Computational Particle Mechanics

, Volume 4, Issue 3, pp 269–284 | Cite as

Performance of mixed formulations for the particle finite element method in soil mechanics problems

  • Lluís Monforte
  • Josep Maria Carbonell
  • Marcos Arroyo
  • Antonio Gens


This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy’s law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.


Particle finite element method (PFEM) Finite deformation Mixed formulations Soil mechanics 



The support of the Ministry of Economy of Spain through research Grants BIA2011-27217 and BIA2014-59467-R is gratefully acknowledged.


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© OWZ 2016

Authors and Affiliations

  1. 1.Universitat Politècnica de Catalunya (UPC)BarcelonaSpain
  2. 2.International Center for Numerical Methods in Engineering (CIMNE)BarcelonaSpain

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