Micro-meso-macro modelling of composite materials

authored by: Peter Wriggers, M. Hain
Abstract: Multi-scale models can be helpful in the understanding of complex materials used in engineering practice. Applications related to this class of problems covers different length scales in the range from μm to m. Using the concept of representative volume elements (RVE), the theoretical background is discussed in this contribution as well as the numerical treatment of the resulting three-dimensional RVEs. The developed methodology is applied to a specific engineering material which is concrete. This construction material has to be investigated on three different scales: the hardened cement paste (hcp), the mortar and finally the concrete. Here, a successive two-stage approach is followed in which first the multi-scale model of hcp and mortar is applied. The resulting homogenization can then be used in the next step for a multi-scale mortar-concrete model. At the micro-scale of hcp, a finite element mesh based on a three-dimensional computer-tomography with different constitutive equations for the three parts unhydrated residual clinker, pores and hydrated products is introduced. With respect to the finite element solution, homogenization techniques are used in order to calculate effective elastic material properties. The constitutive equations at the micro-scale contain inelastic parameters, which cannot be obtained through experimental testings. Therefore, one has to solve an inverse problem which yields the identification of these properties. For computational efficiency and robustness, a combination of the stochastic genetic algorithm and the deterministic Levenberg-Marquardt method is used. In order to speedup the computation time significantly, all calculations are distributed automatically within a network environment. Inelastic behavior occurs when the micro-structure hcp is filled partly with water and a freezing process takes place. A constitutive model for ice is applied to the water filled parts of the micro-structure. The expansion of the ice leads to damage in the hcp which is associated with inelastic material behavior. If such a calculation is performed for different moisture and temperatures, a correlation between moisture, temperature and the inelastic material behavior can be obtained. The effective constitutive equation of hcp will serve as a basis for a multi-scale mortar-concrete model.
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Conference contribution
Pages: 105-122
No. of pages: 18
Publication date: 2007
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Modelling and Simulation, Biomedical Engineering, Computer Science Applications, Fluid Flow and Transfer Processes, Computational Mathematics, Electrical and Electronic Engineering
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{5a1f9d1b0156446b8b08ae52556725d9,
title = "Micro-meso-macro modelling of composite materials",
abstract = "Multi-scale models can be helpful in the understanding of complex materials used in engineering practice. Applications related to this class of problems covers different length scales in the range from μm to m. Using the concept of representative volume elements (RVE), the theoretical background is discussed in this contribution as well as the numerical treatment of the resulting three-dimensional RVEs. The developed methodology is applied to a specific engineering material which is concrete. This construction material has to be investigated on three different scales: the hardened cement paste (hcp), the mortar and finally the concrete. Here, a successive two-stage approach is followed in which first the multi-scale model of hcp and mortar is applied. The resulting homogenization can then be used in the next step for a multi-scale mortar-concrete model. At the micro-scale of hcp, a finite element mesh based on a three-dimensional computer-tomography with different constitutive equations for the three parts unhydrated residual clinker, pores and hydrated products is introduced. With respect to the finite element solution, homogenization techniques are used in order to calculate effective elastic material properties. The constitutive equations at the micro-scale contain inelastic parameters, which cannot be obtained through experimental testings. Therefore, one has to solve an inverse problem which yields the identification of these properties. For computational efficiency and robustness, a combination of the stochastic genetic algorithm and the deterministic Levenberg-Marquardt method is used. In order to speedup the computation time significantly, all calculations are distributed automatically within a network environment. Inelastic behavior occurs when the micro-structure hcp is filled partly with water and a freezing process takes place. A constitutive model for ice is applied to the water filled parts of the micro-structure. The expansion of the ice leads to damage in the hcp which is associated with inelastic material behavior. If such a calculation is performed for different moisture and temperatures, a correlation between moisture, temperature and the inelastic material behavior can be obtained. The effective constitutive equation of hcp will serve as a basis for a multi-scale mortar-concrete model.",
author = "Peter Wriggers and M. Hain",
year = "2007",
language = "English",
isbn = "9781402065767",
series = "Computational Methods in Applied Sciences",
publisher = "Springer Netherlands",
pages = "105--122",
editor = "Eugenio Onate and Roger Owen",
booktitle = "Computational Plasticity",
address = "Netherlands",
note = "8th International Conference on Computational Plasticity, 2005 ; Conference date: 05-09-2005 Through 08-09-2005",
}