发表机构
Technical University of Darmstadt（达姆施塔特工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一个统一有限生长运动学与多相混合物理论的热力学一致连续介质框架，通过体积累积分数耦合生长体积与组分质量，并应用于无血管肿瘤生长模拟。
AI 中文摘要
生物组织通过持续产生、运输和重组多种相互作用的组分而生长。这些过程与有限变形和残余应力内在耦合。现有模型通常要么捕捉有限生长运动学，要么捕捉多组分输运，但很少在热力学一致的框架内同时考虑两者。特别是，现有方法未能一致地将有限生长产生的体积与每种组分产生的质量联系起来。在本工作中，我们开发了一个通用的连续介质框架，将有限生长运动学和多相混合物理论统一起来，适用于包含任意数量稀溶质的完全饱和多组分混合物。该框架基于固体骨架描述，建立在逐组分平衡定律和自由能耗散原理之上，由此推导出所有质量交换、输运、反应和生长过程的热力学容许本构闭合关系。该框架的核心创新在于生长诱导的体积产生与组分质量产生之间的耦合，通过体积累积分数表达，将新产生的体积分配给各组分，同时保持饱和状态。我们将所得模型以总拉格朗日混合弱形式表达，并将一般理论特化为一个四组分、双溶质的无血管肿瘤生长模型，该模型耦合了营养输运、废物产生、增殖细胞、缺氧细胞和坏死细胞之间的表型转变、体积生长、弹性变形和生长诱导的残余应力。该模型在有限元框架内实现，其能力通过代表性基准问题得到验证。
英文摘要
Biological tissues grow by continuously producing, transporting, and reorganizing multiple interacting constituents. These processes are intrinsically coupled to finite deformation and residual stress. Existing models typically capture either finite growth kinematics or multi-constituent transport, but rarely both within a thermodynamically consistent setting. In particular, existing approaches do not consistently link the volume created by finite growth to the mass produced for each individual constituent. In this work, we develop a general continuum framework that unifies finite growth kinematics and multiphase mixture theory for fully saturated multi-constituent mixtures containing an arbitrary number of dilute dissolved solutes. Formulated in a solid-skeleton-based description, the framework rests on constituent-wise balance laws and a free-energy dissipation principle, from which thermodynamically admissible constitutive closures are derived for all mass-exchange, transport, reaction, and growth processes. The central novelty of the framework is a coupling between growth-induced volume creation and constituent mass production, expressed through volume accumulation fractions that distribute the newly created volume among the constituents while preserving saturation. We cast the resulting model in a total Lagrangian mixed weak form and specialize the general theory to a four-constituent, two-solute model of avascular tumor growth that couples nutrient transport, waste production, phenotype transitions between proliferative, hypoxic, and necrotic cells, volume growth, elastic deformation, and growth-induced residual stress. The model is implemented within a finite element setting and its capabilities are demonstrated on representative benchmark problems.
