Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

Navas, Pedro; López‐Querol, Susana; Yu, Rena C.; Pastor, M.

doi:10.1002/nme.5841

Cited by 22 publications

(18 citation statements)

References 68 publications

(140 reference statements)

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“…Due to the paramount influence of the finite element method in Computational Mechanics field, Voigt's notation has been adopted in most of the variational based numerical techniques, such us Discontinuous Galerkin Method [2], the Material Point Method [19,20,40] or Optimal Transportation Mesh-free [17,23], where symmetric gradient of the shape functions B and the matrix of material elasticities D also appear. Voigt based finite element formulation and implementation is also widespread considered in other branches of continuum mechanics like the theory of porous media including large strain setting [16,24,25,35,36,44].…”

Section: Introductionmentioning

confidence: 99%

A component-free Lagrangian finite element formulation for large strain elastodynamics

et al. 2021

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Standard finite element formulation and implementation in solid dynamics at large strains usually relies upon and indicial-tensor Voigt notation to factorized the weighting functions and take advantage of the symmetric structure of the algebraic objects involved. In the present work, a novel component-free approach, where no reference to a basis, axes or components is made, implied or required, is adopted for the finite element formulation. Under this approach, the factorisation of the weighting function and also of the increment of the displacement field, can be performed by means of component-free operations avoiding both the use of any index notation and the subsequent reorganisation in matrix Voigt form. This new approach leads to a straightforward implementation of the formulation where only vectors and second order tensors in $${\mathbb {R}}^3$$ R 3 are required. The proposed formulation is as accurate as the standard Voigt based finite element method however is more efficient, concise, transparent and easy to implement.

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Section: Introductionmentioning

confidence: 99%

A component-free Lagrangian finite element formulation for large strain elastodynamics

et al. 2021

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“…In this Section, the hyperelastic and hyper-elastoplastic models, employed within this research, are outlined. Further information of both constitutive laws can be found in [ 30 , 33 , 34 ].…”

Section: Constitutive Models For the Solid Phasementioning

confidence: 99%

Explicit meshfree $${{\varvec{u}}}-{{\varvec{p}}}_\mathbf{\mathrm{w}}$$ solution of the dynamic Biot formulation at large strain

et al. 2021

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In this paper, an efficient and robust methodology to simulate saturated soils subjected to low-medium frequency dynamic loadings under large deformation regime is presented. The coupling between solid and fluid phases is solved through the dynamic reduced formulation $$u-p_\mathrm{w}$$ u - p w (solid displacement – pore water pressure) of the Biot’s equations. The additional novelty lies in the employment of an explicit two-steps Newmark predictor-corrector time integration scheme that enables accurate solutions of related geomechanical problems at large strain without the usually high computational cost associated with the implicit counterparts. Shape functions based on the elegant Local Maximum Entropy approach, through the Optimal Transportation Meshfree framework, are considered to solve numerically different dynamic problems in fluid saturated porous media.

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“…Within this paper, the traditional finite element scheme has been chosen for simplicity. However, Navas et al 35 . validated for solid the F‐bar methodology within a local maximum‐entropy shape functions framework.…”

Section: Mathematical Frameworkmentioning

confidence: 99%

“…deals with the approach of Sun et al. of the F‐bar by extending this technique to the meshfree field 34,35 …”

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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Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

Cited by 22 publications

References 68 publications

A component-free Lagrangian finite element formulation for large strain elastodynamics

A component-free Lagrangian finite element formulation for large strain elastodynamics

Explicit meshfree $${{\varvec{u}}}-{{\varvec{p}}}_\mathbf{\mathrm{w}}$$ solution of the dynamic Biot formulation at large strain

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

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