粘弹性物质中由生长诱导的转变
Growth-Induced Transitions in Viscoelastic Matter
浏览论文内容
中文总结 AI 辅助
该研究针对生物组织兼具弹性与黏性的特性，建立黏弹性生长理论框架，发现无量纲参数$g\tau$主导生长物质力学，$g\tau$约为1时出现新动力学与力学转变，可用于模拟真实生物材料。
中文摘要 AI 辅助
生长是生命系统的基本过程。尽管生长材料的应力-变形响应常被描述为纯弹性或纯黏性，但从生物膜到肿瘤的多种生物组织均表现出弹性和黏性两种行为。本文表明，当生长速率与应力松弛速率可比时，这种黏弹性响应会关键控制增殖物质的力学性能。首先聚焦于生长弹性梁这一典型案例，发现其动力学由单一无量纲参数$g\tau$控制，其中$g$为生长速率，$\tau$为黏弹性松弛时间。当$g\tau \to 0$和$g\tau \to \infty$时，分别恢复为纯黏性和纯弹性行为，而中间状态并非二者间的平滑过渡，而是在$g\tau \sim 1$时出现质的新动力学，包括在两种极限状态下均不存在的亚稳态间快速转变。随后，本文开发了一种通用的、与生长兼容的理论框架，其中无约束生长本质上是无应力的，将分析扩展至其他典型几何结构，并实现对更真实的生长生物材料的模拟。在该框架内，当指数生长产生的应力积累速度快于黏弹性松弛的耗散速度时，会出现尖锐的力学转变。
英文摘要
Growth is a fundamental process in living systems. Although the stress-deformation response of growing materials is often described as either purely elastic or purely viscous, many biological tissues, from biofilms to tumors, exhibit both elastic and viscous behavior. Here, we show that this viscoelastic response can crucially control the mechanics of proliferating matter when the growth rate becomes comparable to the rate of stress relaxation. Focusing first on the prototypical case of a growing elastic beam, we find that the dynamics are governed by a single dimensionless parameter, $g τ$, where $g$ is the growth rate and $τ$ is the viscoelastic relaxation time. While the limits $g τ\to 0$ and $g τ\to \infty$ recover purely viscous and purely elastic behavior, respectively, the intermediate regime is not merely a smooth crossover between them. Instead, qualitatively new dynamics emerge at $g τ\sim 1$, including rapid transitions between metastable states that occur in neither limiting regime. We then develop a general, growth-compatible theoretical framework in which unconstrained growth is intrinsically stress-free, extending the analysis to other prototypical geometries and enabling simulations of more realistic growing biological materials. Within this framework, sharp mechanical transitions arise when stress generated by exponential growth accumulates faster than it can be dissipated by viscoelastic relaxation.
