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.

薄壳模拟是科学计算的基础工具。它们用于分析囊泡和细胞膜等生物结构的行为，模拟织物和复合材料的变形，在手术训练和可视化工具中预测皮肤的疤痕和皱纹，以及分析建筑物结构元件的屈曲和皱折和车辆。这项研究将建立新的算法，以前所未有的效率模拟薄弯曲材料（如织物、纸张或金属板）的物理行为，而目前这种模拟非常困难且计算成本高昂，因为像一张纸或布这样的薄物体会弯曲它们比拉伸更容易，并且更喜欢以复杂的几何方式弯曲和压皱，而不是压缩。而且，这种复杂性是不可预测的、混乱的；即使对于相同负载下的相同物体，皱纹的确切模式也可能有很大差异。最后，预测薄物体在与自身和环境发生摩擦接触时的行为尤其具有挑战性；由于薄的几何形状，必须使用昂贵的碰撞检测和响应算法来确保薄部件不会相互穿透，无论它们被多快或多强力地推到一起。为了使薄材料模拟在工程中更加实用，设计和机器人应用（其中性能至关重要），该项目将开发一个更有效、更简化的模型来模拟薄材料的变形。借用连续介质力学中的张力场方法的关键见解是，薄物体的行为由穿过材料的张力线主导，而压缩和弯曲引起的细尺度皱纹的解决成本极高，但对解决问题贡献甚微。物体的粗略形状或机械行为。通过利用这种洞察力并将计算工作集中于跟踪和模拟张力线，可以在不牺牲精度的情况下显着提高薄壳模拟的性能。换句话说，在纯张力区域，弹性膜能量是凸的，标准壳有限元方法表现良好。而在纯压缩或混合拉伸和压缩的区域中，会发生屈曲，因为薄材料的抗压缩性和抗弯曲性之间存在尺度分离，并且壳体的屈曲后状态包含许多高度非线性、复杂的皱纹和然而，通过忽略皱纹并将壳体视为与壳体上的拉应力方向对齐的一维曲线的集合，仍然可以近似壳体的粗略形状。详细的工作计划将包括张力主导表面、混合应力表面以及接触和摩擦方面的工作。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。