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Damage plasticity constitutive models

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

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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.

Support for CDPM2:

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.

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).

Currently, we are investigating the localisation properties of CDPM and CDPM2 to understand better the influence of the combination of damage and plasticity on failure patterns observed in structural analyses.

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. In press.
    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.

  • 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.

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