Damage–plasticity constitutive models

Damage–plasticity constitutive modelling research at the Grassl Group — Concrete Mechanics for Performance Based Design at the University of Glasgow.

Support for CDPM / CDPM2

CDPM2 in OOFEM — actively maintained (main implementation).
MAT_CDPM (MAT_273) for LS-DYNA — by Peter Grassl & Dimitrios Xenos (less frequent updates).
CDPM2 in Abaqus — contributed by Seungwook Seok (not verified by Peter Grassl).

We develop computationally efficient damage–plasticity models for cohesive–frictional materials under multiaxial stress states. In tension and low confinement, response is softening (decreasing stress with increasing deformation), with stiffness degradation and inelastic strains localised in cracks or shear bands. At high confinement, concrete exhibits ductile hardening.

CDPM triaxial compression response at varying confinement — CDPM: comparison with experimental triaxial compression at varying confinement.

Common frameworks include plasticity, damage mechanics, and coupled damage–plasticity. Together with Milan Jirásek, we developed the Concrete Damage–Plastic Model (CDPM), validated against a wide range of tests and implemented in OOFEM. See Grassl & Jirásek (2006) for a detailed formulation and a 3D yield surface illustration.

We later introduced CDPM2 (with D. Xenos, in collaboration with K. Gylltoft, R. Rempling and U. Nyström) to handle cyclic loading with tension–compression transitions and high strain rates. See the core formulation in Grassl et al. (2013). CDPM2 is available in OOFEM and as LS-DYNA MAT_CDPM (MAT_273).

Cyclic loading response: CDPM vs CDPM2 — Cyclic loading: CDPM2 captures stiffness transitions between tension and compression.

Ongoing work includes rate dependence in CDPM2 and extensions for 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, vol. s, pp. 11-20, 2016.
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, vol. 50, pp. 3805-3816, 2013.
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, 2011.
P. Grassl. On a damage-plasticity approach to model concrete failure. Engineering and Computational Mechanics, vol. 162, pp. 221-231, 2009.
P. Grassl and M. Jirásek. Damage-plastic model for concrete failure. International Journal of Solids and Structures, vol. 43, pp. 7166-7196, 2006.
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.

See Publications or contact me for more information.

For students: If you are doing an MSc or undergraduate project using CDPM2 in OOFEM or LS-DYNA, please see our Student Projects Instructions, including setup tips, workflow, and examples.