Unlike ordinary solid materials, underground nano-materials such as kerogen, have relatively small dimensions and suffer from unavoidable in-situ stresses. The coexistence of size effects and initial stresses poses a great challenge to the constitutive modeling of deeply buried nano-inclusions. Despite the theories of strain gradient elasticity (SGE) and initially stressed elasticity (ISE) have been separately developed, the phenomenological model that fully considers the impact of the two ingredients remains unexplored. This paper proposes a strain gradient elasticity constitutive model for kerogen with size effects and in-situ stresses. Based on the decomposition of strains and strain gradients, the initially stressed strain gradient elasticity (ISSGE) framework is established. Then, a new form of the volumetric response function for kerogen is derived utilizing the density and porosity independence of the Poisson ratio. On this basis, we construct the corresponding hyperelastic and higher-order strain energy densities embedded with the given initial stress. The new constitutive model is applied to investigate the spherical pore contraction problem. Theoretical analysis and experimental results indicate that combining the in-situ stress and the size effect strengthens the elastic stiffness. Such enhancement cannot be comprehensively described by the existing theories. The model presented here provides the first constitutive relation of initially stressed strain gradient elasticity and lays the foundation for further incorporating more mechanical behaviors of underground nano-materials.

中文翻译：

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初始应力应变梯度弹性：本构模型包含尺寸效应和初始应力


与普通固体材料不同，干酪根等地下纳米材料具有相对较小的尺寸，并且不可避免地受到原位应力的影响。尺寸效应和初始应力的共存对深埋纳米包裹体的本构建模构成了巨大挑战。尽管应变梯度弹性 （SGE） 和初始应力弹性 （ISE） 的理论已经单独发展，但充分考虑这两种成分影响的现象学模型仍未得到探索。本文提出了一种具有尺寸效应和原位应力的干酪根应变梯度弹性本构模型。基于应变和应变梯度的分解，建立了初始应力应变梯度弹性 （ISSGE） 框架。然后，利用泊松比的密度和孔隙率无关性，推导出了干酪根体积响应函数的新形式。在此基础上，我们构建了嵌入给定初始应力的相应超弹性和高阶应变能密度。应用新的本构模型来研究球孔收缩问题。理论分析和实验结果表明，地应力和尺寸效应相结合增强了弹性刚度。现有的理论无法全面描述这种增强。这里介绍的模型提供了初始应力应变梯度弹性的第一个本构关系，并为进一步结合地下纳米材料的更多机械行为奠定了基础。