Grassl Group
Concrete Mechanics for Performance Based Design

Damage plasticity constitutive models

Support for CDPM2:

• CDPM2 in OOFEM (This is the main implementation which is actively maintained.)

• Umat for MAT_CDPM (MAT_273) in LS-DYNA (This implementation was written by Peter Grassl and Dimitrios Xenos. It is less often updated than the OOFEM implementation.

• CDPM2 in Abaqus (This implementation was provided by Seungwook Seok and was not checked by Peter Grassl. For problems with this subroutine, please contact Seungwook Seok.)

Background
We aim to develop computationally efficient damage plasticity models for modelling the failure of cohesive frictional materials subjected to multiaxial stress states.

Cohesive-fricitional materials, such as concrete and certain types of rocks and soils, exibit a complex nonlinear mechanical behaviour. Failure in tension and low confined compression is characterised by softening which is defined as decreasing stress with increasing deformations. This softening response is accompanied by a reduction of the unloading stiffness of concrete, and irreversible (permanent) deformations, which are localised in narrow zones often called cracks or shear bands. On the other hand, the behaviour of concrete subjected to high confined compression is characterised by a ductile hardening response; that is, increasing stress with increasing deformations.

CDPM: Comparison with experimental results for triaxial compression with varying confinement level.

Commonly used frameworks for modelling this nonlinear response are plasticity, damage mechanics and combinations of plasticity and damage mechanics. One popular class of models relies on a combination of stress-based plasticity formulated in the effective stress space combined with a strain based adamage model. Together with Milan Jirásek, I have developed the Concrete Damage-Plastic Model (CDPM), which has been compared to a wide range of experimental results. This model has been implemented into the release version of OOFEM, which is a open source finite element code developed by Bořek Patzák at the Czech Technical University. For more information on the implementation, see the OOFEM manual for the model. A detailed description of the model equations can be found in our article published in Solids and Structures (DOI). An 3D illustration of the yield surface of the plasticity part of the model is found here: 3D yield surface

I have developed an extended version of this model (CDPM2) together with Dimitrios Xenos in collaboration with Kent Gylltoft, Rasmus Rempling and Ulrika Nyström from Chalmers University in Sweden. The main objective was to enhance CPDM for the modelling of cyclic loading with transition from tension to compression and vice versa, and high strain rate loading. A detailed description of the first part of the model equations (without the equations for the rate effect) can be found in our article published in Solids and Structures (DOI). CDPM2 has been implemented in OOFEM and LS-DYNA as MAT_CDPM (MAT_273).

Response for cyclic loading for CDPM and CDPM2. The new model describes the change of stiffness for the transition from tension to compression and vice versa.

Currently, we are investigating different techniques to include rate dependence in CDPM2. We also work on an extension of CDPM2 to fibre reinforced concrete.

Key publications

• D. Xenos, P. Grassl. "Modelling the failure of reinforced concrete with nonlocal and crack band approaches using the damage-plasticity model CDPM2", Finite Elements in Analysis and Design. Volumes 117-118, Pages 11-20, 2016.
  DOI (Open access)

• P. Grassl, D. Xenos, U. Nyström, R. Rempling, K. Gylltoft. "CDPM2: A damage-plasticity approach to modelling the failure of concrete". International Journal of Solids and Structures. Volume 50, Issue 24, pp. 3805-3816, 2013
  DOI || Preprint

• P. Grassl, U. Nyström, R. Rempling and K. Gylltoft, "A damage-plasticity model for the dynamic failure of concrete", 8th International Conference on Structural Dynamics, Leuven, Belgium, 2011.
  Preprint

• P. Grassl. "On a damage-plasticity approach to model concrete failure". Engineering and Computational Mechanics. Volume 162, Issue 4, pp. 221-231, 2009.
  DOI || Preprint

• P. Grassl and M. Jirásek. "Damage-plastic model for concrete failure". International Journal of Solids and Structures. Vol. 43, pp. 7166-7196, 2006.
  DOI || Erratum

• P. Grassl and M. Jirásek. "Plastic model with non-local damage applied to concrete". International Journal for Numerical and Analytical Methods in Geomechanics. Vol. 30, pp. 71-90, 2006.
  DOI

See Publications or contact me for more information.