Overview
This is a tool for generating ABAQUS input data for the Concrete Damaged Plasticity (CDP) material model: compressive hardening, tension stiffening, and the compression and tension damage parameters.
Using the tool
- Compression: choose a model (Carreira & Chu, Eurocode 2, Model Code 1990, GB 50010-2010) or Test data (browse for a file, paste two columns, or load the sample compression test). A value of 0 for E, εc or ftu means “estimate it”; the value actually used is shown in blue beside each field.
- Tension: define tension stiffening as stress vs cracking strain (needs the element characteristic length lo) or stress vs cracking displacement (Linear, Bilinear or Power softening). The fracture energy Gf is entered directly or estimated from the maximum aggregate size dmax.
- Plots and tables update as you type. Each table saves as the same text file the desktop app writes, or copies as tab-separated values for Excel or the ABAQUS/CAE data table.
Compression
- Carreira & Chu (1985): σ = fcu β(ε/εc) / [β − 1 + (ε/εc)β], β = (fcu/32.4)3 + 1.55, up to ε = 0.035. fc0/fcu = 0.3.
- Eurocode 2 (EN 1992-1-1, 3.1.5): σc/fcm = (kη − η2)/[1 + (k − 2)η], η = ε/εc1, k = 1.05Ecmεc1/fcm (Expression 3.14), up to the nominal ultimate strain εcu1 (Table 3.1). fcu is taken as fcm, valid 20–98 MPa. fc0/fcu = 0.4. The curve ends at εcu1, usually well above 0.1fcm, and ABAQUS would hold the last tabulated stress constant beyond it. With Extend beyond εcu1 ticked (default), the curve is continued past εcu1 as an extension beyond EC2: Expression (3.14) has the same form as MC90 eq. (2.1-18) with Eci/Ec1 = k, so it is completed by the MC90 descending branch, i.e. eq. (2.1-18) up to εc,lim (0.5fcm, eq. 2.1-19) and eq. (2.1-20) beyond, with continuous stress and slope. The EC2 part up to εcu1 is unchanged; the extension is dashed in the plots and noted below the tables. Untick it to stop at εcu1.
- Model Code (1990) (§2.1.4.4.1): eq. (2.1-18) from the origin up to εc,lim, then eq. (2.1-20) to 0.022, with εc,lim from eq. (2.1-19) and ξ from eq. (2.1-21). fcu is taken as the mean strength fcm throughout: Eci = 21500(fcm/10)1/3 (eq. 2.1-16), εc1 = 0.0022, Ec1 = fcm/εc1, and ftu = 1.40((fcm − 8)/10)2/3 (eq. 2.1-4; the ftu input is not used). Valid for fcm = 20–50 MPa in this tool.
- GB 50010-2010 (Annex C.2): σ = (1 − dc)Eε with the code's damage expressions, up to 0.022. fcu is the representative axial (not cube) strength fc,r, taken as a mean value, 20–80 MPa. Missing values come from the code: εc,r and αc from Table C.2.4, E from Table 4.1.5 and ftu = ftm from Table 4.1.3-2 via eq. (C.2.1-2), with grades matched through fcm ≈ fck/0.85. fc0/fcu = 0.4.
- For Carreira & Chu, Eurocode 2 and test data, missing E, εc and ftu are taken from EN 1992-1-1 Table 3.1 (Ecm, εc1, fctm), interpolated on fcm.
The curve is then processed for ABAQUS. The elastic limit is fc0 = (fc0/fcu) fcu, and the elastic modulus used is the secant to that point, E = fc0/εc0. Beyond it:
εin = ε − σ/E, dc = 1 − σ/fcu (after the peak; 0 before)
The hardening table stops once σ drops to 0.1fcu; the damage table starts at the peak and stops before dc reaches 0.999.
Tension
The fracture energy from dmax follows Model Code 1990: Gf = Gf0(fcu/10)0.7 with Gf0 = 0.025, 0.030, 0.058 N/mm and α = 8, 7, 5 for dmax = 8, 16, 32 mm (interpolated).
- Power (Reinhardt & Cornelissen 1984): σ/ftu = [1 + (3x)3]e−6.93x − 28xe−6.93, x = w/wc, wc = 5.14Gf/ftu. In stress–strain form εck = w/lo.
- Linear: σ = ftu(1 − w/wc), wc = 2Gf/ftu.
- Bilinear (Model Code 1990): σ = ftu(1 − 0.85w/w1) up to w1 = 2Gf/ftu − 0.15wc, then linear to zero at wc = αGf/ftu.
- GB 50010-2010: with the Chinese Code compression model, stress–strain tension stiffening uses the code's tension curve instead.
dt = 1 − σ/ftu (tables stop at σ = 0.1ftu and before dt reaches 0.95)
ABAQUS keywords
*Elastic
E, 0.2
*Concrete Damaged Plasticity
ψ, ε, fb0/fc0, K, μ (e.g. 40, 0.1, 1.16, 0.667, 0)
*Concrete Compression Hardening
<Comp. hardening: stress, inelastic strain>
*Concrete Tension Stiffening[, type=DISPLACEMENT]
<Tens. stiffening: stress, cracking strain or displacement>
*Concrete Compression Damage
<Comp. damage: dc, inelastic strain>
*Concrete Tension Damage[, type=DISPLACEMENT]
<Tens. damage: dt, cracking strain or displacement>
The plasticity parameters on the second data line are typical values for illustration (dilation angle, flow potential eccentricity, biaxial-to-uniaxial strength ratio, Kc, viscosity); this tool does not generate them.
Citation & references
Elkady, A. (2023) “ABAQUS_CDP_Generator: A tool for generating concrete damage parameters for ABAQUS”, Zenodo, Version v23.04. doi:10.5281/zenodo.7755926
- Reinhardt, H. W. and Cornelissen, H. A. W. (1984). Post-peak cyclic behaviour of concrete in uniaxial tensile and alternating tensile and compressive loading. Cement and Concrete Research, 14(2), 263–270. doi:10.1016/0008-8846(84)90113-3
- Carreira, J. D. and Chu, K.-H. (1985). Stress-strain relationship for plain concrete in compression. ACI Journal Proceedings, 82(6). doi:10.14359/10390
- CEB-FIP (1990). Model Code for Concrete Structures. Comité Euro-International du Béton and Fédération Internationale de la Précontrainte, Lausanne, 241–263.
- GB (2010). Code for Design of Concrete Structures, GB 50010-2010. National Standard of the People's Republic of China, Beijing.
- EN 1992-1-1 (2004). Eurocode 2: Design of concrete structures. Part 1-1: General rules and rules for buildings, Table 3.1 and Expression (3.14).
Author: Dr Ahmed Elkady, University of Southampton
To report bugs or give feedback, raise an issue through the GitHub repository or e-mail a.elkady@soton.ac.uk.
Web version of ABAQUS CDP Generator v26-01. Relative to the desktop app: results update live and estimated values are shown beside the inputs instead of overwriting them; with dmax selected, Gf is always re-estimated; with test data, fcu for the Gf and EC2 estimates is the peak of the test curve. Revised October 2026 (also in the desktop source): EC2 Table 3.1 fcm for C60/75 corrected to 68 MPa; Model Code 1990 uses fcm consistently with εc,lim from eq. (2.1-19) and no linear start; GB 50010 uses its own tables for missing values. Eurocode 2 (Expression 3.14) added as a compression model, with an optional Model Code 1990 descending branch as an extension beyond εcu1.
Disclaimer
These tools are provided for research and educational purposes only, without warranty of any kind. The generated material data are estimates from the cited models and your inputs, and are only as reliable as those models within their validity ranges. Results should be checked independently by a qualified engineer before being used in design or assessment.
