Concrete Damaged Plasticity Model (CDP)
Concrete Damaged Plasticity Model (CDP): Theoretical Foundations
What is the CDP Model?
Professor, what is the CDP model?
CDP (Concrete Damaged Plasticity) is a constitutive model for concrete in Abaqus. It is a combination of Plasticity (based on DP criterion) + Damage (tensile cracking + compressive crushing).
Special Characteristics of Concrete
CDP Composition
Settings in FEM
```
*CONCRETE DAMAGED PLASTICITY
dilation_angle, eccentricity, fb0/fc0, K, viscosity
*CONCRETE COMPRESSION HARDENING
stress, inelastic_strain
*CONCRETE TENSION STIFFENING
stress, cracking_strain
*CONCRETE COMPRESSION DAMAGE
damage, inelastic_strain
*CONCRETE TENSION DAMAGE
damage, cracking_strain
```
Summary
Key Points:
- CDP = Drucker-Prager plasticity + Tensile/Compressive damage — Dedicated to concrete
- Tensile softening (cracking) + Compressive softening (crushing) — Special behavior of concrete
- Stiffness recovery — Recovery under compression when tensile cracks close
- Abaqus CDP is the de facto standard in research
The Two Fathers of the CDP Model
The Concrete Damaged Plasticity (CDP) model originates from the 1989 paper "A plastic-damage model for concrete" by J. Lubliner and J. Oliver (Universitat Politècnica de Catalunya). Later in 1998, Lee & Fenves from the Abaqus team significantly improved the numerical stability of strain softening, leading to the formulation now most widely used worldwide. This Lee-Fenves version was commercialized as Concrete Damaged Plasticity in Abaqus/Standard.
Computational Methods for Concrete Damaged Plasticity Model (CDP)
CDP Parameters
| Parameter | Typical Value | Meaning |
|---|---|---|
| Dilation angle ($\psi$) | 30–40° | Dilatancy angle |
| Eccentricity | 0.1 | Eccentricity of the hyperbola |
| $f_{b0}/f_{c0}$ | 1.16 | Biaxial/uniaxial compressive strength ratio |
| $K$ | 2/3 | Yield surface shape parameter |
| Viscosity | 0.0001–0.001 | Viscosity regularization |
Why is viscosity regularization (Viscosity) necessary?
Concrete tensile softening has strong mesh dependency. Viscosity regularization "smoothes out" localization to improve convergence. $\mu = 10^{-4} \sim 10^{-3}$ is typical. Too large makes the response inaccurate.
Summary
Tensile Strength is Only 1/10 of Compression
Ordinary concrete compressive strength is generally 24–60 N/mm², but its tensile strength is only about 1/10 of that, at 2–5 N/mm². The CDP model expresses this extreme asymmetry with independent damage variables for tension and compression (d_t, d_c). In FEM analysis, the input of the tensile stress-strain relationship most sensitively affects the final results, so the accuracy of the tensile softening curve setting determines the analysis quality.
Concrete Damaged Plasticity Model (CDP) in Practice
CDP in Practice
Used for seismic analysis of RC buildings, concrete dams, nuclear containment vessels, detailed analysis of PCa members.
Practical Checklist
The Great East Japan Earthquake and Seismic Analysis
After the 2011 Great East Japan Earthquake, FEM analysis using the CDP model was utilized to evaluate the seismic performance of many existing RC buildings. In commissioned research by the Ministry of Land, Infrastructure, Transport and Tourism (2012–2014), it was confirmed that the maximum load prediction by static incremental analysis (pushover analysis) using the CDP model fell within ±15% of loading test values, and it was officially recognized as a complementary method for seismic diagnosis of existing buildings.
Concrete Damaged Plasticity Model (CDP): Software & Solver Comparison
CDP Tools
Selection Guide
Implementation Differences Between Midas and Abaqus
The CDP model is also implemented in Midas FEA NX, LS-DYNA (MAT_CDPM), and OpenSees (Concrete07) besides Abaqus. However, the yield function forms differ slightly; Abaqus uses a hyperbolic Drucker-Prager...
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