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

IF 1.8 4区 工程技术 Q3 ENGINEERING, MECHANICAL
José Luís Medeiros Thiesen, Bruno Klahr, Thiago André Carniel, Eduardo Alberto Fancello
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Abstract

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 nonzero, 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.

Abstract Image

用于表示微尺度体积变化的孔力学一阶计算均质化的局限性
孔机械计算均质化模型将宏观尺度的孔弹性连续体行为与较小(也是孔弹性)空间尺度的现象联系起来。本文全面分析了孔隙压力场的经典微尺度边界条件,即泰勒边界条件(TBC-p)、线性边界条件(LBC-p)、周期边界条件(PBC-p)和均匀边界通量(UBF-p),分析了它们在有限应变多尺度孔隙力学问题中表示主场(孔隙压力)和双场(相对流体速度)的准确性。我们制定了一个具体的基准问题,以研究这些方法在体积雅各布率不为零的情况下的性能,这种情况具有重要的物理意义,尤其是在膨胀等情况下。数值结果表明,UBF-p 和 PBC-p 方法能有效捕捉早期时间步长内直接数值模拟 (DNS) 的行为。然而,当代表体积元素(RVE)发生显著体积变化时,就会出现与预期行为的偏差。结论是,观察到的局限性是由于多尺度模型的一阶性质造成的。这项研究强调,需要更复杂的计算均质化孔隙力学模型,以准确捕捉不同长度尺度上流体流动与变形之间复杂的相互作用。二阶计算均质化模型可以通过丰富来自宏观尺度的信息和放宽对 RVE 边界流体流动的约束来克服一阶多尺度孔力学模型的局限性。
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来源期刊
CiteScore
3.60
自引率
13.60%
发文量
536
审稿时长
4.8 months
期刊介绍: The Journal of the Brazilian Society of Mechanical Sciences and Engineering publishes manuscripts on research, development and design related to science and technology in Mechanical Engineering. It is an interdisciplinary journal with interfaces to other branches of Engineering, as well as with Physics and Applied Mathematics. The Journal accepts manuscripts in four different formats: Full Length Articles, Review Articles, Book Reviews and Letters to the Editor. Interfaces with other branches of engineering, along with physics, applied mathematics and more Presents manuscripts on research, development and design related to science and technology in mechanical engineering.
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