Concrete Material Modeling and ANSYS Implementation Using SOLID65 Elements

7 minute read

Published: February 27, 2025

Defining Material Properties for Concrete model using SOLID 65 elements in ANSYS

1. Overview of Concrete Material Properties

Concrete is a composite material with nonlinear behavior under compressive and tensile loads. When modeling concrete in ANSYS (especially using the SOLID65 element), key material properties must be defined, including:

Density (ρ)
Elastic modulus (Ec)
Poisson’s ratio (ν)
Tensile strength (ft)
Yield surface models (Drucker-Prager or Multilinear Isotropic Hardening - MISO)
Shear transfer coefficients
Stress-strain curves

2. Key Material Parameters for Concrete in ANSYS using SOLID65 Elements

SOLID65 is a 3D solid element that simulates concrete cracking, crushing, and nonlinear behavior. The primary input parameters required for this element include:

Parameter	Description
Density (ρ)	Defines the mass density (kg/m³)
Elastic Modulus (Ec)	Defines stiffness (MPa)
Poisson’s Ratio (ν)	Defines lateral strain effects
Tensile Strength (ft)	Defines cracking initiation
Shear Transfer Coefficients	Controls shear across cracks
Yield Surface Model	Drucker-Prager (DP) or Multilinear Isotropic Hardening (MISO)
Stress-Strain Behavior	Defines the parabolic compressive response for MISO

3. Density of Concrete

Concrete’s density depends on type and composition:

Normal-weight concrete: 2300 - 2500 kg/m³
Lightweight concrete: 1400 - 1800 kg/m³
Heavyweight concrete: 3000 - 5000 kg/m³

🔹 ANSYS Implementation:

MP,DENS,1,0.0024 ! Normal-weight concrete

4. Elastic Modulus and Poisson’s Ratio

(a) Eurocode Equation

Elastic modulus (Ec) for concrete is estimated using Eurocode 2:

\[E_c = 22 \times (f_c + 8)^{0.3} \quad \text{(MPa)}\]

✅ Example for \( f_c = 40 \) MPa:

\[E_c = 22 \times (40 + 8)^{0.3} = 34,145 \text{ MPa}\]

(b) ACI Equation

According to ACI 318, the elastic modulus is:

\[E_c = 4700 \sqrt{f_c} \quad \text{(MPa)}\]

✅ Example for \( f_c = 40 \) MPa:

\[E_c = 4700 \times \sqrt{40} = 29,748 \text{ MPa}\]

🔹 ANSYS Implementation:

MP,EX,1,34145   ! Eurocode
MP,EX,1,29748   ! ACI
MP,PRXY,1,0.2   ! Poisson's Ratio

5. Yield Surface Models

Concrete is modeled using two main yield surface models:

(a) Drucker-Prager (DP) Model

The Drucker-Prager model defines based on:

\(c\) = cohesion (MPa)
\(\phi\) = internal friction angle (°)

Interpolation for Cohesion & Friction Angle

Using data from Ertekin Öztekin et al [1]., cohesion (c) and friction angle (φ) are interpolated:

fc (MPa)	Cohesion (MPa)	Internal Friction Angle (°)
22.2	5.25	27.5
30.2	8.14	29.5
41.2	10.85	30.9
51.9	12.40	32.8
70.1	16.22	36.7

✅ Python Code for Interpolation:

import numpy as np
from scipy.interpolate import interp1d

fc_values = [22.2, 30.2, 41.2, 51.9, 70.1]
c_values = [5.25, 8.14, 10.85, 12.40, 16.22]
phi_values = [27.5, 29.5, 30.9, 32.8, 36.7]

fc_target = 40
c_interp = interp1d(fc_values, c_values, kind='linear')(fc_target)
phi_interp = interp1d(fc_values, phi_values, kind='linear')(fc_target)

print(f"Cohesion: {c_interp:.2f} MPa")
print(f"Friction Angle: {phi_interp:.2f}°")

🔹 ANSYS Implementation:

! Define Drucker-Prager Parameters
TB,DP,SOLID65_MATID
TBDATA,1,cohesion,friction_angle,0  ! Cohesion & Internal Friction Angle Interpolated

(b) Multilinear Isotropic Hardening (MISO) with Parabolic-Plastic Curve Stress-strain relationship

From PCA’s Notes on ACI 318, the compressive stress-strain relation is:

\[f_c = f_{c,max} \times (2(\epsilon/\epsilon_0) - (\epsilon/\epsilon_0)^2)\]

🔹 ANSYS Implementation [2]:

TB,MISO,SOLID65_MATID,1,8,0  
TBTEMP,22
! Assign Computed Stress-Strain Data to ANSYS
TBPT,,0,0
TBPT,,0.00036,13.1
TBPT,,0.00060,20.40
TBPT,,0.00130,35.10
TBPT,,0.00190,39.90
TBPT,,0.00200,40.00
TBPT,,0.00243,40.00
TBPT,,0.00350,40.00

6. Concrete-Specific Properties – Cracking and Shear Transfer

Shear Transfer Coefficients

ShrCf-Op (Open Crack): 0.5 (normal), 0.25 (high-stress)
ShrCf-Cl (Closed Crack): 0.9 - 1.0

🔹 ANSYS Implementation:

TB,CONC,1,1,9
TBDATA,1,0.5,0.9,ft,-1

7. Tensile Strength

(a) Eurocode 2:

For concrete class \(\leq\) C50/60

\[f_t = 0.3 \times f_c^{2/3}\]

For concrete class \(\geq\) C50/60

\[f_{t} = 2.12 \times \ln\left(1 + \frac{f_{cm}}{10} \right) \quad \text{(MPa)}\]

🔹 ANSYS Implementation:

! Compute Tensile Strength ft Based on EC2
*IF,fc,LE,50,THEN
  ft=0.3*(fc)**(2/3)   
*ELSE
  ft=2.12*LOG(1+0.1*fc) 
*ENDIF

✅ For \(f_c = 40\) MPa:

\[f_t = 0.3 \times 40^{2/3} = 3.5 \text{ MPa}\]

(b) ACI 318:

\[f_t = 0.623 \sqrt{f_c}\]

✅ For \(f_c = 40\) MPa:

\[f_t = 0.623 \times \sqrt{40} = 3.94 \text{ MPa}\]

8. Complete ANSYS Code

✅ MISO implementations

! Complete ANSYS implementation for fc = 40 MPa
!Author: Dr. Han
!Automatically determine parameters and define the material model for the SOLID65 concrete element, using the input values of fc and e0.
/PREP7
! Define Material ID
SOLID65_MATID = 1234 !Material ID
! Define Constants
f2max=40        ! Maximum compressive stress fc (MPa)
e0=0.002        ! Peak strain

! Compute Tensile Strength ft Based on EC2
*IF,f2max,LE,50,THEN
  ft=0.3*(f2max)**(2/3)   
*ELSE
  ft=2.12*LOG(1+0.1*f2max) 
*ENDIF

! Define Predefined Strain Values (ε2)
*DIM,eps_array,ARRAY,8
eps_array(1)=0.00000
eps_array(2)=0.00036
eps_array(3)=0.00060
eps_array(4)=0.00130
eps_array(5)=0.00190
eps_array(6)=0.00200
eps_array(7)=0.00243
eps_array(8)=0.00350  

! Define Stress Values Manually
*DIM,f2_array,ARRAY,8
f2_array(1)=0.0
f2_array(2)=f2max*(2*(eps_array(2)/e0)-(eps_array(2)/e0)*(eps_array(2)/e0))
f2_array(3)=f2max*(2*(eps_array(3)/e0)-(eps_array(3)/e0)*(eps_array(3)/e0))
f2_array(4)=f2max*(2*(eps_array(4)/e0)-(eps_array(4)/e0)*(eps_array(4)/e0))
f2_array(5)=f2max*(2*(eps_array(5)/e0)-(eps_array(5)/e0)*(eps_array(5)/e0))
f2_array(6)=f2max  ! Stress remains constant for ε ≥ ε0
f2_array(7)=f2max  ! Stress remains constant for ε ≥ ε0
f2_array(8)=f2max  ! Stress remains constant for ε ≥ ε0

EC=f2_array(2)/eps_array(2)

! Define Solid5 element
ET,SOLID65_MATID,SOLID65
R,SOLID65_MATID,0,0,0,0,0,0
RMORE,0,0,0,0,0
! Define Material Properties
MP,EX,SOLID65_MATID,EC  ! Young's Modulus
MP,PRXY,SOLID65_MATID,0.2  ! Poisson's Ratio
MP,DENS,SOLID65_MATID,0.0024 ! Density of Concrete  2400 (kg/m³)

! Define Concrete Material Model
TB,CONCR,SOLID65_MATID,1,9
TBTEMP,22
TBDATA,1,0.3,0.8,ft,-1  ! Tensile strength automatically calculated

! Define Multilinear Isotropic Hardening for Stress-Strain
TB,MISO,SOLID65_MATID,1,8,0  
TBTEMP,22

! Assign Computed Stress-Strain Data to ANSYS
TBPT,,eps_array(1),f2_array(1)
TBPT,,eps_array(2),f2_array(2)
TBPT,,eps_array(3),f2_array(3)
TBPT,,eps_array(4),f2_array(4)
TBPT,,eps_array(5),f2_array(5)
TBPT,,eps_array(6),f2_array(6)
TBPT,,eps_array(7),f2_array(7)
TBPT,,eps_array(8),f2_array(8)

✅ Drucker-Prager (DP) implementations

/PREP7
! Complete ANSYS implementation for fc = 40 MPa
!Author: Dr. Han
!Automatically determine parameters and define the material model for the SOLID65 concrete element, using the input values of fc 
! Define Material ID
!SOLID65_MATID=1  ! Concrete Material

! Define Constants
fc=40   ! Given Compressive Strength (MPa)

! Compute Young’s Modulus Ec Based on Eurocode 2
Ec=22000*(((fc+8)/10)**0.3)  ! Young's Modulus in MPa

! Define Sorted Data Points (fc, c, Ø) for Interpolation
*DIM,fc_table,ARRAY,16
fc_table(1)=22.216
fc_table(2)=24.717
fc_table(3)=30.240
fc_table(4)=40.618
fc_table(5)=41.175
fc_table(6)=45.232
fc_table(7)=51.934
fc_table(8)=53.209
fc_table(9)=56.498
fc_table(10)=58.838
fc_table(11)=61.803
fc_table(12)=62.235
fc_table(13)=70.109
fc_table(14)=71.562
fc_table(15)=81.164
fc_table(16)=84.443

*DIM,cohesion_table,ARRAY,16
cohesion_table(1)=5.245
cohesion_table(2)=5.907
cohesion_table(3)=8.142
cohesion_table(4)=9.013
cohesion_table(5)=10.849
cohesion_table(6)=10.638
cohesion_table(7)=12.403
cohesion_table(8)=12.814
cohesion_table(9)=13.807
cohesion_table(10)=13.839
cohesion_table(11)=14.319
cohesion_table(12)=14.530
cohesion_table(13)=16.228
cohesion_table(14)=16.735
cohesion_table(15)=17.875
cohesion_table(16)=18.892

*DIM,friction_table,ARRAY,16
friction_table(1)=27.497
friction_table(2)=28.765
friction_table(3)=29.479
friction_table(4)=31.087
friction_table(5)=30.904
friction_table(6)=33.071
friction_table(7)=32.805
friction_table(8)=33.897
friction_table(9)=34.184
friction_table(10)=34.564
friction_table(11)=35.368
friction_table(12)=35.572
friction_table(13)=36.732
friction_table(14)=36.399
friction_table(15)=37.133
friction_table(16)=38.636

! Linear Interpolation Function for Cohesion and Friction Angle
*DO,i,1,15
  *IF,fc,GE,fc_table(i),THEN
    *IF,fc,LE,fc_table(i+1),THEN
      ratio=(fc - fc_table(i)) / (fc_table(i+1) - fc_table(i))
      cohesion=cohesion_table(i) + ratio * (cohesion_table(i+1) - cohesion_table(i))
      friction_angle=friction_table(i) + ratio * (friction_table(i+1) - friction_table(i))
      *EXIT
    *ENDIF
  *ENDIF
*ENDDO

! Compute Tensile Strength ft Based on EC2
*IF,fc,LE,50,THEN
  ft=0.3*(fc)**(2/3)   
*ELSE
  ft=2.12*LOG(1+0.1*fc) 
*ENDIF

! Define Material Properties
MP,EX,SOLID65_MATID,Ec      ! Young's Modulus from EC2
MP,PRXY,SOLID65_MATID,0.2   ! Poisson's Ratio
MP,DENS,SOLID65_MATID,0.0024  ! Density of Concrete 2400 (kg/m³)

! Define Drucker-Prager Parameters
TB,DP,SOLID65_MATID
TBDATA,1,cohesion,friction_angle,0  ! Cohesion & Internal Friction Angle Interpolated

! Define Concrete Cracking Properties
TB,CONC,SOLID65_MATID,1,9
TBTEMP,0

! Open Crack and Closed Crack Shear Transfer Coefficients
! - `β_t = 0.3` → Shear transfer coefficient for **open cracks** (low value reduces shear after cracking)
! - `β_c = 0.8` → Shear transfer coefficient for **closed cracks** (higher value restores shear when cracks close)
! - `ft` → Tensile strength (computed from EC2)
! - `-1` → Disables crushing capability (crushing not considered)
TBDATA,1,0.3,0.8,ft,-1  
!*
ET,solid65_matid,SOLID65
!KEYOPT,solid65_matid,7,1 !Include tensile stress relaxation after cracking to help convergence
!KEYOPT,solid65_matid,6,3 !Print solution also at each integration point

References:

[1] Öztekin, E., Pul, S., & Hüsem, M. (2016). Experimental determination of Drucker-Prager yield criterion parameters for normal and high strength concretes under triaxial compression. Construction and Building Materials, 112, 725-732.

[2] Thanapon Buamongkol, ANSYS Tutorial: Learn APDL Command for SOLID65 Concrete Modeling Using ANSYS Workbench 2019, https://youtu.be/0JiKNWt095I?si=7lz3-Ja3Qj6o1dT2

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Tran-Van Han

Concrete Material Modeling and ANSYS Implementation Using SOLID65 Elements

Defining Material Properties for Concrete model using SOLID 65 elements in ANSYS

1. Overview of Concrete Material Properties

2. Key Material Parameters for Concrete in ANSYS using SOLID65 Elements

3. Density of Concrete

4. Elastic Modulus and Poisson’s Ratio

(a) Eurocode Equation

(b) ACI Equation

5. Yield Surface Models

(a) Drucker-Prager (DP) Model

Interpolation for Cohesion & Friction Angle

(b) Multilinear Isotropic Hardening (MISO) with Parabolic-Plastic Curve Stress-strain relationship

6. Concrete-Specific Properties – Cracking and Shear Transfer

Shear Transfer Coefficients

7. Tensile Strength

(a) Eurocode 2:

(b) ACI 318:

8. Complete ANSYS Code

References:

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