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TECHNICAL PAPER

Inverse analysis for the tensile constitutive
relation of concrete

A more important output of the fracture research at IIT Madras
was the development of a robust inverse analysis procedure for
obtaining the tensile stress-crack width (σ-w) relation from the
load-CMOD curve of a notched beam. This follows the approach
[32]
of Sousa and Gettu , which was formulated on the basis of a
rotating hinge model at the crack plane (see also Sousa et al.
[33]
[34]
(2018) , and RILEM TC 187-SOC ). This was extended, in the
work of Stephen et al. (2007) to the commonly used EN 14651
[35]
geometry by developing closed-form solutions and an open
software sigw-Concrete that is automated to provide the σ-w
curve from the beam test data , which is graphically explained
[36]
in Figure 5. This complements a generic methodology, derived
from extensive testing, for determining the complete stress- Figure 6: Comparison of the prediction of segment response with
[37]
strain curve of concrete, including the strain-softening regime . experimental data, where the stress-strain curve of FRC obtained from
inverse analysis is used
The sigw-Concrete software has also been used at IIT Madras
to determine the constitutive relation for concrete under Fatigue and fracture of cracked fibre reinforced
uniaxial tension at different loading rates and for different concrete
[38]
[39]
compositions . The relations obtained have been used in the
[40]
analysis of failure of tunnel segments and in compression The time-dependence of the fracture response of FRC is
[41]
splitting , in conjunction with finite element analysis. The of prime importance in many applications as its structural
prediction of the response of a tunnel segment under bending applications are designed to permit cracking. The fatigue
with the σ-w relation from the inverse analysis is seen to behaviour of cracked FRC was investigated extensively by
[44]
compare well with experimental data and other predictions Stephen and Gettu . About 120 beams with different dosages
[42]
[43]
from the literature , as shown in Figure 6. of steel fibres were tested, as in Figure 7, to obtain the S-N

Figure 5: Schematic explanation of the inverse analysis procedure for obtaining the σ-w relation of concrete from the load-CMOD response

THE INDIAN CONCRETE JOURNAL | FEBRUARY 2026 45