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

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...

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Veröffentlicht in:	Computational particle mechanics Jg. 4; H. 3; S. 269 - 284
Hauptverfasser:	Monforte, Lluís, Carbonell, Josep Maria, Arroyo, Marcos, Gens, Antonio
Format:	Journal Article Verlag
Sprache:	Englisch
Veröffentlicht:	Cham Springer International Publishing 01.07.2017 Springer Nature B.V Springer
Schlagworte:	Benchmarks Classical and Continuum Physics Clay Computational Science and Engineering Conservation Deformation Displacement Engineering Finite deformation Finite element analysis Finite element method Formulations Geotechnical engineering Incompressibility Locking Matemàtiques i estadística Mecànica dels sòls Mixed formulations Nonlinear programming Numerical analysis Particle finite element method (PFEM) Porous media Saturated soils Soil conditions Soil mechanics Stabilization Theoretical and Applied Mechanics Water pressure Àrees temàtiques de la UPC Mixed formulations Particle finite element method (PFEM) Finite deformation Soil mechanics
ISSN:	2196-4378, 2196-4386, 2196-4386
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Abstract	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.
AbstractList	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. 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. Peer Reviewed
Author	Arroyo, Marcos Gens, Antonio Monforte, Lluís Carbonell, Josep Maria
Author_xml	– sequence: 1 givenname: Lluís surname: Monforte fullname: Monforte, Lluís organization: Universitat Politècnica de Catalunya (UPC) – sequence: 2 givenname: Josep Maria orcidid: 0000-0002-2378-5053 surname: Carbonell fullname: Carbonell, Josep Maria email: cpuigbo@cimne.upc.edu organization: International Center for Numerical Methods in Engineering (CIMNE) – sequence: 3 givenname: Marcos surname: Arroyo fullname: Arroyo, Marcos organization: Universitat Politècnica de Catalunya (UPC) – sequence: 4 givenname: Antonio orcidid: 0000-0001-7588-7054 surname: Gens fullname: Gens, Antonio organization: Universitat Politècnica de Catalunya (UPC)
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Snippet	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...
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SubjectTerms	Benchmarks Classical and Continuum Physics Clay Computational Science and Engineering Conservation Deformation Displacement Engineering Finite deformation Finite element analysis Finite element method Formulations Geotechnical engineering Incompressibility Locking Matemàtiques i estadística Mecànica dels sòls Mixed formulations Nonlinear programming Numerical analysis Particle finite element method (PFEM) Porous media Saturated soils Soil conditions Soil mechanics Stabilization Theoretical and Applied Mechanics Water pressure Àrees temàtiques de la UPC
Title	Performance of mixed formulations for the particle finite element method in soil mechanics problems
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