Variational approaches to defect mechanics

布尔丹1312739 这个项目的目标是有助于发展，分析和实施变分模型的力学缺陷的固体，归纳从第一原理，分析使用相同的数学方法，并在并行超级计算机上实现兼容的数值框架。 具体而言，研究者研究了一个概念，作为替代全球最小率无关的材料模型的一致性演化。 这些演变是基于临界性和能量平衡，避免了一些全球最小化的矛盾，同时保持兼容的第一原则。 研究人员还开发了一种新的，严格的，有效的数值方法塑性，也基于变分模型。 围绕页岩中的水力刺激，地热田附近的地震活动和沉降，以及由坍塌的人造洞穴和从含水层过度抽水引起的天坑的争议突出了技术如何领先于对固体故障的预测性理解。 本项目的目标是研究缺陷力学的一致模型。 这些断裂、损伤和塑性模型在理论上有很好的基础，但也适用于实际情况。 它们在并行超级计算机上实现，可以很容易地组合起来研究复杂的问题。 作为应用，研究人员研究了导致表面天坑的深层地下盐丘断裂，薄膜断裂，这通常用于涡轮机的热障涂层，以及微机械设备和传感器制造中的损坏。 该项目的成果影响到从地质力学到结构工程的各个领域和行业。

Bourdin1312739 The goal of this project is to contribute to the development, analysis, and implementation of variational models for the mechanics of defects in solids, derived inductively from first principles, analyzed using the same mathematical methodology, and implemented on parallel supercomputers in a compatible numerical framework. Specifically, the investigator studies a concept of thermodynamically consistent evolutions as an alternative to global minimality for rate-independent material models. These evolutions are based on criticality and energy balance and avoid some of the paradoxes of global minimization while remaining compatible with first principles. The investigator also develops a novel, rigorous, and efficient numerical approach to plasticity, also based on a variational model. The controversies around hydraulic stimulation in gas shales, induced seismicity and subsidence near geothermal fields, and sinkholes caused by collapsing made-man caverns and over-extraction of water from aquifers highlight how technology has gotten ahead of the predictive understanding of failure in solids. The goal of this project is to study consistent models for the mechanics of defects. These models for fracture, damage, and plasticity are well-rooted in theory yet applicable to realistic situations. They are implemented on parallel supercomputers in such a way that they can easily be combined in order to study complex problems. As applications, the investigator studies fracture of deep underground salt domes leading to surface sinkholes, fracture in thin films, which are commonly used in thermal barrier coatings in turbines, and damage in the manufacturing of micro-mechanical devices and sensors. The outcomes of this project affect diverse areas and industries ranging from geo-mechanics to structural engineering.