| 1. |
- Aggestam, Emil, 1992, et al.
(författare)
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Numerical model reduction with error control in computational homogenization of transient heat flow
- 2017
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 326, s. 193-222
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Tidskriftsartikel (refereegranskat)abstract
- Numerical Model Reduction (NMR) is exploited for solving the finite element problem on a Representative Volume Element (RVE) that arises from the computational homogenization of a model problem of transient heat flow. Since the problem is linear, an orthogonal basis is obtained via the classical method of spectral decomposition. A symmetrized version of the space–time variational format is adopted for estimating the error from the model reduction in (i) energy norm and in (ii) given Quantities of Interest. This technique, which was recently developed in the context of the (non-selfadjoint) stationary diffusion–convection problem, is novel in the present context of NMR. By considering the discrete, unreduced, model as exact, we are able to obtain guaranteed bounds on the error while using only the reduced basis and with minor computational effort. The performance of the error estimates is demonstrated via numerical results, where the subscale is modeled in both one and three spatial dimensions.
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| 6. |
- Bargmann, Swantje, 1980, et al.
(författare)
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Modeling of polycrystals with gradient crystal plasticity: A comparison of strategies
- 2010
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Ingår i: Philosophical Magazine. - : Informa UK Limited. - 1478-6435 .- 1478-6443. ; 90:10, s. 1263-1288
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Tidskriftsartikel (refereegranskat)abstract
- This paper treats the computational modeling of size dependence in microstructure models of metals. Different gradient crystal plasticity strategies are analyzed and compared. For the numerical implementation, a dual-mixed finite element formulation which is suitable for parallelization is suggested. The paper ends with a representative numerical example for polycrystals.
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| 9. |
- Brouzoulis, Jim, 1984, et al.
(författare)
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Strategies for planar crack propagation based on the concept of material forces
- 2011
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 47:3, s. 295-304
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a computational framework for the simulation of planar crack growth (including kinking) driven by "material forces". An evolution law for the crack tip position is formulated, which is shown to give rise to different propagation strategies when subjected to certain assumptions on regularity. Three such strategies, that previously have been proposed in the literature in principle: Explicit Proportional Extension (EPE), Implicit Proportional Extension (IPE) and Maximum Parallel Release Rate (MPRR), are outlined and assessed. Based on the results of two numerical examples, it is concluded that the presented propagation strategies produce almost identical results and are robust with respect to time discretization.
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| 10. |
- Börjesson, Elias, 1992, et al.
(författare)
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Variationally consistent homogenisation of plates
- 2023
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825. ; 413
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Tidskriftsartikel (refereegranskat)abstract
- Advanced fibre composite materials are often used for weight-efficient thin-walled designs, making a plate-based modelling approach suitable for their structural assessment. However, as the sub-structural geometrical features of these materials govern much of their behaviour, a multi-scale approach is necessary. A related challenge, however, is that the in-plane variation of these sub-structural features may be much larger than the total thickness of the material, whereby tailored homogenisation techniques for shell elements are needed. Existing frameworks for plate- and shell-based homogenisation are typically developed using second-order homogenisation in combination with the Hill–Mandel (macro-homogeneity) condition. However, it has been reported in the literature that this approach can lead to kinematic inconsistencies in the macro- to micro-scale transition. One inconsistency that is commonly reported, is the inability to correctly account for the macro-scale transverse shear behaviour on the sub-scale level. In this contribution, we show how the method of Variationally Consistent Homogenisation (VCH) can be used to develop a homogenisation framework for Reissner-Mindlin plate elements, which guarantees kinematically consistent prolongation and homogenisation operations. The homogenisation approach is demonstrated in four numerical examples, where it is shown that the method accurately homogenise the effective sectional plate stiffnesses of homogeneous and heterogeneous sub-structures.
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