Abstract
AbstractThe numerical analysis of the dynamic evolution problem concerning an elastic–plastic saturated porous media in the presence of softening (or non‐associativity) is considered in the framework of the Biot formulation extended to take into account plastic phenomena. The finite step boundary value problem, obtained by discretization in time of the continuous initial boundary value problem, is studied and the issue of its ill‐posedness is particularly addressed. The conditions for the loss of ellipticity are established for the linearized problem solved at each iteration when using the Newton–Raphson scheme. In particular, the roles of the algorithmic properties on this loss of ellipticity are derived in detail. The integration scheme of the balance of mass equation plays a major role and it is shown that the fluid flow (Darcy's law) does indeed introduce a length scale but in addition to being dependent on the integration time step, it is found to be insufficient for regularization. To illustrate and corroborate the obtained results, a one‐dimensional example (exhibiting all the features of the three‐dimensional situation) is considered and the corresponding linearized finite step problem is solved in closed form. Copyright © 2002 John Wiley & Sons, Ltd.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal for Numerical Methods in Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
