Filtern
Dokumenttyp
- Beitrag zu einem Tagungsband (2)
- Zeitschriftenartikel (1)
- Vortrag (1)
- Posterpräsentation (1)
Sprache
- Englisch (5) (entfernen)
Schlagworte
- Multiscale (5) (entfernen)
Eingeladener Vortrag
- nein (1)
In this paper, a new methodology based on the Hill–Mandel lemma in an FE² sense is proposed that is able to deal with localized deformations. This is achieved by decomposing the displacement field of the fine scale model into a homogeneous part, fluctuations, and a
cracking part based on additional degrees of freedom (X¹)—the crack opening in normal and tangential directions. Based on this decomposition, the Hill–Mandel lemma is extended to relate coarse and fine scale energies using the assumption of separation of scales such
that the fine scale model is not required to have the same size as the corresponding
macroscopic integration point. In addition, a procedure is introduced to mimic periodic
boundary conditions in the linear elastic range by adding additional shape functions for the boundary nodes that represent the difference between periodic boundary conditions and pure displacement boundary conditions due to the same macroscopic strain. In order to decrease the computational effort, an adaptive strategy is proposed allowing different
macroscopic integration points to be resolved in different levels on the fine scale.
Concrete is one of the most attractive building materials consumed by humans more than any other material, except water. The particular importance of concrete for a sustainable, energy-efficient economy is highlighted by the fact that about 5% of worldwide CO2 emissions are created from the cement industry.
Concrete is a very complex material. Its properties are time dependent, which includes the solidification after casting or creep and shrinkage. In addition, concrete is a quasi-brittle material which requires to model the softening behavior including the challenge of appropriate regularization strategies. Many characteristic features are strongly related to its complex heterogeneous structure, including particles and mortar on the mesoscale or the CSH-phases on the micro scale.
At first, a short introduction to the generation of mesoscale geometries as a three phase composite including particles, mortar matrix and the interfacial transition zone is given. Afterwards, the numerical model including meshing (XFEM and aligned meshes) as well as regularized material models for the mortar phase are presented.
The focus of the presentation is the discussion of multiscale approaches to combine mesoscale models with realistic macroscale models. This includes a concurrent approach using an adaptive transition between mesoscale and macroscale models which are coupled using the mortar method. A second hierarchical approach is based on the concept of FE², which is extended to incorporate softening by solving a fine scale boundary value problem for each macroscopic integration point.
Concrete is a complex material. Its properties evolve over time, especially at early age, and are dependent on environmental conditions, i.e. temperature and moisture conditions, as well as the composition of the material.
This leads to a variety of macroscopic phenomena such as hydration/solidification/hardening, creep and shrinkage, thermal strains, damage and inelastic deformations. Most of these phenomena are characterized by specific set of model assumptions and often an additive decomposition of strains into elastic, plastic, shrinkage and creep components is performed. Each of these phenomena are investigated separately and a number of respective independent models have been designed. The interactions are then accounted for by adding appropriate correction factors or additional models for the particular interaction. This paper discusses the importance of reconsider even in the experimental phase the model assumptions required to generalize the experimental data into models used in design codes. It is especially underlined that the complex macroscopic behaviour of concrete is strongly influenced by its multiscale and multiphyscis nature and two examples (shrinkage and fatigue) of interacting phenomena are discussed.
A coupled thermomechanical mesoscale model for concrete under heating is presented. When considering the heterogeneous structure under coupled loads, complex macroscopic material properties can be modelled using simple constitutive relations. For instance, damage evolution is directly driven by the incompatibility of thermal strains between matrix and aggregates. Without prescribing
fc = f(T), a decline in compressive strength with rising temperatures will be shown.