| 1. |
- Ricker, S, et al.
(författare)
-
Variational issues in the homogenization of discrete systems
- 2007
-
Ingår i: Multi-scale Computational Methods for Solids and Fluids. ; , s. 186-191
-
Konferensbidrag (refereegranskat)abstract
- The main objective of this work is the application of variational concepts to microscopic multiple particle systems (MPS) which are assigned to corresponding points of a macroscopic continuum. Due to this underlying micro-structure it is not sufficient to simulate the macroscopic behavior with pre-assumed (overall) material parameters, or rather constitutive-law-based standard methods. Therefore, the challenge is to determine macroscopic material behaviors, by means of e.g. stresses and numerical tangent-stiffnesses, based on the analysis of the underlying multiple particle system. With the assistance of the applied variational principle and the so-called continuization, which corresponds to the limit of an infinite number of particles in the system, the analogy of homogenization of discrete and continuous micro-systems is elaborated. Within this work we focus on the so-called computational homogenization scheme, which provides the stage for a coupling between a macroscopic system simulated by the Finite Element Method and different microscopic simulation techniques.
|
|
| 2. |
|
|
| 3. |
- Utzinger, J, et al.
(författare)
-
Aspects of bifurcation in an isotropic elastic continuum with orthotropic inelastic interface
- 2008
-
Ingår i: European Journal of Mechanics. A, Solids. - : Elsevier BV. - 1873-7285 .- 0997-7538. ; 27:4, s. 532-547
-
Tidskriftsartikel (refereegranskat)abstract
- This manuscript investigates possible bifurcations into stationary wave-type solutions in situations where an isotropic elastic bulk is bonded by a non-coherent orthotropic interface to a rigid substrate. The interface is characterised by a tractionseparation-law capturing elastic and inelastic material behaviour. Based on an ansatz for stationary waves at the surface of the bulk being connected to the interface, a bifurcation condition is elaborated. Thereby, the orthotropy of the interface is taken into account by considering the fully three-dimensional elastic half space and allowing for arbitrary orientations of the stationary wave-type solutions with respect to the interface co-ordinate system. The bifurcation condition is studied under the assumption of prevailing ellipticity in the bulk for a number of different examples. The results are graphically explored.
|
|
| 4. |
|
|
| 5. |
- Utzinger, J, et al.
(författare)
-
Investigation of microcracks in ferroelectric materials by application of a grain--boundary--motivated cohesive law
- 2008
-
Ingår i: PAMM. - : Wiley. - 1617-7061. ; 7:1, s. 4070017-4070018
-
Konferensbidrag (refereegranskat)abstract
- Ferroelectric materials exhibit a huge potential for engineering applications - ranging from electrical actuators (inverse piezoelectric effect) to sensor technology (direct piezoelectric effect). To give an example, lead zirconate titanate (PZT) is a typical perovskite ion crystal possessing ferroelectric properties. In this contribution, we are particularly interested in the modelling of microcracking effects in ferroelectric materials. In view of Finite-Element-based simulations, the geometry of a natural grain structure, as observed on the so-called micro-level, is represented by an appropriate mesh. While the response on the grains themselves is approximated by coupled continuum elements, grain boundaries are numerically incorporated via so-called cohesive-type elements. For the sake of simplicity, switching effects in the bulk material will be neglected. The behaviour of the grain boundaries is modelled by means of cohesive-type laws. Identifying grain boundaries as potential failure zones leading to microcracking, cohesive-type elements consequently offer a great potential for numerical simulations. As an advantage, in the case of failure they do not a priori result in ill-conditioned systems of equations as compared with the application of standard continuum elements to localised deformations. Finally, representative constitutive relations for both the bulk material and the grain boundaries, enable two-dimensional studies of low-cycle-fatigue motivated benchmark boundary value problems.
|
|
| 6. |
|
|
| 7. |
- Utzinger, J, et al.
(författare)
-
On the simulation of cohesive fatigue effects in grain boundaries of a piezoelectric mesostructure
- 2008
-
Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 45:17, s. 4687-4708
-
Tidskriftsartikel (refereegranskat)abstract
- Ferroelectric materials offer a variety of new applications in the field of smart structures and intelligent systems. Accordingly, the modelling of these materials constitutes an active field of research. A critical limitation of the performance of such materials is given when electrical, mechanical, or mixed loading fatigue occurs, combined with, for instance, microcracking phenomena. In this contribution, fatigue effects in ferroelectric materials are numerically investigated by utilisation of a cohesive-type approach. In view of finite element-based simulations, the geometry of a natural grain structure, as observed on the so-called meso-level, is represented by an appropriate mesh. While the response of the grains themselves is approximated by coupled continuum elements, grain boundaries are numerically incorporated via so-called cohesive-type or interface elements. These offer a great potential for numerical simulations: as an advantage, they do not result in bad-conditioned systems of equations as compared with the application of standard continuum elements inhering a very high ratio of length and height. The grain boundary behaviour is modelled by cohesive-type constitutive laws, designed to capture fatigue phenomena. Being a first attempt, switching effects are planned to be added to the grain model in the future. Two differently motivated fatigue evolution techniques are applied, the first being appropriate for low-cycle-fatigue, and a second one adequate to simulate high-cycle-fatigue. Subsequent to a demonstration of the theoretical and numerical framework, studies of benchmark boundary value problems with fatigue-motivated boundary conditions are presented.
|
|
