AI 中文总结
研究针对活性生物组织模拟，提出相互作用势公式，根据四面体边缘应变重铸超弹性本构定律，保留边缘能量耦合，引入避免体积锁定策略，经数值测试和心室主动变形应用，有效模拟并保持能量平衡，再现相关值。
AI 中文摘要
模拟诸如心肌等活性生物组织，需要物理上忠实且计算高效的本构模型。最常见方法依赖有限元法，需在每个时间步进行全局非线性求解。快速的相互作用势方法用独立链接网络近似机械响应。本文提出一种相互作用势公式来弥合差距。该方法根据四面体边缘应变重铸连续体超弹性本构定律，保留相邻边缘能量耦合。被动组织力学由超弹性本构定律描述，主动收缩通过主动应变乘法分解纳入。还引入避免体积锁定的材料不可压缩性约束策略。数值测试表明该方法能有效模拟不同超弹性本构定律并保持能量平衡方程。最后将该方法应用于真实心室的主动变形，再现与文献一致的纵向缩短和壁增厚值。
英文摘要
Simulating active biological tissues, such as the myocardium, requires constitutive models that are both physically faithful and computationally efficient. The most common approach relies on finite element methods that accurately discretize the underlying continuum hyperelastic problem which, in turn, require global nonlinear solve at each time step. On the other hand, fast, interaction-potential methods replace the continuum with a network of independent links approximating the mechanical response. We propose an interaction potential formulation for simulating active biological tissues that bridges this gap. The method recasts continuum hyperelastic constitutive laws in terms of tetrahedral edge strain. Unlike classical mass-spring models, the proposed formulation does not approximate the tissue as independent spring elements but preserves the energetic coupling between adjacent edges. Passive tissue mechanics is described by hyperelastic constitutive laws, while active contraction is incorporated through the active-strain multiplicative decomposition. Within the edge-based formulation, the active strain is incorporated through a time-dependent activated reference configuration. We further introduce a strategy for enforcing the material incompressibility constraint while avoiding volumetric locking. The resulting method can be interpreted as an edge-strain representation of a constant-strain tetrahedral continuum element, providing a bridge between continuum mechanics and discrete interaction potential solvers. Numerical tests demonstrate the capability of the method to effectively simulate different hyperelastic constitutive laws and to properly preserve the energy balance equation. Finally, the proposed method is applied to the active deformation of a realistic ventricle, reproducing longitudinal shortening and wall-thickening values consistent with the literature.
