非线性孔隙弹性变分模型
A variational model of nonlinear poroelasticity
- Tufts University（塔夫茨大学）
- Texas A&M University – Corpus Christi（德克萨斯农工大学科珀斯克里斯蒂分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该文提出热力学一致的孔隙弹性变分模型，从能量与耗散泛函导出力平衡与输运方程，恢复Biot方程，并给出能量相容离散化及固结数值研究。
AI中文摘要：
我们推导了一个热力学一致的孔隙弹性介质中流体流动模型。从弹性和流体自由能密度、能量耗散率以及运动学约束出发，利用变分原理推导出力平衡方程，其中压力-密度本构关系作为变分结构的直接结果出现；相同的运动学约束也提供了总通量输运结构。在理想气体极限下，模型线性化恢复经典线性Biot方程。对于幂律流体能量，它产生等熵压力-密度关系。变分公式的一个关键优势是，扩展到更丰富的物理现象，如热效应、化学反应或多组分流体，可以通过增广能量和耗散泛函系统地纳入，而无需重新设计力平衡或输运闭合。我们用能量相容的两场离散化支持该模型，并研究了在表面载荷下具有三种侧向边界处理和三种流体可压缩性指数的固结。
英文摘要：
We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure--density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure--density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.
