response of ceramic matrix composites with damage is presented. The mechanisms of damage considered are those observed in unidirectionally fiber-reinforced ceramic matrix composites, viz. matrix cracking, fiber/matrix interfacial slip and fiber/matrix debonding. Four basic configurations of distributed damage at the microscopic level are treated: matrix cracks only, matrix cracks in conjunction with interfacial slip, debonds only and matrix cracks in conjunction with debonds. The elementary damage entities, i.e. cracks, debonds and slipped surfaces, are represented by second-order tensors which are regarded as internal variables. Using a thermodynamics based formulation of constitutive relationships with internal variables, the stress-strain-damage relationships are derived. Specific expressions are given for changes in the engineering elastic moduli in terms of the densities of damage entities for sparsely distributed damage

  • 13.
    Wedberg, Dan
    et al.
    AB Sandvik Coromant, Metal Cutting Research.
    Lindgren, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Modelling flow stress of AISI 316L at high strain rates2015In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 91, no 1, p. 194-207Article in journal (Refereed)
    Abstract [en]

    Modelling of the material behaviour is crucial for machining simulations. Strain and strain rates can reach values of 1–10 and 103–106 s−1 during the severe deformations associated with machining. An existing dislocation density model for AISI 316L based on a coupled set of evolution equations for dislocation density, mono vacancy concentration is enhanced in order to accommodate plastic deformation at high strain rates. Two mechanisms are evaluated with respect to their contribution in this respect. One is rate dependent cell formation and the other is dislocation drag due to phonons and electrons. Furthermore a temperature and strain rate dependent recovery and a proportionality interaction factor and short range component that both depends on the dislocation density are also considered. High strain rate compression tests are performed using Split-Hopkinson technique at various initial temperatures. Experimental results are then used to calibrate the models via an optimization procedure. Evaluation of various flow stress models shows that the flow stress behaviour of 316L stainless steel is best modelled by the model with a rate dependent cell formation. Its numerical solution is implemented in a format suitable for large-scale finite element simulations

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