A mechanistic understanding of morphogenesis in biology, the fabrication of advanced meta surfaces with specific functionalities and structures with enhanced energy dissipation often have in common that the combined effects of energy dissipation due to viscoelasticity and a loss of stability govern both their mechanical response and their final forms. In this paper we show that the interplay between viscoelasticity and multistability crucially influences the evolution of deformations in viscoelastic structures undergoing large deformations. The influence is studied on a prototypical system of a uniaxially growing film on a semi-infinite planar viscoelastic substrate, where it is shown that during the evolution of deformation the choice of multiple developing modes is greatly affected by this interplay. For the analysis of the underlying mechanics of the mode competition in the post-buckling regime, when the system undergoes large deformations, a 3D general finite-strain visco-hyperelastic theory is built. It includes kinematic and material nonlinearities in the film and in the substrate. For the case of ramp-loading time functions the phase space of the solutions is characterized and the evolution of a deformation pattern is analyzed. We find that the interaction between multistability and viscoelasticity greatly increases the evolution time of the system and that the growth rate and viscoelastic stress-relaxation rate influence the choice of the final equilibrium deformation state of the structure. This shows that viscoelastic structures can evolve into (meta)stable equilibrium states that are unattainable using purely elastic structures. The nonlinear problem is solved numerically with the use of the finite-element method. In parallel, we develop analytical solutions for a simplified problem that is based on Föppl–von Karman plate kinematics to describe the mechanics of the film and substrate that is modeled as a 2D linear-viscoelastic continuum. A remarkably good match between the analytical and the numerical results was obtained.

对生物学形态发生的机械理解，具有特定功能的高级元表面的制造和具有增强能量耗散的结构通常具有共同点，即由于粘弹性和稳定性损失引起的能量耗散的综合影响决定了它们的机械响应和它们的最终形式。在本文中，我们表明粘弹性和多稳定性之间的相互作用对经历大变形的粘弹性结构的变形演化具有至关重要的影响。对半无限平面粘弹性基板上单轴生长薄膜的原型系统的影响进行了研究，结果表明，在变形演化过程中，多种发展模式的选择受这种相互作用的影响很大。为了分析后屈曲状态下模式竞争的基本力学，当系统经历大变形时，建立了 3D 通用有限应变粘超弹性理论。它包括薄膜和基板中的运动学和材料非线性。对于斜坡加载时间函数的情况，解决方案的相空间被表征，并且分析了变形模式的演变。我们发现多稳定性和粘弹性之间的相互作用大大增加了系统的演化时间，并且增长率和粘弹性应力松弛率影响了结构最终平衡变形状态的选择。这表明粘弹性结构可以演化为使用纯弹性结构无法达到的（元）稳定平衡状态。使用有限元方法对非线性问题进行数值求解。同时，我们针对基于 Föppl–von Karman 板运动学的简化问题开发了解析解决方案，以描述被建模为 2D 线性粘弹性连续体的薄膜和基板的力学。获得了解析结果和数值结果之间非常好的匹配。