CHS: Small: Efficient Simulation of Thin Materials With Discrete Tension Field Theory

CHS：小型：利用离散张力场理论对薄材料进行有效模拟

基本信息

批准号：
1910274
负责人：
Paul Vouga
金额：
$ 49.41万
依托单位：
University of Texas at Austin
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2022-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1910274&HistoricalAwards=false
关键词：
CHS Small Efficient Simulation Thin

项目摘要

Thin shell simulations are a foundational tool in scientific computing. They are used to analyze the behavior of biological structures such as vesicles and cell membranes, to simulate deformation of fabrics and composites, to predict scarring and wrinkling of skin in surgery training and visualization tools, and to analyze buckling and crumpling of structural elements in buildings and vehicles. This research will establish new algorithms for simulating the physical behavior of thin curved materials such as fabric, paper, or sheet metal, with unprecedented efficiency, whereas such simulations currently are notoriously difficult and computationally expensive because thin objects like a sheet of paper or cloth bend far more readily than they stretch and will prefer to buckle and crumple in geometrically complex ways rather than compress. Moreover, this complexity is unpredictable and chaotic; the exact pattern of wrinkles can vary wildly even for identical objects under identical loads. Finally, predicting how a thin object behaves under frictional contact with itself and the environment is especially challenging; due to the thin geometry, expensive collision detection and response algorithms must be used to ensure that thin parts do not tunnel through each other, no matter how quickly or forcefully they are pushed together.To make thin material simulations more practical for use in engineering, design, and robotics applications, where performance is critical, this project will develop a more efficient, simplified model for how to simulate deformation of thin materials. The key insight, borrowed from the tension field approach in continuum mechanics, is that the behavior of thin objects is dominated by lines of tension through the material, while fine-scale wrinkles induced by compression and bending are extraordinarily expensive to resolve yet contribute little to the object's coarse-scale shape or mechanical behavior. By exploiting this insight and focusing computational effort on tracking and simulating the lines of tension, the performance of thin shell simulations can be substantially improved without sacrificing accuracy. Put another way, in regions of pure tension the elastic membrane energy is convex and standard shell finite element methods perform well. Whereas in regions of pure compression, or mixed tension and compression, buckling occurs since there is a scale separation between the resistance of thin materials to compression and to bending, and the post-buckled state of the shell contains many highly nonlinear, complex wrinkles and creases, yet the coarse shape of the shell can nevertheless be approximated by ignoring the wrinkles and treating the shell as a collection of 1D curves aligned to the tensile stress directions on the shell. The detailed work plan will comprise work on tension-dominated surfaces, mixed-stress surfaces, and contact and friction.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

薄外壳模拟是科学计算中的基础工具。它们用于分析生物结构（例如囊泡和细胞膜）的行为，模拟织物和复合材料的变形，以预测手术训练和可视化工具中皮肤的疤痕和皱纹，并分析建筑物和车辆中结构元素的屈曲和弯曲。这项研究将建立新的算法，以模拟薄弯曲材料的物理行为，例如织物，纸张或钣金，并具有前所未有的效率，而当前的模拟众所周知，众所周知，这在计算上是昂贵的，因为薄的物体（如一张纸或布料）比伸展和弯腰更容易弯曲，而不是在地球上弯曲而不是压缩的方式而不是压缩。而且，这种复杂性是不可预测和混乱的。即使对于相同的载荷下相同的对象，皱纹的确切模式也会差异很大。最后，预测薄物物体在与自身和环境之间的摩擦接触下的行为特别具有挑战性。由于几何形状，必须使用昂贵的碰撞检测和响应算法来确保薄零件不会彼此隧道，无论将它们推到多快或有力地被压在一起。要使薄材料模拟在工程，设计和机器人应用中更实用，在绩效的地方，重要的是，该项目将更加有效地模拟材料的材料，以便在效率上进行更重要的模拟模拟材料的模拟材料，从而更加有效地模拟材料。从连续力学中借用的张力场方法借用的关键见解是，薄物体的行为是通过材料通过张力线主导的，而由压缩和弯曲引起的细尺度皱纹则非常昂贵，无法解决，但对物体的粗尺度形状或机械行为几乎没有任何贡献。通过利用这种洞察力并将计算工作集中在跟踪和模拟张力线上，可以在不牺牲准确性的情况下显着改善薄壳模拟的性能。换句话说，在纯张力区域中，弹性膜能是凸，标准壳有限元方法的性能很好。 Whereas in regions of pure compression, or mixed tension and compression, buckling occurs since there is a scale separation between the resistance of thin materials to compression and to bending, and the post-buckled state of the shell contains many highly nonlinear, complex wrinkles and creases, yet the coarse shape of the shell can nevertheless be approximated by ignoring the wrinkles and treating the shell as a collection of 1D curves aligned to the tensile stress directions在外壳上。详细的工作计划将包括有关张力主导的表面，混合压力表面以及联系和摩擦的工作。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评估评估标准来通过评估来支持的。