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

• 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

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，提出了计算随机分析的使用，以构建非线性随机构成定律的新建模和计算框架。在非线性材料的本构行为中建模不确定性是计算力学和材料力学的核心挑战。特别地，软生物组织（例如血管血管）表现出的大变异性是目前针对计算辅助手术的障碍，特定于患者的心血管疾病治疗以及广泛采用组织工程方法。在该项目中，提出了计算随机分析的使用，以构建非线性随机构成定律的新建模和计算框架。血管构建体的特定情况被目的选择为典型的应用，结合了强度强的各向异性和高水平的随机性。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，并将与大量材料（包括损坏的复合材料的情况）相关。在这项工作中促进的跨学科角度将使参与各个领域的学生（例如应用数学和材料科学）的广泛接触，并将通过当地高中的外展活动来引入理论和计算方面。这项研究的重点是针对非线性本构定律的计算随机分析。更具体地说，它旨在得出概率模型，这是一种在平滑的歧管和方法上采样的高性能计算环境，用于鉴定和验证与空间依赖的各向异性应变能函数。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明显推进新的信息理论类别的随机方法，其中可以从潜在的多尺度实验到粗尺度模拟的随机性来解释随机性。该项目将涉及一组方法论和理论发展，包括（1）基于物理学的随机现场模型以及一类PolyConvex存储的能量函数的采样算法的构建，以及（2）数据抑制方法的定义，用于数据差的逆向校准和验证模型的多验证验证。该新型框架将特别用于大规模的非线性模拟中，以研究具有患者特异性几何形状的随机血管构建体失败的可能性。

项目成果

Stochastic Modeling and identification of material parameters on structures produced by additive manufacturing

增材制造结构材料参数的随机建模和识别

• DOI: 10.1016/j.cma.2021.114166
• 发表时间: 2021
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Chu, Shanshan;Guilleminot, Johann;Kelly, Cambre;Abar, Bijan;Gall, Ken
• 通讯作者: Gall, Ken

Topology optimization under topologically dependent material uncertainties

拓扑相关材料不确定性下的拓扑优化

• DOI: 10.1007/s00158-019-02247-1
• 发表时间: 2019
• 期刊: Structural and Multidisciplinary Optimization
• 影响因子: 3.9
• 作者: Guilleminot, Johann;Asadpoure, Alireza;Tootkaboni, Mazdak
• 通讯作者: Tootkaboni, Mazdak

Stochastic multiscale modeling with random fields of material properties defined on nonconvex domains

在非凸域上定义材料属性随机场的随机多尺度建模

• DOI: 10.1016/j.mechrescom.2019.01.008
• 发表时间: 2019
• 期刊: Mechanics Research Communications
• 影响因子: 2.4
• 作者: Chu, S.;Guilleminot, J.
• 通讯作者: Guilleminot, J.

Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites

• DOI: 10.1016/j.cma.2018.12.036
• 发表时间: 2019-04
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: B. Staber;J. Guilleminot;Christian Soize;J. Michopoulos;A. Iliopoulos

A random field model for anisotropic strain energy functions and its application for uncertainty quantification in vascular mechanics

各向异性应变能函数的随机场模型及其在血管力学不确定性量化中的应用

• DOI: 10.1016/j.cma.2018.01.001
• 发表时间: 2018
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Staber, B.;Guilleminot, J.
• 通讯作者: Guilleminot, J.