自然界中生长与形貌的关系是发育生物学研究的重要内容之一，研究生物软组织的生长失稳，有助于理解生物组织中不同形貌形成的力学机制，并为某些疾病的诊断和治疗提供参考，因而引起了力学、生物医学等领域的广泛关注。本文基于连续介质力学方法，对几种典型几何构型生物软组织的失稳行为开展了理论分析、数值模拟和实验研究。首先，观察了花瓣表皮角质层上微褶皱的形成过程，进而探究了花瓣表面微褶皱形成的力学机制。实验测量表明，非均匀组织生长引起的表面失稳是微褶皱形成的关键因素。通过将表面蜡层等效为膜，角化层和表皮细胞等效为基底层，从而将花瓣表面褶皱形成过程简化为膜－基系统的失稳问题。理论预测的褶皱波长与实验结果吻合。进一步采用有限元方法模拟了微褶皱形成和演化的过程，并探讨了微褶皱的形成对花瓣浸润性质的影响。建立了单层膜夹层组织失稳的理论模型，通过理论分析求得了临界失稳的发生条件和失稳特征，并采用有限元方法对结果进行了验证。通过有限元方法对单层膜夹层组织的后屈曲演化进行了模拟，给出了双周期形貌出现的条件。进一步研究了双层膜夹层组织的失稳问题，理论分析和有限元模拟表明，随着中间层基底模量变化，可能出现长波失稳和短波失稳两种模态。此外，利用有限元方法模拟了双层和多层膜夹层组织的后屈曲演化，结果表明在多层膜夹层组织的后屈曲中，可能出现多级失稳形貌。发展了可考虑外部生物环境影响生物体内圆柱管腔结构失稳的理论分析模型。通过将载流物体的力学效应等效为内压和表面张力的作用，研究其对失稳发生和发展的影响。讨论了粘膜厚度、粘膜和粘膜下层模量比等因素对临界失稳的影响。结果表明，内压使失稳的临界生长因子增大，并影响后屈曲演化中形貌转变时的生长因子；表面张力使系统更稳定，提高了临界生长因子，并使临界波数减少。最后，利用考虑体生长效应的增量变形理论，分析了圆柱管腔结构的三维失稳问题。结果表明，圆柱外边界自由时，系统可能出现欧拉失稳、轴对称失稳和四方失稳这三种不同的失稳形貌；圆柱外边界固定时，系统出现轴对称失稳和四方失稳两种不同形貌。进一步给出了两种边界条件下，不同形貌出现的相图。并采用伪动力学方法对形貌的后屈曲演化进行了有限元模拟。
The relationship between growth and morphology is a significant content in developmental biology. Exploring the growth–induced wrinkling in soft tissues holds great importance in understanding the internal mechanical mechanism during morphologenesis, providing clue for the diagnosis of some diseases, and thus, it has attracted considerable attention in the fields of mechanics and biomedicine. Within the framework of continuum mechanics, we focus on the instability behavior of a few representative soft biological tissues through theoretical analysis, numerical simulations and experimental observations.First, a series of experiments are carried out to observe the formation process of minute wrinkles on petal cuticle. Based on experimental measurements, we propose that the competition between the anisotropic growth of epidermal cells and the isotropic secretion of wax dictates the formation of different wrinkling patterns on different flower petals. Besides, we establish a computational model, incorporated measured properties of the petal, to verify the wavelength of the morphology. A computational FEM model based on measured geometrical and mechanical parameters is constructed to reemerge the formation process of minute wrinkles. In addition, we explore the connection between wrinkles and wetting property of petals. Secondly, theoretical analysis and numerical simulations are performed to investigate the buckling and postbuckling behaviors of stiff films embedded in compliant soft tissues. A theoretical solution is derived for the critical strain and wavelength of a stiff film sandwiched between two different soft substrates. During postbuckling, the system may keep the sinusoidal buckling pattern or bifurcate into period-doubling morphology. A phase diagram which enables us to predict the morphological evolution in terms of the geometrical and material parameters of the system is established. Then the above analysis is extended to two or more parallel films embedded in compliant soft tissues. Different buckling modes i.e., short-wave mode, long-wave mode, and hierarchical mode, are found in such multilayer systems.Thirdly, the instability of a cylindrical tube consisting of a mucosal layer and a submucosal layer is investigated. We focus on the effects of internal pressure and surface tension on the critical growth factor and the mode number of surface wrinkling. And we also discuss the effects of geometrical and material parameters of the system on the morphological instabilities. It is found that the internal pressure plays a stabilizing role in the buckling and postbuckling of the system. Surface tension not only stabilizes the system but also reduces the critical mode number of surface patterns. Besides, the thinner the mucosal layer, the more significant the effect of surface tension.Finally, a three-dimensional model is established to analyze the instability of cylindrical tubular structures induced by the volumetric growth. We consider the different three-dimensional wrinkling patterns in cases of free and fixed boundary conditions. It is found that Euler buckling pattern, axial symmetrical pattern and checkerboard pattern may occur for free boundary condition, while axial symmetrical pattern and checkerboard pattern may occur under fixed boundary condition. Phase diagrams are established to predict the morphologies in terms of the geometrical and material parameters of the system. Besides, a pseudo dynamic method is adopted to simulate the postbuckling evolutions of different buckling patterns.
