Limit analysis of debonding states in multi-body systems of stochastic hyperelastic material

本计画的目的是建立有效的数学公式，并建构可靠的数值解程序，以分析随机超弹性材料在大应变变形下的多体系统的脱粘问题。这些系统提出的理论和计算挑战范围从单个物体的大变形，到它们之间的接触和开口的检测，到临界载荷的概率分布的估计，使得通过接触损失可能发生或不发生脱粘。尽管在许多天然和工程材料中，通过接触损失引起的脱粘是损伤引发和裂纹扩展的机制，但它尚未得到充分的研究。对于这些材料，基于平均数据值的确定性方法可能会大大低估或高估损坏，并且还需要考虑数据分散的随机表示。 近年来，人们对工程和生物医学应用中的随机建模技术越来越感兴趣，其中校准到稀疏和近似观测数据的材料参数的不确定性不容忽视。在寻求估计材料的不确定性，随机有限弹性引入随机功能到有限弹性理论，以消除材料的弹性响应的变化，这是很少确定的。在这个框架内，随机超弹性材料是先进的唯象模型描述的应变能函数的参数是随机变量的概率密度函数。这些模型依赖于熵（或不确定性）的概念和离散概率分布的最大熵原理，并且能够将不确定性从输入数据传播到输出量。在这种情况下，拟议的调查是新颖的，并将有助于许多相关的研究领域的工程，生物力学和材料科学的发展。具体应用包括软生物材料（例如，植物、关节软骨、动脉壁、脑组织）和工程结构（例如，软致动器，3D打印复合材料）。

The aim of this project is to establish effective mathematical formulations and construct reliable numerical solution procedures for the debonding analysis of multi-body systems of stochastic hyperelastic material subject to large strain deformations. The theoretical and computational challenges raised by these systems range from the large deformation of individual bodies, to the detection of contact and openings between them, to the estimation of the probability distribution for the critical load such that debonding through loss of contact can or cannot occur. Even though debonding through loss of contact is a mechanism for damage initiation and crack propagation in many natural and engineered materials, it has been insufficiently investigated. For these materials, deterministic approaches, which are based on average data values, can greatly underestimate or overestimate the damage, and stochastic representations accounting also for data dispersion are needed. In recent years, there has been a growing interest in stochastic modelling techniques for engineering and biomedical applications, where uncertainties in the material parameters calibrated to sparse and approximate observational data cannot be ignored. In the quest for estimating material uncertainties, stochastic finite elasticity introduces stochastic features into the finite elasticity theory in order to characterise the variability in the elastic responses of materials, which are rarely deterministic. Within this framework, stochastic hyperelastic materials are advanced phenomenological models described by a strain-energy function where the parameters are random variables characterised by probability density functions. These models rely on the notion of entropy (or uncertainty) and on the maximum entropy principle for a discrete probability distribution, and are able to propagate uncertainties from input data to output quantities. In this context, the proposed investigation is novel and will contribute to the development of many associated research areas in engineering, biomechanics, and materials science. Specific applications include soft biological materials (e.g., plants, articular cartilages, arterial walls, brain tissue) and engineering structures (e.g., soft actuators, 3D printing composites) at large strains.