AI 中文总结
本研究提出一种热力学一致的可压缩新胡克本构模型，以孔隙率为控制变量，可描述开孔材料的非线性致密化等特性，经实验验证适用于高可压缩开孔材料的有限元实现与多尺度建模。
AI 中文摘要
开孔材料具有显著的可压缩性、非线性致密化特性，以及刚度随密度变化的幂律标度关系。本研究针对开孔固体提出了一种热力学一致的可压缩新胡克本构模型，其中孔隙率作为主要控制变量。应变能密度被构建为将固体骨架的畸变弹性与由变形诱导的孔隙演化所控制的体积响应耦合，包括对孔隙坍塌的有界描述。该公式引入了一组最少的参数，即初始孔隙率、固有骨架模量，以及控制致密化起始的标量参数。该模型的一个关键特征是修改了体积项，其响应由当前孔隙率归一化，确保从多孔状态到致密状态的转变在物理上一致，不会出现人工硬化。在小应变极限下，该模型恢复了经典线性弹性，其有效模量可选择自均匀化界限（如Hashin-Shtrikman估计值），或选择自Gibson-Ashby型幂律标度以捕捉与拓扑相关的行为。在有限应变下，该公式可捕捉与渐进孔隙坍塌相关的特征性非线性硬化和凸应力-拉伸响应。因此，所提出的框架提供了一种紧凑、灵活且可扩展的本构描述，将有效介质一致性与实验观察到的标度行为相统一，非常适用于有限元实现和高可压缩开孔材料的多尺度建模。最后，该模型通过现有实验数据得到验证。
英文摘要
Open-porous materials exhibit pronounced compressibility, nonlinear densification, and power-law scaling of stiffness with density. In this work, we propose a thermodynamically consistent compressible neo-Hookean constitutive model for open-porous solids in which porosity serves as the primary governing variable. The strain-energy density is formulated to couple distortional elasticity of the solid skeleton with a volumetric response governed by deformation-induced porosity evolution, including a bounded representation of pore collapse. The formulation introduces a minimal set of parameters, namely the initial porosity, intrinsic skeleton moduli, and a scalar parameter controlling the onset of densification. A key feature of the model is a modified volumetric term in which the response is normalised by the current porosity, ensuring a physically consistent transition from a porous to a densified state without artificial stiffening. In the small-strain limit, the model recovers classical linear elasticity with effective moduli that may be chosen either from homogenisation bounds, such as the Hashin-Shtrikman estimates, or from Gibson-Ashby-type power-law scaling to capture topology-dependent behaviour. At finite strains, the formulation captures the characteristic nonlinear stiffening and convex stress-stretch response associated with progressive pore collapse. The proposed framework thus provides a compact, flexible, and extensible constitutive description that unifies effective-medium consistency with experimentally observed scaling behaviour, and is well suited for finite element implementation and multiscale modelling of highly compressible open-porous materials. The model is finally validated against available experimental data.
