Initial stress is widely observed in porous materials. However, its constitutive theory remains unknown due to the lack of a framework for modeling the interactions between initial stress and porosity. In this study, we construct the porous hyperelastic constitutive model with arbitrary initial stresses through the multiplicative decomposition approach. Based on the compression experiment of shale samples, the parameters in the constitutive equation are determined. Then, the explicit equations of in-plane elastic coefficients are proposed by linearizing the finite deformation formulation. The influences brought by the coexistence of initial stresses and porosity on these coefficients are revealed. Later, comparative analyses of the linearized equations between the present model, the initially-stressed models without pores, the Biot poroelasticity, and the porous hyperelastic model without initial stress are conducted to illustrate the performances of the two ingredients. As a specific example, we investigate the variation of pore sizes under external pressures and initial stresses since changes in pore sizes during deformation are crucial for understanding the accumulation and migration of shale oil and gas. The newly proposed model provides the first initially stressed porous hyperelasticity (ISPH), which is suitable for describing the finite deformation behavior of solid materials with large porosity and significant initial stress simultaneously.

中文翻译：

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具有初始应力的多孔材料的超弹性本构关系


在多孔材料中广泛观察到初始应力。然而，由于缺乏模拟初始应力和孔隙率之间相互作用的框架，其本构理论仍然未知。在本研究中，我们通过乘法分解方法构建了具有任意初始应力的多孔超弹性本构模型。基于页岩样品的压缩实验，确定了本构方程中的参数。然后，通过线性化有限变形公式，提出了面内弹性系数的显式方程。揭示了初始应力和孔隙率共存对这些系数的影响。随后，对本模型、无孔初始应力模型、Biot 多孔弹性模型和无初始应力的多孔超弹性模型之间的线性方程进行了比较分析，以说明这两种成分的性能。作为一个具体的例子，我们研究了孔径在外部压力和初始应力下的变化，因为变形过程中孔径的变化对于理解页岩油气的积累和迁移至关重要。新提出的模型提供了第一个初始应力多孔超弹性 （ISPH），适用于同时描述具有大孔隙率和显着初始应力的固体材料的有限变形行为。