Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

Monforte, Lluís; Navas, Pedro; Carbonell, Josep Maria; Arroyo, Marcos; Gens, Antonio

doi:10.1002/nag.2923

Cited by 43 publications

(27 citation statements)

References 61 publications

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“…This work has presented a numerical strategy in which several techniques are combined towards that goal. The Particle Finite Element Method (PFEM) has the advantage of facilitating the link to well-established FEM techniques, like mixed field formulations or stabilization procedures for low-order elements (Monforte et al, , 2019). Here this advantage has been exploited again to incorporate:…”

Section: Discussionmentioning

confidence: 99%

“…As already mentioned, only linear triangular elements are used in PFEM. Therefore, in the case of the hydromechanical problem, displacements and water pressure are discretized with the same shape functions, which is known to cause instabilities in the undrained limit (Pastor et al, 1999;Monforte et al, 2019); thus, the mass conservation equation of the byphasic medium is stabilized with the Polynomial Projection tech-10 0 10 2 10 4 10 6 10 -5 10 0…”

Section: G-pfemmentioning

confidence: 99%

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A stable mesh-independent approach for numerical modelling of structured soils at large strains

Monforte

Ciantia

Carbonell

et al. 2019

Computers and Geotechnics

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We describe the large strain implementation of an elasto-plastic model for structured soils into G-PFEM, a code developed for geotechnical simulations using the Particle Finite Element Method. The constitutive model is appropriate for naturally structured clays, cement-improved soils and soft rocks. Structure may result in brittle behavior even in contractive paths; as a result, localized failure modes are expected in most applications. To avoid the pathological mesh-dependence that may accompany strain localization, a nonlocal reformulation of the model is employed. The resulting constitutive model is incorporated into a numerical code by means of a local explicit stress integration technique. To ensure computability this is hosted within a more general Implicit-Explicit integration scheme (IMPLEX). The good performance of these techniques is illustrated by means of element tests and boundary value problems.

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Section: Discussionmentioning

confidence: 99%

Section: G-pfemmentioning

confidence: 99%

A stable mesh-independent approach for numerical modelling of structured soils at large strains

Monforte

Ciantia

Carbonell

et al. 2019

Computers and Geotechnics

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“…References [84,104,106,107] applied their PFEM-solid methods to different types of manufacturing processes, [4,11,12] analyzed tunneling and excavation applications, while bed erosion in river dynamics was tackled in [81,82,86]. Several PFEM-solid formulations have been proposed in the field of soil mechanics and geotechnal engineering, especially for the modelling of frictional materials and granular flows [10,24,56,66,127,128] and for different types of geomechanics problems [75][76][77][78]…”

Section: Pfem For Non-linear Solid and Contact Mechanicsmentioning

confidence: 99%

A State of the Art Review of the Particle Finite Element Method (PFEM)

Cremonesi

Franci

Idelsohn

et al. 2020

Arch Computat Methods Eng

117

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The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.

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“…One of the most employed technique resides in the addition of a stabilization term. Monforte et al 4 . analyzed the two most employed: divergence of the momentum equation (DME) and polynomial projection technique (PPP).…”

Section: Introductionmentioning

confidence: 99%

“…Jeremić et al 21 . employed a small strain

u - U - p_{w}

formulation with different order of interpolation for the different variables, meanwhile Monforte et al 4 . made an assessment of both PPP and DME techniques in a large strain

u - U - p_{w}

framework.…”

Section: Introductionmentioning

confidence: 99%

Fluid stabilization of the u−w Biot's formulation at large strain

Navas

Pastor

Yagüe

et al. 2020

Num Anal Meth Geomechanics

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Dynamic problems of fluid‐saturated soils have to be assessed through a complete formulation where dynamic terms take place. The main dynamic Biot's formulation, the u−w, is employed widely in the literature in order to accurately study the dynamic phenomena. However, depending on the spatial discretization this formulation is utilizing, numerical errors may appear within this approach. The proposed methodology, which is presented in this research, aims to solve the aforementioned problems within an elegant algorithm. Two interesting environmental applications, a consolidation of a fluid‐saturated soil and the seepage of the water through an earth dam, are presented in this paper.

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Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

Cited by 43 publications

References 61 publications

A stable mesh-independent approach for numerical modelling of structured soils at large strains

A stable mesh-independent approach for numerical modelling of structured soils at large strains

A State of the Art Review of the Particle Finite Element Method (PFEM)

Fluid stabilization of the u−w Biot's formulation at large strain

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