A fully general and adaptive inverse analysis method for cementitious materials


The paper presents an adaptive method for inverse determination of the tensile \(\sigma -w\) relationship, direct tensile strength and Young’s modulus of cementitious materials. The method facilitates an inverse analysis with a multi-linear \(\sigma -w\) function. Usually, simple bi- or tri-linear functions are applied when modeling the fracture mechanisms in cementitious materials, but the vast development of pseudo-strain hardening, fiber reinforced cementitious materials require inverse methods, capable of treating multi-linear \(\sigma -w\) functions. The proposed method is fully general in the sense that it relies on least square fitting between test data obtained from various kinds of test setup, three-point bending or wedge splitting test, and simulated data obtained by either FEA or analytical models. In the current paper adaptive inverse analysis is conducted on test data obtained from three-point bending of notched specimens and simulated data from a nonlinear hinge model. The paper shows that the results obtained by means of the proposed method is independent on the initial shape of the \(\sigma -w\) function and the initial guess of the tensile strength. The method provides very accurate fits, and the increased number of variables describing the \(\sigma -w\) relationship constitutes the basis for obtaining detailed information of crack propagation in any cementitious material.

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Correspondence to Michael S. Jepsen.

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Jepsen, M.S., Damkilde, L. & Lövgren, I. A fully general and adaptive inverse analysis method for cementitious materials. Mater Struct 49, 4335–4348 (2016). https://doi.org/10.1617/s11527-015-0791-3

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  • Inverse analysis
  • Adaptive method
  • Multi-line \(\sigma -w\)
  • Least square fitting
  • Search direction