A variational RVE-based multiscale poromechanical formulation applied to soft biological tissues under large deformations

Klahr, Bruno; Thiesen, José Luís Medeiros; Pinto, Otávio Teixeira; Carniel, Thiago André; Fancello, Eduardo Alberto

doi:10.1016/j.euromechsol.2023.104937

Cited by 6 publications

(14 citation statements)

References 49 publications

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“…To obtain such terms we need to account: (i) the homogenization rules of macro-scale dual variables as defined in (37), (38) and ( 40), (ii) the unified format of micro-scale constitutive laws specified in (54)-( 56), and finally (iii) the time integration procedure given by expressions (61) and (62). In what follows, we include some useful details about this topic in order to complete the presentation:…”

Section: Discussionmentioning

confidence: 99%

“…Such material laws are not explicitly defined at the macro-scale level. Instead, they are implicitly obtained from a variationally consistent multiscale formulation which is detailed below (see in particular homogenization formulae (37), (38), and (40), respectively, in Section 3.4.1).…”

Section: Constitutive Equations Of the Macro-scalementioning

confidence: 99%

“…Klahr et al 38 established a variational RVE‐based multiscale formulation applied to a saturated porous medium under large strains. In this scenario, they found that there is also a dependence on the size of the Micro‐Cell domain which can be observed through the homogenized flow velocity.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

Reinaldo A.,

Javier L.,

Pablo J.

2023

Numerical Meth Engineering

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SummaryA multiscale model for saturated porous media is proposed, based on the concept of representative volume element (RVE). The physics between macro and micro‐scales is linked in terms of virtual power measures given by the general theory of poromechanics. Then, applying the so‐called Principle of Multiscale Virtual Power, together with suitable admissible constraints on micro‐scale displacement and pore pressure fields, a well‐established variational framework is obtained. This setting allows deriving the weak form of micro‐scale balance equations as well as the homogenization rules for the macro‐scale stress‐like variables and body forces. Whenever the micro‐scale mechanical constitutive functionals admit, as input arguments, the full‐order expansion of the micro‐scale pore pressure field, a size effect is inherited on the macro‐scale material response. The current literature attributes this issue to the so‐called “dynamical” or “second‐order” term of the homogenized flux velocity. It has been commonly suggested that the influence of this term is negligible by assuming infinitely small micro‐scale dimensions. However, such an idea compromises the fundamental notion of the existence of RVE for highly heterogeneous media. In this work, we show that the micro‐scale size dependence can be consistently eliminated by a simple constitutive‐like assumption. Accordingly, slight and selective redefinitions in the input arguments of micro‐scale material laws are proposed, leading to a constitutive formulation that allows the combination of micro‐scale variables with different orders of expansion. Just at this specific (constitutive) level, a reduced‐order expansion is selectively adopted for the micro‐scale pore pressure field. Thus, the RVE notion is restored while still retaining the major effects of the “dynamical” component of the homogenized flux velocity. The proposed formulation is implemented within a finite element squared (FE) environment. Some numerical experiments are presented showing the viability of the methodology, including comparisons against analytical, mono‐scale and DNS solutions.

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Section: Discussionmentioning

confidence: 99%

Section: Constitutive Equations Of the Macro-scalementioning

confidence: 99%

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Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

Reinaldo A.,

Javier L.,

Pablo J.

2023

Numerical Meth Engineering

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“…In recent years, poroelastic multiscale theories have been incorporated into a wide range of applications, including asphalt-concrete particle composites [10], seismic attenuation of oil and gas reservoirs [11], design of rechargeable batteries [12], micro-fractured porous domains [13] and others [14][15][16]. Multiscale theories applied to decoupled and coupled consolidation problems were covered by Larsson et al [10] and Su et al [17], where the authors discuss the dependence of the Representative Volume Element (RVE) size on the transient response of the problem at the micro scale.…”

Section: Introductionmentioning

confidence: 99%

“…Preliminary numerical results obtained by Klahr et al [14] allowed us to hypothesize that the assumed first-order pore pressure field for the micro-scale introduces excessive constraints on the fluctuating pore pressure fields, limiting the allowable modes of fluid flow at the RVE boundaries, and hence generating classes of multiscale boundary conditions that are not able to represent micro-scale volume changes.…”

Section: Introductionmentioning

confidence: 99%

Limitations of poromechanical first-order computational homogenization for the representation of micro-scale volume changes

Thiesen,

Klahr,

Carniel

et al. 2024

Preprint

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Poromechanical computational homogenization models relate the behavior of a macro-scale poroelastic continuum to phenomena occurring at smaller (and also poroelastic) spatial scales. This paper presents a comprehensive analysis of classical micro-scale boundary conditions for the pore pressure field, namely Taylor Boundary Condition (TBC-p), Linear Boundary Condition (LBC-p), Periodic Boundary Condition (PBC-p) and Uniform Boundary Flux (UBF-p), in terms of their accuracy in representing primary (pore pressure) and dual (relative fluid velocity) fields in finite-strain multiscale poromechanical problems. A specific benchmark problem was formulated to investigate the performance of these approaches in scenarios where the rate of the volumetric Jacobian is non-zero, a condition of significant physical interest, especially in contexts such as swelling. Numerical results show that the UBF-p and PBC-p approaches effectively capture the behavior of Direct Numerical Simulation (DNS) during the early time steps. However, deviations from the expected behavior occur when the Representative Volume Element (RVE) undergoes significant volume changes. It is concluded that the observed limitations are due to the first-order nature of the multiscale model. This study highlights the need for more sophisticated computational homogenization poromechanical models that can accurately capture the complex interplay between fluid flow and deformation at different length scales. Second-order computational homogenization models can be alternatives to overcome the limitations of first-order multiscale poromechanical models by enriching the information coming from the macro-scale and relaxing the constraints on the fluid flow at the RVE boundaries.

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A Second-Order Multiscale Model for Finite-Strain Poromechanics Based on the Method of Multiscale Virtual Power

Thiesen,

Klahr,

Carniel

et al. 2024

J Elast

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A variational RVE-based multiscale poromechanical formulation applied to soft biological tissues under large deformations

Cited by 6 publications

References 49 publications

Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

Limitations of poromechanical first-order computational homogenization for the representation of micro-scale volume changes

A Second-Order Multiscale Model for Finite-Strain Poromechanics Based on the Method of Multiscale Virtual Power

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