A symmetric constitutive matrix for the non‐linear analysis of hypoelastic solids based on a formulation leading to a non‐symmetric stiffness matrix

a b s t r a c tThe main goal of the present paper is to present a mathematical framework for modelling multi-phase non-saturated soil consolidation with pollutant transport based on stress state configurations with special emphasis in its versatility. Non-linear saturation and permeability dependence on suction for both water and pollutant transport is regarded. Furthermore, through the introduction of a suction saturation surface instead of simple suction saturation curves, the implementation of the saturation-suction coupling effect is considerably simplified. The achieved differential equation system is discretized within a Galerkin approach along with the finite element method implementation. A widespread set of practical situations is encompassed by simply setting certain coefficients of the discrete system of equation according to concrete problem conditions. When the model is coped with certain selected fringe conditions, the approach adaptability feature came up showing a robust performance.

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“…To validate Eqs. (38), (39) and (42), different fringe cases were suggested and the adaptability of the model is put forward under consideration.…”

Section: Versatilitymentioning

confidence: 99%

“…[15,19,25,39]) using isoparametric elements with eight nodes for displacements and four for pore pressures.…”

Section: Water Phasementioning

confidence: 99%

A versatile mathematical approach for environmental geomechanic modelling based on stress state decomposition

Beneyto

Rado

Mroginski

et al. 2015

Applied Mathematical Modelling

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“…In reference [3], the following equation for the weak form of the equilibrium equations, was conveyed:…”

Section: The Weak Form Of the Equilibrium Equation For Dry Soilmentioning

confidence: 99%

“…As co-rotated magnitudes remain invariant to rigid body motion, no restrictions are imposed to C f b . In reference [3], the relationship between the Lie derivative of Kirchhoff stress tensor and the co-rotational Kirchhoff stress was addressed. Furthermore and for the non symmetry arising in the constitutive equations is too strong a disadvantage, an alternative that avoids this situation was addressed through the following expression:…”

Section: Hypoelastic Materials Descriptionmentioning

confidence: 99%

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A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils

Rado

Beneyto²,

Mroginski³

et al. 2015

AJAM

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The main scope of this paper is to present an alternative to tackle the problem of the non symmetries arising in the solution of the nonlinear couple consolidation problem based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The geometric model was developed considering an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This description leads to a non-symmetric stiffness matrix and a simple alternative, using a symmetric constitutive matrix, is addressed to overcome this situation. The whole equation system was solved using an open finite element code FECCUND, developed by the authors. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non linear and no symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and on the shear efforts level, as well. A numerical example show the predictive capability of this geometrically non linear fully coupled model for attaining the proposed goal.

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Non-symmetric stiffness of origami-graphene metamaterial plates

Fan

Shen

2022

Composite Structures

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A symmetric constitutive matrix for the non‐linear analysis of hypoelastic solids based on a formulation leading to a non‐symmetric stiffness matrix

Cited by 6 publications

References 13 publications

A versatile mathematical approach for environmental geomechanic modelling based on stress state decomposition

A versatile mathematical approach for environmental geomechanic modelling based on stress state decomposition

A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils

Non-symmetric stiffness of origami-graphene metamaterial plates

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