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

随机超弹性材料多体系统脱粘状态极限分析

基本信息

批准号：
EP/S028870/1
负责人：
Angela Mihai
金额：
$ 37.06万
依托单位：
CARDIFF UNIVERSITY
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2019
资助国家：
英国
起止时间：
2019 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FS028870%2F1
关键词：
Limit analysis debonding states multi

项目摘要

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.

本课题旨在建立大应变变形下随机超弹性材料多体系统脱粘分析的有效数学公式和可靠的数值解程序。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，到检测它们之间的接触和开口，到估计临界载荷的概率分布，以便通过失去接触可能发生或不发生脱粘。尽管在许多天然材料和工程材料中，由于失去接触而产生的剥离是一种损伤起裂和裂纹扩展的机制，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伤，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，在这些技术中，根据稀疏和近似观测数据校准的材料参数中的不确定性是不可忽视的。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可变性，而材料弹性响应很少是确定性的。在此框架内，随机超弹性材料是由应变-能量函数描述的高级现象学模型，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，并且能够将不确定性从输入数据传播到输出量。在这种背景下，提出的研究是新颖的，将有助于在工程，生物力学和材料科学的许多相关研究领域的发展。具体应用包括大应变下的软生物材料（如植物、关节软骨、动脉壁、脑组织）和工程结构（如软致动器、3D打印复合材料）。