Homogenised governing equations for pre-stressed poroelastic composites

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2023-08-09 DOI:10.1007/s00161-023-01247-3

Laura Miller, Salvatore Di Stefano, Alfio Grillo, Raimondo Penta

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Abstract

We propose the governing equations for a pre-stressed poroelastic composite material. The structure that we investigate possesses a porous elastic matrix with embedded elastic subphases with an incompressible Newtonian fluid flowing in the pores. Both the matrix and individual subphases are assumed to be linear elastic and pre-stressed. We are able to apply the asymptotic homogenisation technique by exploiting the length-scale separation that exists between the porescale and the overall size of the material (the macroscale). We derive the novel macroscale model which describes a poroelastic composite material where the elastic phases possess a pre-stress. We extend the current literature for poroelastic composites by addressing the role of the pre-stresses in the functional form of the new system of derived partial differential equations and its coefficients. The latter are computed by solving appropriate periodic cell differential problems which encode the specific contribution related to the pre-stresses. The model in the first instance is derived in the most general scenario and then specified for a variety of particular cases which are associated with different macroscale behaviour of materials.

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预应力孔弹性复合材料的均匀化控制方程

我们提出了预应力多孔弹性复合材料的控制方程。我们研究的结构具有一个多孔弹性基体，其中嵌入了弹性子相，不可压缩的牛顿流体在孔隙中流动。矩阵和单个子相都被假定为线性弹性和预应力。我们能够通过利用孔隙尺度和材料总体尺寸（宏观尺度）之间存在的长度尺度分离来应用渐进均匀化技术。我们推导了一个新的宏观模型，该模型描述了弹性相具有预应力的多孔弹性复合材料。我们通过讨论预应力在导出的偏微分方程及其系数的新系统的函数形式中的作用，扩展了当前关于多孔弹性复合材料的文献。后者是通过求解适当的周期性单元微分问题来计算的，该问题对与预应力相关的特定贡献进行编码。第一种情况下的模型是在最普遍的情况下导出的，然后针对与材料的不同宏观行为相关的各种特定情况进行指定。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.