In this paper a new mathematical function is proposed for describing the S-shape relationship in both normal x and y scale and the semi-logarithmic x and y scale. Basic features of the proposed function have been demonstrated. The proposed function has then been used to simulate the S-shape relationship for seven categories of engineering phenomena. It is seen that the proposed mathematical function has a great potential for representing various S-shape relationships and provides a powerful tool for characterising properties of materials or response of systems; it is thus useful for further numerical analysis.
Liu, M. D., Xu, K. J. & Horpibulsuk, S. (2013). A mathematical function to represent S-shaped relationships for geotechnical applications. Institution of Civil Engineers. Proceedings. Geotechnical Engineering, 166 (GE3), 321-327.