Abaqus-CDPM2

This repository contains the Abaqus/Explicit user-material (VUMAT) of the concrete damage-plasticity model 2 (CDPM2). The CDPM2 was originally developed by the research group of Dr. Peter Grassl at University of Glasgow and has been implemented in LS-DYNA as MAT_CDPM (MAT_273). Afterwards, it was revised for use in ABAQUS as VUMAT, so-called Abaqus-CDPM2, by Seungwook Seok, a PhD student at Purdue University.

Background: CDPM2 Vs. CDP Model

The concrete damaged-plasticity (CDP) model available in ABAQUS is one of the most commonly used concrete material models readily found in the literature. However, the CDP model was designed only for applications in which concrete is subjected to monotonic, cyclic, and/or dynamic load under low confining pressures [Simulia, 2013]. On the other hand, the CDPM2 has shown its capability to model the material response under various range of confining pressures [Grassl et al., 2013]. In Figure 1, The performance of these two concrete models (CDPM2 and CDP model) for the modeling of the plain concrete under triaxial compression states with different lateral confining pressure levels is presented and compared with the corresponding experimental results [Imran and Pantazopoulou, 1996]. The numerical models consisted of a single cubic finite element (FE) with the characteristic length of 100 mm, subjected to a constant lateral confining pressure in 2- and 3-directions and axially compressed in 1-direction until enough ductile hardening curve was obtained. The analyses were repeated for three different confining pressure levels: 17.2 MPa, 30.1 MPa, and 43 MPa. It is shown that the results with the CDPM2 agree quite with the test data, whereas significant deviation is observed for the CDP model. Such deviation of the CDP model gets prominent with higher pressure levels.

Figure 1. Stress-strain responses of concrete material models (CDPM2 and CDP model) for triaxial compression states with different constant lateral confining pressures (17.2 MPa, 30.1 MPa, and 43 MPa), compared with the test data [Imran and Pantazopoulou, 1996]

Furthermore, the CDPM2 has shown robust nonlinear behavior of concrete material under wide range of experimental results, including the material responses under monotonic loading, cyclic loading, and even high strain rate loading. For more information, please visit the related website.

Material Properties/Parameters and State Variables

Material Properties/Parameters

The concrete material properties and parameters that have to be properly defined for ABAQUS-CDPM2 ("cdpm2vumat.f " shared in this repository) are listed below:

• (1) unit flag : 0 for US Costumery units or 1 for SI units.

• (2) Young's modulus.

• (3) Poisson's ratio.

• (4) uniaxial compressive strength.

• (5) uniaxial tensile strength.

• (6) fracture energy.

• (7) crushing energy.

• (8) ~ (11) a_h , b_h , c_h , and d_h : parameters for hardening ductility measure and typically defined as 0.08, 0.003, 2, and 1E-6, respectively.

• (12) h_p : hardening modulus for q_h2 and typically defined as 0.01.

• (13) a_s : parameter for softening ductility measure. This value varies from 1.5 to 15 according to Grassl et al. (2013)

  Note

  *The crushing energy (7) is not currently used, but has to be inputted with any value, e.g., "0" (do not leave in blank!).

  For the detailed information about the parameters (8) ~ (13), please see Grassl et al. (2013)

Figure 2. Material Properties and parameters defined for CDPM2 (imamge captured from "cdpm2vumat.f")

Solution-Dependent State Variables (SDVs)

The solution-dependent state variables (hereafter termed state variables or SDVs) are values that can be defined to evolve with the solution of an analysis [Simulia, 2013]. The SDVs can be used to store (both current and old) data for each material point and can also be used for updating next field/state variables. The cdpm2vumat consists of a total of 49 SDVs with 21 SDVs related to the Jacobian matrix for return mapping (to be updated). The details about these SDVs are given below in Figure 3.

Figure 3. state variables (SDVs) defined for CDPM2 (imamge captured from "cdpm2vumat.f")

How to Input Properties/Parameters for CDPM2

To link the VUMAT of CDPM2 (cdpm2vumat.f) with ABAQUS, the values for the parameters discussed above have to be inputted by creating a material in Abaqus/CAE. This material must be defined with Depvar and User Material. The Density, associated with gravitational force, is optional. To do this, in ABAQUS/CAE, go to Property module and create material (here, named conc_grassl_imran) and include Depvar, User Material, and Density (if necessary), with the associated input variables for each as detailed below.

• Depvar

  • Number of solution-dependent state variables

    : 49 SDVs (as explained in the previous section)

  • Variable number controlling element deletion

    : 28 (this indicates that the 28th state plays a role in determining element deletion when that function is ON, but the currently shared cdpm2vumat does not consider element deletion function)

Figure 4. "Depvar" defined for cdpm2vumat.f

• User Material

  ​ : all the material properties and parameters must be provided in the User Material in the same order presented in the previous section.

Figure 5. "User Material" defined for cdpm2vumat.f

Then, go to Step module. Edit Field output request. Check SDV, solution dependent state variables under State/Field/User/Time. This should be done to record SDV output data throughout the analysis.

Figure 6. Field output request to include SDV

Running ABAQUS with CDPM2

This section introduces two ways to run ABQUS input file with VUMAT of CDPM2 (cdpm2vumat.f): one (1) on Abaqus/CAE and the other (2) on server.

On Abaqus/CAE

The step-by-step procedure for running ABAQUS with CDPM2 on Abaqus/CAE is as follows:

1. open CAE file

2. Go to Job module and do Edit Job.

   Under General, locate the folder that contains cdpm2vumat.f.

   

3. Submit the job.

On Server

Prerequisite: Abaqus input file (***.inp) and cdpm2vumat.f must be located in the same folder.

The step-by-step procedure for running ABAQUS with CDPM2 on a server platform is as follows:

1. open any ssh (Secure Shell) client and access the server

   

2. move to the folder where the input file and cdpm2vumat.f are located.

3. run your job by typing the following command:

   ​ abaqus job=input_file_name user=cdpm2vumat.f double=both

   

   (here, "opt/abaqus/6.14.6/ecn/bin/" was aforetyped to specify the folder that contains Abaqus command file)

4. open the created odb file via Abaqus/CAE once the run is done.

References

[1] 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.

[2] 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.

[3] P. Grassl and M. Jirásek. "Damage-plastic model for concrete failure". International Journal of Solids and Structures. Vol. 43, pp. 7166-7196, 2006.

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(Last Updated on: September 5, 2019 )