| 1. |
- Abiri, Olufunminiyi, et al.
(author)
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Comparison of Multiresolution Continuum Theory and Nonlocal Dame model for use in Simulation of Manufacutring Processes
- 2016
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 14:1, s. 81-94
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Journal article (peer-reviewed)abstract
- Modelling and simulation of manufacturing processes may require the capability to account for localization behavior, often associated with damage/fracture. It may be unwanted localization indicating a failure in the process or, as in the case of machining and cutting, a wanted phenomenon to be controlled. The latter requires a higher accuracy regarding the modelling of the underlying physics, as well as the robustness of the simulation procedure. Two different approaches for achieving mesh-independent solutions are compared in this paper. They are the multiresolution continuum theory (MRCT) and nonlocal damage model. The MRCT theory is a general multilength-scale finite element formulation, while the nonlocal damage model is a specialized method using a weighted averaging of softening internal variables over a spatial neighborhood of the material point. Both approaches result in a converged finite element solution of the localization problem upon mesh refinement. This study compares the accuracy and robustness of their numerical schemes in implicit finite element codes for the plane strain shear deformation test case. Final remarks concerning ease of implementation of the methods in commercial finite element packages are also given.
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| 2. |
- Carlsson, Kristoffer, 1989, et al.
(author)
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ON THE PRIMAL AND MIXED DUAL FORMATS IN VARIATIONALLY CONSISTENT COMPUTATIONAL HOMOGENIZATION WITH EMPHASIS ON FLUX BOUNDARY CONDITIONS
- 2020
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 18:6, s. 651-675
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Journal article (peer-reviewed)abstract
- In this paper, we view homogenization within the framework of variational multiscale methods. The standard (primal) variational format lends itself naturally to the choice of Dirichlet boundary conditions on the Representative Volume Element (RVE). However, how to impose flux boundary conditions, treated as Neumann conditions in the standard variational format, is less obvious. Therefore, in this paper we propose and investigate a novel mixed variational setting, where the fluxes are treated as additional primary fields, in order to provide the natural variational environment for such flux boundary conditions. This mixed dual formulation allows for a conforming implementation of (lower bound) flux boundary conditions in the framework of discretization-based homogenization. To focus on essential features, a very simple problem is studied: the classical stationary linear heat equation. Furthermore, we consider the standard context of model-based homogenization (without loss of generality), since we are only concerned with the RVE problem and merely assume that the relevant macroscale fields are properly prolonged. Numerical results from the primary and the mixed dual variational formats are compared and their convergence properties for mesh finite element (FE) refinement and RVE size are assessed.
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| 3. |
- Dobrovat, A. M., et al.
(author)
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Computational Modeling of Damage Based on Microcrack Kinking
- 2015
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 13:3, s. 201-217
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Journal article (peer-reviewed)abstract
- The paper presents numerical results for a two-scale damage model accounting for mixed-mode propagation of micro-cracks. A time-dependent propagation criterion is assumed for microcrack growth and a kinking direction criterion based on the maximum of the energy-release rate is used. The macroscopic damage evolution laws are obtained by homogenization based on asymptotic developments. A numerical procedure based on finite elements is developed for the two-scale model and simulations illustrating the structural response are presented. A priori microscopic computations increase the efficiency of the computational model at the scale of macroscopic structures. The resulting homogenized behavior involves softening and localization of damage. Direct links between macroscopic damage evolution and microscopic propagation of micro-cracks are established within the two-scale model.
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| 4. |
- Helsing, Johan, et al.
(author)
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A Seventh-Order Accurate and Stable Algorithm for the Computation of Stress Inside Cracked Rectangular Domains
- 2004
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 2:1, s. 47-68
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Journal article (peer-reviewed)abstract
- A seventh-order accurate and extremely stable algorithm for the rapid computation of stress fields inside cracked rectangular domains is presented. The algorithm is seventh-order accurate since it incorporates basis functions, taking the asymptotic shape of the stress fields close to crack tips and corners into account at least up to order six. The algorithm is stable since it is based on a Predholm integral equation of the second kind. The particular form of the integral equation represents the solution as the limit of a function which is analytic inside the domain. This allows for an efficient implementation. In an example, involving 112 discretization points on an elastic square with a center crack, values of normalized stress intensity factors and T-stress with a relative error of 10(-6) are computed in seconds on a workstation. More points reduce the relative error down to 10(-15), where it saturates in double precision arithmetic. A large-scale setup with up to 1024 cracks in an elastic square is also studied, using up to 740,000 discretization points. The algorithm is intended as a basic building block in general-purpose solvers for fracture mechanics. It can also be used as a substitute for benchmark tables.
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| 5. |
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| 6. |
- Jänicke, Ralf, 1980, et al.
(author)
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Micromorphic two-scale modelling of periodic grid structures
- 2013
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 11:2, s. 161-176
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Journal article (peer-reviewed)abstract
- The present contribution focuses on the numerical homogenization of periodic grid structures. In order to investigate the micro-to-macroscale transition, a consistent numerical homogenization scheme will be presented, replacing a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic substitute continuum on the macroscale. The extended degrees of freedom, namely, the microdeformation and its gradient, are to be interpreted in terms of geometrical deformation modes and the related loading conditions of the underlying unit cells. Assuming strain energy equivalence of the macro- and the microscale, the effective constitutive properties of a square and a honeycomb grid structure are identified and quantitatively validated in comparison to reference calculations with microscopic resolution.
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| 7. |
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| 8. |
- Lillbacka, R., et al.
(author)
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Error Controlled Use of the Taylor Assumption in Adaptive Hierarchial Modeling of DSS
- 2015
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 13:2, s. 163-180
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Journal article (peer-reviewed)abstract
- A strategy for macroscale modeling adaptivity in fully nested two-scale computational (first-order) homogenization based on assumed scale separation is proposed. The representative volume element (RVE) for a substructure pertinent to duplex stainless steel is considered with its typical phase morphology, whereby crystal plasticity with hardening is adopted for the subscale material modeling. The quality of the macroscale constitutive response depends on, among the various assumptions regarding the modeling and discretization, the choice of a prolongation condition defining the deformation mapping from the macro- to the subscale This is the sole source of model error discussed in the present contribution. Two common choices are (in hierarchical order) (1) a "simplified" model based on homogeneous (macroscale) deformation within the RVE, that is the Taylor assumption, and (2) a "reference" model employing Dirichlet boundary conditions on the RVE, which is taken as the exact model in the present context. These errors are assessed via computation of the pertinent dual problem. The results show that both the location and the number of qudrature points where the reference model is employed depend on the chosen goal function.
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| 9. |
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| 10. |
- Sandström, Carl, 1978, et al.
(author)
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VARIATIONALLY CONSISTENT HOMOGENIZATION OF STOKES FLOW IN POROUS MEDIA
- 2013
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In: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 11:2, s. 117-138
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Journal article (peer-reviewed)abstract
- Seepage through a strongly heterogeneous material, consisting of open saturated pores, is modeled as a Stokes flow contained in a rigid matrix. Through homogenization of the problem, a two-scale formulation is derived. The subscale problem is that of a Stokes flow whereas the macroscale problem pertains to a Darcy flow. The prolongation of the macroscale Darcy flow fulfills the variational consistent macrohomogeniety condition and is valid for both linear and nonlinear subscale flows. The subscale problem is solved using the finite element method. Numerical results concerning both linear and nonlinear flow are presented.
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