Related to multiphysics description of concrete structures several constitutive models have to be considered. The material behavior of concrete is changing over the life cycle and varies depending on composition, environmental and loading influences. Models are needed for different chemical, transport and mechanical processes operating on different spatial and temporal scales. Often changes of the material behavior in time are described by the term degradation.
Damage occurs mainly due to insufficient consideration of environmental effects during planning of reinforced concrete structures. Corrosion of embedded steel reinforcements due to carbonation and chloride attack are the main causes of damage. Whereas chloride that is dissolved in the pore solution will attack the steel directly, chemical reactions of the carbon dioxide with the cement matrix reduce the alkalinity of the pore solution. Cement hydration, chloride binding, carbonation, sulphate attack and dehydration due to high temperatures are considered in the constiutive models developed.
The balance equations for transport porocesses incorporate advective flow of water and gas described by Darcy's law and diffuson described by Fick's law. The influence of porosity and pore pressure to permeability are taken into account.
The model for the mechanical behaviour of concrete has to consider the internal heterogeneous structure of porous cement paste as well as mineral aggregates and is based on the theory of plasticity and on continuum damage mechanics. For limiting the admissible stresses, a combined yield surface of Rankine and Drucker-Prager criteria is used to describe the brittle failure due to tensile stresses and the ductile behaviour due to compressive stresses, also with respect to different damage evolutions of these two types of loading.
Compressive normal stress σc evolutes with increasing strain. Loading and unloading behaviour depends on increasing damage. The influence of the chemical damage Mchemon the local stress-strain strain behavior is taken into account.
Beside the elastic and irreversible strains, thermal and hygric strains are included in the mechanical model. The model for the irreversible strains is implemented by means of a non-local approach, so that a unique mesh-independent solution at mechanically degrading material is achieved.
The influence of pore pressure via effective stress concept is incorporated as well as a description of mechanical properties dependent on degree of hydration. The strains are decomposed related to elastic strain rate, shrinkage strain rate, non-local multi-surface plasticity, mechanical and chemical damage.
The strength and deformation characteristics of young concrete develop in the process of cement hydration accompanied by heat release and chemical water linkage. For the description of stress deformation behavior related to the hydration process, variable temperature and humidity conditions as well as material viscosity are taken into account.
The dehydration mainly influences the stress-strain-behaviour of concrete due to high temperatures. The elastic properties are reduced during dehydration, since the cement paste between the aggregates is gradually dissolved. Furthermore, the limit stresses decrease similarly during dehydration, which is related to the tensile strength of concrete as well as the compressive strength.
Intrusion of sulphate into the porous medium concrete causes increased pore pressures yielding irreversible deformations and anisotropic damage. When the idealised material structure is homogenised, the macroscopic material model for the description of this phenomenon may be developed basing on micromechanical considerations.
Example: Effect of anisotropic damage to the yield surface
Yield surfaces for undamaged and for damaged material are compared by depicting nominal stresses. κmc describes the modified related crack length. Crack closure is not taken into account.
For the realistic analysis of concrete structures subjected to dynamic loading anisotropic damage due to micro-cracking and post-fracture behavior under compression and tension has to be considered within the framework of continuum damage mechanics as well as strain softening and the concepts of nonlocal damage and tension stiffening.