| 1. |
- 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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| 2. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Minimal loading conditions for higher order numerical homogenisation schemes
- 2012
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Ingår i: Archive of Applied Mechanics. - : Springer Science and Business Media LLC. - 0939-1533 .- 1432-0681. ; 82:8, s. 1075-1088
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Tidskriftsartikel (refereegranskat)abstract
- The present study deals with the formulation of minimal loading conditions for microscale applications in numerical two-scale modelling (FE2) approaches. From the homogenisation concept, a set of volume average rules constrains the microscale PDE to be solved. They are considered to be the minimal set of loading conditions and can be specified by additional polynomial or periodic assumptions, for example, on the microscale displacement field. Whereas the resulting volume integrals can be transformed into surface integrals for so-called first-order homogenisation schemes, this is not possible for a second-order homogenisation of second gradient or micromorphic effective media substituting a heterogeneous microcontinuum represented by a volume element on the microscale. Several numerical examples compare the minimal loading condition concept with standard techniques discussed in literature.
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| 3. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Numerical homogenization of mesoscopic loss in poroelastic media
- 2015
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Ingår i: European Journal of Mechanics, A/Solids. - : Elsevier BV. - 0997-7538. ; 49, s. 382-395
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Tidskriftsartikel (refereegranskat)abstract
- This contribution deals with the numerical homogenization of mesoscopic flow phenomena in fluid-saturated poroelastic media. Under compression, mesoscopic heterogeneities induce pore pressure gradients and consequently pressure diffusion of the pore fluid. Since this process takes place on a scale much smaller than the observable level, the dissipation mechanism is considered as a local phenomenon. The heterogeneous poroelastic medium is substituted by an overall homogeneous Cauchy medium accounting for viscoelastic properties. Applying volume averaging techniques we derive a consistent upscaling procedure based on an appropriate extension of the Hill-Mandel lemma. We introduce various sets of boundary conditions for the poroelastic problem and discuss the relation between size of the SVEm (Statistical Volume Element) and maximum diffusion length. Numerical examples for two- and three-dimensional problems are given.
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| 4. |
- Quintal, Beatriz, et al.
(författare)
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S-wave attenuation in fluid-saturated rocks containing connected and unconnected fractures
- 2014
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Ingår i: Geophysics. - : Society of Exploration Geophysicists. - 1942-2156 .- 0016-8033. ; 79, s. WB15-WB24
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Tidskriftsartikel (refereegranskat)abstract
- Biot’s equations of poroelasticity were solved to study the effects of fracture connectivity on S-wave attenuation caused by wave-induced fluid flow at the mesoscopic scale. The methodology was based on numerical quasistatic pure-shear experiments performed on models of water-saturated rocks containing pairs of either connected or unconnected fractures of variable inclination. Each model corresponded to a representative elementary volume of a periodic medium. Inertial terms were neglected, and hence, the observed attenuation was entirely due to wave-induced fluid flow at the mesoscopic scale. We found that when fractures are not connected, fluid flow in the embedding matrix governs S-wave attenuation, whereas fluid flow through highly permeable fractures, from one fracture into the other one, may dominate when fractures are connected. Each of these energy-dissipation phenomena has a distinct characteristic frequency, with the S-wave attenuation peak associated with flow through connected fractures occurring at higher frequencies than that associated with flow in the embedding matrix. Exploring a range of geometric arrangements of either connected or unconnected fractures at different inclinations, we also observed that the magnitude of S-wave attenuation at both characteristic frequencies shows a strong dependence on fracture inclination. For comparison, we performed quasistatic uniaxial compressibility tests to compute P-wave attenuation in the same models. We found that the attenuation patterns of S-waves tend to differ fundamentally from those of P-waves with respect to fracture inclination. The attenuation characteristics of P- and S-waves in fractured media are thus, largely complementary. With respect to fracture connectivity, we observed that S-wave attenuation tends to follow a specific pattern, indeed, more consistently than that of the P-waves. Our results point to the promising perspective of combining estimates of attenuation of P- and S-waves to infer information on fracture connectivity as well as on the effective permeability of fractured media.
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| 5. |
- Rubino, J. German, et al.
(författare)
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Energy dissipation of seismic P- and S-waves in fluid-saturated rocks: An overview focusing on hydraulically connected fractures
- 2015
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Ingår i: Journal of Earth Science. - : Springer Science and Business Media LLC. - 1674-487X .- 1867-111X. ; 26, s. 785-790
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Tidskriftsartikel (refereegranskat)abstract
- An important characteristic of fractured rocks is their high seismic attenuation, which so far has been mainly attributed to wave-induced fluid flow (WIFF) between the fractures and the embedding matrix. The influence of fracture connectivity on seismic attenuation has, however, recently, only been investigated. Numerical compressibility and shear tests based on Biot’s quasi-static poro-elastic equations illustrate that an important manifestation of WIFF arises in the presence of fracture connectivity. The corresponding energy loss, which can be significant for both P- and S-waves, is mainly due to fluid flow within the connected fractures and is sensitive to the permeabilities as well as the lengths and intersection angles of the fractures. Correspondingly, this phenomenon contains valuable information on the governing hydraulic properties of fractured rocks and hence should be accounted for whenever realistic seismic models of such media are needed.
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| 6. |
- Saenger, Erik H., et al.
(författare)
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Digital material laboratory: Wave propagation effects in open-cell aluminium foams
- 2012
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Ingår i: International Journal of Engineering Science. - : Elsevier BV. - 0020-7225. ; 58, s. 115-123
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Tidskriftsartikel (refereegranskat)abstract
- This paper is concerned with numerical wave propagation effects in highly porous media using digitized images of aluminium foam. Starting point is a virtual material laboratory approach. The aluminium foam microstructure is imaged by 3D X-ray tomography. Effective velocities for the fluid-saturated media are derived by dynamic wave propagation simulations. We apply a displacement-stress rotated staggered finite-difference grid technique to solve the elastodynamic wave equation. The used setup is similar to laboratory ultrasound measurements and computed results are in agreement with our experimental data. Theoretical investigations allow to quantify the influence of the interaction of foam and fluid during wave propagation. Together with simulations using an artificial dense foam we are able to determine the tortuosity of aluminium foam.
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| 7. |
- Schüler, Thorsten, et al.
(författare)
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Multi-scale modelling of elastic/visoelastic compounds
- 2013
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Ingår i: ZAMM Zeitschrift für Angewandte Mathematik und Mechanik. - : Wiley. - 1521-4001 .- 0044-2267. ; 93:2, s. 126-137
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Tidskriftsartikel (refereegranskat)abstract
- The present contribution is concerned with the requirements of an efficient multi-scale modelling approach for elastic/viscoelastic compounds such as bituminous asphalt concrete. Typically, this heterogeneous composite material consist of a mineral filler (e.g. crushed rock), a bituminous binding agent, pores and further additives. The contrast in stiffness between the different is extremely high and accounts for several orders of magnitude. Prediction of effective mechanical properties of such complex materials on the macroscopic level requires a detailed knowledge of the micro-scale behaviour of the particular constituents. In this study, we will focus on modelling aspects due to upscaling routines based on volume averaging. Particularly, we will show that the choice of micro-level boundary conditions not only influences the effective stiffness of the viscoelastic substitute material (upper/lower limit), but also the viscous contribution to the macro-model (shift of maximal attenuation in frequency space). In order to study these fundamental homogenization properties, we introduce a simplified compound consisting of homogeneous viscoelastic binder phase and spherical filler particles with a volume fraction low compared to realistic asphalt concrete. Depending on the chosen boundary condition, stress-relaxation and creep tests are considered. After transformation of the effective stress-strain-relations from time- to frequency space, the viscoelastic properties of the compound will be discussed in frequency domain.
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| 8. |
- Schüler, Thorsten, et al.
(författare)
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Nonlinear modeling and computational homogenization of asphalt concrete on the basis of XRCT-scans
- 2016
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Ingår i: Construction and Building Materials. - : Elsevier BV. - 0950-0618. ; 109, s. 99-108
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a methodological framework to investigate the effective mechanical properties of asphalt concrete. We, therefore, use numerical tools based on morphological X-ray Computed Tomography (XRCT) data from asphalt concrete specimens. Asphalt concrete is a multi-component material with spatially varying constituents, but in contrast to many other microstructures used in materials science, the partial microscopic material bulk properties of the constituents of asphalt concrete are accessible by physical testing and, therefore, can be considered as well investigated and known. The information gained by the XRCT is used to create artificial Statistical Volume Elements (SVEs) for our numerical investigations. We apply a discrete particle simulation to generate a densely packed sphere model with a pre-defined particle size distribution (PSD) as a first representation of the mineral filler particles. This model serves as the starting point for a weighted Voronoi diagram. Finally, the volume fractions are adjusted by a stochastic shrinkage process of the Voronoi cells. The artificial microstructures are, a priori, generated in a periodic manner and, therefore, possible boundary layer effects during computational homogenization are minimized. The SVEs are considered to be statistically similar to the real structure and serve as its best possible representation. Besides the SVE generation, this paper focuses on the constitutive description of the bituminous binding agent, which we interpret as a viscoelastic fluid. In our analysis of the results we concentrate on the upscaling properties of morphological and material nonlinearities.
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| 9. |
- Sehlhorst, H.-Georg, et al.
(författare)
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Nume- rical investigations of foam-like materials by nested high-order finite element methods
- 2009
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 45:1, s. 45-59
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a multiscale framework suited for geometrically nonlinear computations of foam-like materials applying high-order finite elements (p-FEM). This framework is based on a nested finite element analysis (FEA) on two scales, one nonlinear boundary value problem on the macroscale and k independent nonlinear boundary value problems on the microscale allowing for distributed computing. The two scales are coupled by a numerical projection and homogenization procedure. On the microscale the foam-like structures are discretized by high-order continuum-based finite elements, which are known to be very efficient and robust with respect to locking effects. In our numerical examples we will discuss in detail three characteristic test cases (simple shear, tension and bending). Special emphasis is placed on the material’s deformation-induced anisotropy and the macroscopic load-displacement behavior.
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