2.1.1 Concrete and Brittle Materials

To model concrete structures, or in general structures made of brittle and quasi-brittle materials, DIANA offers a broad range of element types [Vol. Element Library]. The constitutive behavior of quasi-brittle material is characterized by tensile cracking and compressive crushing, and by long-term effects like shrinkage and creep.

Cracking.

The cracking can be modeled with a multi-directional fixed crack model with tension softening and shear retention. Brittle cracking, linear tension softening, multi-linear softening, and nonlinear softening according to Moelands et al. and Hordijk et al. is available [Ch.6]. Also a plasticity-based formulation for cracking is available: the principal stress criterion of Rankine which shows much resemblance with the rotating crack model [§5.1.3]. However, this model is only applicable for plane stress, plane strain and axisymmetric elements.

In multi-axial stress states the compressive stress can exceed the compressive strength of the material. In this case the crack model can be combined with a plasticity model which describes the crushing of the material. Especially the Mohr-Coulomb and Drucker-Prager model are applicable for quasi-brittle structures [§5.1.2].

The combination of tensile and compressive stresses can also be modeled with a multi-surface plasticity model, available for biaxial stress states. However, this model too is only applicable for plane stress, plane strain and axisymmetric elements [§5.1.3].

The Maekawa concrete model, modified for DIANA [§9.4], combines a multi-axial damage plasticity model for the compressive regime with a crack model based on total strain for the tensile regime. This model also describes hysteresis effects.

Shrinkage and creep.

The influence of the temperature, concentration and maturity can be modeled for the elasticity-based crack model and the Mohr-Coulomb and Drucker-Prager models. Long term effects like creep can be modeled with a viscoelasticity model where three models are available: a Power Law, a Maxwell Chain and a Kelvin Chain [Ch.7].

DIANA can also generate the parameters of the Maxwell and Kelvin Chain for concrete where the input can be a discrete creep or relaxation function, or a code model. Currently the models according to the European CEB-FIP Model Code 1990, the American Concrete Institute code 209, and the Dutch NEN 6720 code are available for automatic preprocessing [§7.4.2].

Shrinkage of concrete can also be modeled according to these three code regulations, but also according to a discrete shrinkage function. For the modeling of young hardening concrete, i.e., aging, the parameters of the creep models can be made a function of ambient influences, like temperature, maturity and concentration.