A smart increment technique and its application to a bounding surface model

Most constitutive equations describe the non-linear and irreversible behaviour of engineering materials in termsof increments or rates of strain and stress.These mathematical models are generally complicated and cannot provide an analytical solution of the stress-strain response of the samples that are uniformly strained and stressed in the laboratory. In most instances, they must be integrated numerically to produce simulated stress-strain curves analogous to experimental results. There are numerous integration techniques applicable to constitutive models of porous media. Normally, increasing the speed of analysis is obtained by using more complicated algorithms like implicit method,while, less cumbersome techniques like explicit integration schemes experience stability problems when step sizes are large. In application of explicit method, a simple procedure is to select a uniform and small step size during the analysis. This method has some disadvantages. As an example, a suitable uniform size for a specific initial condition does not guaranty the stability if the condition is changed. Besides, there may be some particular steps which need smaller size than the others, and if these steps determine the uniform step sizes the analysis will be slower. The objective of this research is to develop an algorithm which smartly assigns the largest possible increment in different steps, and has the ability to adjust automatically to different initial conditions to guaranty the convergence and stability during the analysis. A series of numerical experiments are performed on a bounding surface model to illustrate the accuracy and convergence properties of the algorithm.