| 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. |
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| 3. |
- 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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| 4. |
- 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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