Modern anisotropic criteria and limiting surfaces of masonry strength under plane stress state for calculations in software packages

Introduction. Assessing the strength of elements in spatial load-bearing structures during automated calculations using plastic flow theory requires establishing a strength condition, the geometric interpretation of which is represented as a surface in stress space. The exit of the point depicting the stressed state beyond the described surface during the loading of the computational model indicates material failure. Evaluating the strength of masonry structures implies considering material characteristics such as differential resistance, the dependence of strength on the angle of anisotropy, and various values of biaxial strength, which imposes limitations on the use of existing limiting surfaces.

Aim. To review existing strength criteria, describe their advantages and disadvantages, as well as their applicability limits for strength modeling of masonry elements.

Materials and methods. The review of existing strength criteria is based on relevant sources. Assessing the accuracy of approximation for the strength conditions of the experimental data obtained from tests involved numerical methods implemented in Python using Numpy, Sympy, and Matplotlib libraries for graphical visualization of the results. Tensor calculus theory is utilized to describe the actual and ultimate stress states at an elementary point of the structure, while aspects of linear algebra are used to record the relationships of mechanical constants of the material.

Results. The accuracy of approximation for experimental data using the Willam-Warnke strength criterion is assessed in comparison with the Geniev strength criterion for the plane stress state of masonry. The paper provides a brief overview of existing masonry strength models, describing their physical interpretations and applied approaches.

Conclusions. Existing strength criteria have disadvantages, such as inaccuracies in approximation of experimental data, complexity in implementing computational calculations, incomplete descriptions of strength properties, and phenomenology of the approaches used. The development of a new specialized criterion for a comprehensive description of masonry strength models is considered relevant.

1. <i>Kapustin S.A., Likhacheva S.Yu</i>. Modeling the processes of deformation and destruction of materials with a periodically repeating structure. Nizhny Novgorod: Nizhny Novgorod State University of Architecture and Civil Engineering (NNGASU); 2012. (In Russian).

2. <i>Tsai S.W., Wu E.M</i>. A General Theory of Strength for Anisotropic Materials. Journal of Composite Materials. 1971;5(1):58–80. https://doi.org/10.1177/002199837100500106

3. <i>Vishnyakov L.R., Grudina T.V., Kadyrov V.H</i>. Composite materials. Kiev: Naukova dumka Publ.; 1985. (In Russian).

4. <i>Polilov A.N</i>. Studies on the mechanics of composites. Moscow: Physics and Mathematics Literature; 2015. (In Russian).

5. <i>Voronov A.N</i>. Static plane problems of the deformation theory of plasticity of orthotropic bodies [dissertation]. Moscow; 1984. (In Russian).

6. <i>Hoffman O</i>. The Brittle Strength of Orthotropic Materials. Journal of Composite Materials. 1967;1(2):200–206. https://doi.org/10.1177/002199836700100210

7. <i>Lourenco P.J.B.B</i>. Computational strategies for masonry structures [dissertation]. Delft University Press; 1996.

8. <i>Syrmakezis C.A., Asteris P.G</i>. Masonry Failure Criterion under Biaxial Stress State. Journal of Materials in Civil Engineering. 2001;13(1):58–64. https://doi.org/10.1061/(asce)0899-1561(2001)13:1(58)

9. <i>Ganz H.R</i>. Mauerwerksscheiben unter normalkraft und schub [PhD Thesis]. ETH Zurich; 1985. (In German).

10. <i>Lourenco P.B</i>. An orthotropic continuum model for the analysis of masonry structures [Report]. The Netherlands, TU Delft; 1995.

11. <i>Małyszko L., Jemioło S., Bilko P., Gajewski M</i>. MES i modelowanie konstytutywne w analizie zniszczenia konstrukcji murowych. Olsztyn: Wydawnictwo Uniwersytetu Warmińsko-Mazurskiego; 2015. (In Polish).

12. <i>Geniev G.A., Kurbatov A.S., Samedov F.A</i>. Issues of strength and plasticity of anisotropic materials. Moscow: Interbuk-biznes Publ.; 1993. (In Russian).

13. <i>Drobiec L., Šlivinskas T</i>. Determination of mortar and brick failure surface based on research in a complex state of stress. Materiały Budowlane. 2016;(12):42–44. https://doi.org/10.15199/33.2016.12.13

14. <i>Willam K.J., Warnke E.P</i>. Constitutive model for the triaxial behavior of concrete. Proceedings of IABSE, Structural Engineering. 1975;19:1–30.

15. <i>Page A.W</i>. The biaxial compressive strength of brick masonry. Proceedings of the Institution of Civil Engineers. 1981;71(3):893–906. https://doi.org/10.1680/iicep.1981.1825

16. <i>Plizzari G., Vecchio F.J</i>. Fiber reinforced concrete and mortar for enhanced structural elements and structural repair of masonry walls [Ph.D. Thesis]. University of Brescia, Italy; 2012.

17. <i>Bigoni D., Piccolroaz A</i>. Yield criteria for quasibrittle and frictional materials. International journal of solids and structures. 2004;41(11–12):2855–2878. https://doi.org/10.1016/j.ijsolstr.2003.12.024

18. <i>Piccolroaz A., Bigoni D</i>. Yield criteria for quasibrittle and frictional materials: a generalization to surfaces with corners. International Journal of Solids and Structures. 2009;46(20):3587–3596. https://doi.org/10.1016/j.ijsolstr.2009.06.006