Stochastic Constitutive Laws in Nonlinear Mechanics: Application to the Multiscale Modeling of Arterial Walls for Robust Vascular Grafting

非线性力学中的随机本构定律：在稳健血管移植的动脉壁多尺度建模中的应用

基本信息

批准号：
1726403
负责人：
Johann Guilleminot
金额：
$ 29.71万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1726403&HistoricalAwards=false
关键词：
Stochastic Constitutive Laws Nonlinear Mechanics

项目摘要

In this project, the use of computational stochastic analysis is put forward in order to construct a new modeling and computational framework for nonlinear stochastic constitutive laws. Modeling the uncertainties in the constitutive behavior of nonlinear materials is a central challenge in computational mechanics and mechanics of materials. In particular, the large variability exhibited by soft biological tissues, such as vascular vessels, is a current roadblock to computational assisted surgeries, patient-specific treatments for cardiovascular diseases and wide adoption of tissue engineering approaches. In this project, the use of computational stochastic analysis is put forward in order to construct a new modeling and computational framework for nonlinear stochastic constitutive laws. The specific case of vascular constructs is purposely chosen as a prototypical application combining strong anisotropy and a high level of stochasticity. The research supported by this award will enhance the predictive capabilities of simulations involving biological materials, such as arterial and brain tissues, and will be relevant to a large class of materials, including the case of damaged composites. The interdisciplinary standpoint promoted in this effort will enable a broad exposure to students involved in various fields, such as applied mathematics and materials science, and will allow theoretical and computational aspects to be introduced through outreach activities in local high schools. This research is focused on computational stochastic analysis for nonlinear constitutive laws. More specifically, it aims at deriving probabilistic models, a high-performance-computing environment for sampling on smooth manifolds and methodologies for the identification and validation of spatially dependent anisotropic strain energy functions. By addressing the proper mathematical randomization of nonlinear constitutive equations in close relation with calibration and validation concerns, the research supported by this award will notably advance a new information-theoretic class of stochastic methods where randomness can be accounted for from potentially multiscale experiments to coarse-scale simulations. The project will involve a set of methodological and theoretical developments, including (1) the construction of physics-based random field models and sampling algorithms for a class of polyconvex stored energy functions, and (2) the definition of methodologies for the data-poor inverse calibration and multiscale validation of the stochastic models. The novel framework will notably be used within large-scale nonlinear simulations to investigate the probability of failure of stochastic vascular constructs with patient-specific geometries.

在该项目中，提出使用计算随机分析来构建非线性随机本构律的新建模和计算框架。对非线性材料本构行为的不确定性进行建模是计算力学和材料力学的核心挑战。特别是，血管等软生物组织表现出的巨大变异性是当前计算辅助手术、心血管疾病患者特异性治疗和组织工程方法广泛采用的障碍。在该项目中，提出使用计算随机分析来构建非线性随机本构律的新建模和计算框架。特意选择血管结构的具体情况作为结合了强各向异性和高水平随机性的原型应用。该奖项支持的研究将增强涉及生物材料（例如动脉和脑组织）的模拟的预测能力，并将与一大类材料（包括受损复合材料的情况）相关。这项工作所提倡的跨学科立场将使学生能够广泛接触应用数学和材料科学等各个领域，并允许通过当地高中的外展活动介绍理论和计算方面的内容。这项研究的重点是非线性本构律的计算随机分析。更具体地说，它的目标是导出概率模型、用于在平滑流形上采样的高性能计算环境以及用于识别和验证空间相关的各向异性应变能函数的方法。通过解决与校准和验证问题密切相关的非线性本构方程的适当数学随机化，该奖项支持的研究将显着推进一类新的信息论随机方法，其中可以考虑从潜在的多尺度实验到粗略的随机性。规模模拟。该项目将涉及一系列方法和理论发展，包括（1）构建基于物理的随机场模型和一类多凸存储能量函数的采样算法，以及（2）数据贫乏的方法的定义随机模型的逆校准和多尺度验证。该新颖的框架将特别用于大规模非线性模拟，以研究具有患者特定几何形状的随机血管结构的失败概率。