| 1. |
- Conroy, Melanie, et al.
(författare)
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Uncertainty in humanities network visualization
- 2024
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Ingår i: Frontiers in Communication. - : Frontiers Media S.A.. - 2297-900X. ; 8
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Tidskriftsartikel (refereegranskat)abstract
- Network visualization is one of the most widely used tools in digital humanities research. The idea of uncertain or “fuzzy” data is also a core notion in digital humanities research. Yet network visualizations in digital humanities do not always prominently represent uncertainty. In this article, we present a mathematical and logical model of uncertainty as a range of values which can be used in network visualizations. We review some of the principles for visualizing uncertainty of different kinds, visual variables that can be used for representing uncertainty, and how these variables have been used to represent different data types in visualizations drawn from a range of non-humanities fields like climate science and bioinformatics. We then provide examples of two diagrams: one in which the variables displaying degrees of uncertainty are integrated into the graph and one in which glyphs are added to represent data certainty and uncertainty. Finally, we discuss how probabilistic data and what-if scenarios could be used to expand the representation of uncertainty in humanities network visualizations.
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| 2. |
- 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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| 3. |
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| 4. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Micromorphic two-scale modelling of periodic grid structures
- 2013
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Ingår i: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 11:2, s. 161-176
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Tidskriftsartikel (refereegranskat)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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| 5. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Numerical homogenisation of micromorphic media
- 2010
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Ingår i: Technische Mechanik. - 0232-3869. ; 30:4, s. 364-373
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Tidskriftsartikel (refereegranskat)abstract
- Due to their underlying microtopology, cellular materialsare known to show a complex mechanical behaviour. For the material modelling, the heterogeneous microcontinuum is commonly replaced by a homogeneous macrocontinuum involving extended kinematics. An appropriate homogenisation methodology will be introduced in order to replace a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic macrocontinuum. For an artificial 2-D periodic microstructure, the present contribution draws a comparison between extended two-scale calculations on the one hand, and a reference solution as well as a first-order FE2 calculation on the other hand.
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| 6. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Two-scale modelling of micromorphic continua
- 2009
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer Science and Business Media LLC. - 0935-1175 .- 1432-0959. ; 21:4, s. 297-315
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Tidskriftsartikel (refereegranskat)abstract
- According to their peculiar mechanical properties, the description of cellular materials is of high interest. Modelling aspects to be considered are, e.g. pronounced size depending boundary layer effects as well as a deformation-driven evolution of anisotropy or porosity. In the present contribution, we pay special attention to the description of size-dependent microtopological effects on the one hand. On the other hand, we focus on the relevance of extended continuum theories describing the local deformation state of microstructured materials. We, therefore, introduce a homogenization scheme for two-scale problems replacing a heterogeneous Cauchy continuum on the microscale by a homogeneous effective micromorphic continuum on the macroscale. The transitions between both scales are obtained by appropriate projection and homogenization rules which have to be derived, on the one hand, by kinematic assumptions, i.e. the minimization of the macroscopic displacement field, and, on the other hand, by energetic considerations, i.e. the evaluation of an extended Hill–Mandel condition.
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| 7. |
- 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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| 8. |
- Trinh, Duy Khanh, et al.
(författare)
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Evaluation of generalized continuum substitution models for heterogeneous materials
- 2012
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Ingår i: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 10:6, s. 527-549
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Tidskriftsartikel (refereegranskat)abstract
- Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.
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