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

该项目的目的是建立有效的数学公式和建立可靠的数值解程序，用于受大应变变形的随机超弹性材料多体系统的脱粘分析。这些系统提出的理论和计算挑战从单个物体的大变形到检测它们之间的接触和开口，再到估计临界载荷的概率分布，从而可能发生或不发生因失去接触而脱粘。尽管在许多天然和工程材料中，通过失去接触来脱粘是一种损伤引发和裂纹扩展的机制，但对它的研究还不够充分。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害，因此需要考虑数据分散的随机表示法。近年来，随机建模技术在工程和生物医学中的应用引起了人们越来越大的兴趣，其中稀疏和近似观测数据校准的材料参数的不确定性是不容忽视的。在寻求估计材料不确定性的过程中，随机有限弹性将随机特征引入有限弹性理论，以表征材料弹性响应的变异性，而材料的弹性响应很少是确定性的。在这个框架内，随机超弹性材料是由应变能函数描述的高级唯象模型，其中参数是由概率密度函数表征的随机变量。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，并能够将不确定性从输入数据传播到输出量。在这种背景下，拟议的研究是新颖的，并将有助于工程、生物力学和材料科学中许多相关研究领域的发展。具体应用包括大应变的软生物材料(如植物、关节软骨、动脉壁、脑组织)和工程结构(如软驱动器、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.