| 1. |
- Bharali, Ritukesh, 1991, et al.
(författare)
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Computational aspects of the weak micro‐periodicity saddle point problem
- 2021
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Ingår i: Proceedings in Applied Mathematics and Mechanics. - : Wiley. - 1617-7061. ; 20:1
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Tidskriftsartikel (refereegranskat)abstract
- The finite element implementation of the weak micro-periodicity problem in computational homogenisation requires special preconditioning techniques owing to the saddle point formulation. The saddle point nature arises from enforcing periodicity constraints using Lagrange multipliers. This manuscript addresses the solution techniques and preconditioning options for the aforementioned problem in a monolithic setting. Furthermore, an alternative technique is proposed, based on a linear multi-point constraints strategy. The latter approach eliminates the Lagrange multiplier Degrees of Freedom (DOFs), thereby preventing the break-down of conventional incomplete LU (ILU) variants and multi-grid method based preconditioners.
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| 2. |
- Bharali, Ritukesh, 1991, et al.
(författare)
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Computational homogenisation of phase-field fracture
- 2021
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Ingår i: European Journal of Mechanics, A/Solids. - : Elsevier BV. - 0997-7538. ; 88
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Tidskriftsartikel (refereegranskat)abstract
- In this manuscript, the computational homogenisation of phase-field fractures is addressed. To this end, a variationally consistent two-scale phase-field fracture framework is developed, which formulates the coupled momentum balance and phase-field evolution equations at the macro-scale as well as at the Representative Volume Element (RVE) scale. The phase-field variable represent fractures at the RVE scale, however, at the macro-scale, it is treated as an auxiliary variable. The latter interpretation follows from the homogenisation of the phase-field through volume or a surface-average. For either homogenisation choices, the set of macro-scale and sub-scale equations, and the pertinent macro-homogeneity satisfying boundary conditions are established. As a special case, the concept of selective homogenisation is introduced, where the phase-field is chosen to live only in the RVE domain, thereby eliminating the macro-scale phase-field evolution equation. Numerical experiments demonstrate the local macro-scale material behaviour of the selective homogenisation based two-scale phase-field fracture model, while its non-selective counterpart yields a non-local macro-scale material behaviour.
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| 3. |
- Bharali, Ritukesh, 1991, et al.
(författare)
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Multi-scale phase-field fracture model: Selective homogenization and macroscopic bounds
- 2021
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this work, a multi-scale phase-field model for fracture is developed from the fully resolved phasefield model using the variationally consistent homogenization technique. The concept of selective homogenization is applied to the phase-field variable. Allowing the phase-field variable to live only on the sub-scale yields a conventional local damage model at the macro-scale, as the phase-field becomes an internal variable.
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| 4. |
- Carlstedt, David, 1984, et al.
(författare)
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Variationally consistent modeling of a sensor-actuator based on shape-morphing from electro-chemical–mechanical interactions
- 2023
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Ingår i: Journal of the Mechanics and Physics of Solids. - 0022-5096. ; 179
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns the computational modeling of a class of carbon fiber composites, known as shape-morphing and strain-sensing composites. The actuating and sensing performance of such (smart) materials is achieved by the interplay between electrochemistry and mechanics, in particular the ability of carbon fibers to (de)intercalate Li-ions repeatedly. We focus on the actuation and sensing properties of a beam in conjunction with the appropriate “through-the-thickness” properties. Thus, the electro-chemo-mechanical analysis is essentially two-dimensional, and it is possible to rely heavily on the results in Carlstedt et al. (2020). More specifically, the cross-sectional design is composed of two electrodes, consisting of (partly) lithiated carbon fibers embedded in structural battery electrolyte (SBE), on either side of a separator. As a result, the modeling is hierarchical in the sense that (macroscale) beam action is combined with electro-chemo-mechanical interaction along the beam. The setup is able to work as sensor or actuator depending on the choice of control (and response) variables. Although quite idealized, this design allows for a qualitative investigation. In this paper we demonstrate the capability of the developed framework to simulate both the actuator and sensor modes. As proof of concept, we show that both modes of functionality can be captured using the developed framework. For the actuator mode, the predicted deformation is found to be in close agreement with experimental data. Further, the sensor-mode is found to agree with experimental data available in the literature.
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| 5. |
- Ekre, Fredrik, 1992, et al.
(författare)
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A posteriori error estimation for numerical model reduction in computational homogenization of porous media
- 2020
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 121:23, s. 5350-5380
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction is adopted for solving the microscale problem that arizes from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using (i) spectral decomposition (SD) and (ii) proper orthogonal decomposition (POD). This strategy has been used in previous work—the main contribution of this article is the extension with an a posteriori estimator for assessing the error in (i) energy norm and in (ii) a given quantity of interest. The error estimator builds on previous work by the authors; the novelty presented in this article is the generalization of the estimator to a coupled problem, and, more importantly, to accommodate the estimator for a POD basis rather than the SD basis. Guaranteed, fully computable and low-cost bounds are derived and the performance of the error estimates is demonstrated via numerical results.
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| 6. |
- Ekre, Fredrik, 1992, et al.
(författare)
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Combining spectral and POD modes to improve error estimation of numerical model reduction for porous media
- 2022
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 69:3, s. 767-786
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction (NMR) is used to solve the microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. The reduction technique and an associated error estimator for the NMR error have been presented in prior work, where both spectral decomposition (SD) and proper orthogonal decomposition (POD) were used to construct the reduced basis. It was shown that the POD basis performs better w.r.t. minimizing the residual, but the SD basis has some advantageous properties for the estimator. Since it is the estimated error that will govern the error control, the most efficient procedure is the one that results in the lowest error bound. The main contribution of this paper is further development of the previous work with a proposed combined basis constructed using both SD and POD modes together with an adaptive mode selection strategy. The performance of the combined basis is compared to (i) the pure SD basis and (ii) the pure POD basis via numerical examples. The examples show that it is possible to find a combination of SD/POD modes which is improved, i.e. it yields a smaller estimate, compared to the cases of pure SD or pure POD.
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| 7. |
- Ekre, Fredrik, 1992, et al.
(författare)
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Efficient Two-Scale Modeling of Porous Media Using NumericalModel Reduction with Fully Computable Error Bounds
- 2022
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Ingår i: Current Trends and Open Problems in Computational Mechanics. - Cham : Springer International Publishing. ; , s. 121-129
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The microscale problem arizing from computational homogenization of porous media problems is solved by adopting the concept of Numerical Model Reduction. Thereby, the displacement and pore pressure are the unknown fields. A suitable reduced basis is constructed for the pore pressure approximation using Proper Orthogonal Decomposition (POD), whereby it is possible to compute the appropriate basis for the displacement field in the spirit of Nonlinear Transformation Field Analysis (NTFA). Inexpensive fully computable error bounds are obtainable, and the performance of the error estimates is illustrated in this paper.
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| 8. |
- Johlitz, Michael, et al.
(författare)
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Effective properties and size effects in filled polymers
- 2008
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Ingår i: GAMM-Mitteilungen. - : Wiley. - 1522-2608 .- 0936-7195. ; 31:2, s. 210-224
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Tidskriftsartikel (refereegranskat)abstract
- Filled polymers are of special interest according to their superior mechanical properties. Special attention is given to nano-filled polymers where not only the volume fraction but also the internal surface has a significant contribution to the effective properties. In the present contribution the increase in stiffness with decreasing size of the fillers at constant volume fraction of the fillers is modelled by a phenomenological, i.e. continuum-based, approach taking into account large deformations. The proposed multiphase model allows for a systematic investigation of increasing surface-to-volume ratio which becomes important for micro- and nanosized fillers. The numerical treatment of the proposed model is based on a coupled Galerkin finite element formulation.
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| 9. |
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| 10. |
- Jänicke, Ralf, 1980, et al.
(författare)
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A poro-viscoelastic substitute model of fine-scale poroelasticity obtained from homogenization and numerical model reduction
- 2020
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 65:4, s. 1063-1083
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for the displacement field is constructed in the spirit of the NTFA strategy. Evolution equations that define an apparent poro-viscoelastic macro-scale model are obtained from the continuity equation pertinent to the RVE. The present model represents an extension of models available in literature in the sense that the pressure gradient is allowed to have a non-zero macro-scale component in the nested FE2 setting. The numerical results show excellent agreement between the results from numerical model reduction and direct numerical simulation. It was also shown that even 3D RVEs give tractable solution times for full-fledged FE2 computations.
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