Nonlinear Thermomechanics of Accretion

这项研究计划将侧重于制定一个热力学理论的吸积（表面生长）。吸积是可变形固体通过在其边界上逐渐添加材料而生长，例如，增材制造增材制造，如3D打印，毫无疑问是制造业革命时代的核心部分，它在我们的日常生活中发挥着越来越大的作用。它已经发现了许多应用，从业余艺术到机械，航空航天和医疗等各个行业的精密制造。尽管增材制造具有巨大的潜力和商业成功，但在增材制造完全融入工业之前，仍有许多挑战有待克服。从力学的角度来看，理解并能够预测和控制残余应力（或内力）是至关重要的，以便定制和设计一个增生过程，以这种方式，制造的零件满足其工作条件下所需的属性。该研究计划将通过建立一个基于课程开发的教育和外展计划，以及通过格鲁吉亚理工学院的教育外展中心为K-12和代表性不足的少数民族外展提供补充。在自然界和工程中，许多物体/结构是通过在运动中的现有物体的边界上添加材料来逐渐构建的。自然界中吸积过程的例子是生物组织和晶体的生长，火山岩和沉积岩的形成，冰结构的形成，行星的形成等。本研究计划的目标是制定弹性体的非线性耦合扩散-热-力学，该弹性体由于在其边界上添加新材料而同时变形而生长。有四个直接的问题，任何力学/数学模型的吸积应该能够回答：i）什么是状态的变形和应力在一个过程中的吸积？ii）在吸积过程结束时和去除外部载荷后，物体内部应力（残余应力）的状态是什么？iii）现在，该附加结构处于使用载荷下。如何分析这样的结构？iv）为了建造具有所需的残余应力分布和在使用载荷下的最佳刚度的结构，应如何设计增大过程？该研究计划旨在制定一个非线性理论的吸积力学，将使人们能够回答这些问题。 在这个项目中，一个新的吸积理论将被开发出来，该理论将使用微分几何方法来解释有限应变，而不需要任何对称性假设。这个奖项反映了NSF的法定使命，并且通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research program will focus on formulating a thermo-mechanical theory of accretion (surface growth). Accretion is the growth of a deformable solid by the gradual addition of material on its boundary, for e.g., additive manufacturing. Additive manufacturing, such as 3D printing, is unarguably a central part of what seems to be a revolutionary era in manufacturing and it is playing an ever increasing role in our everyday lives. It has already found many applications ranging from hobbyist art to precise manufacturing in various industries such as mechanical, aerospace, and medical. Despite its tremendous potential and commercial success, many challenges have yet to be overcome before additive manufacturing can be fully integrated in industry. From a mechanics point of view, understanding and being able to predict and control the residual stresses (or internal forces) is crucial in order to tailor and design an accretion process in such a way that the manufactured piece meets the required properties in its working conditions. The research program will be complemented by establishing an educational and outreach program based on curriculum development, and K-12 and underrepresented minority outreach through an educational outreach center at Georgia Tech. In nature and engineering many objects/structures are built gradually by adding material on the boundary of an existing object that is in motion. Examples of accretion processes in nature are the growth of biological tissues and crystals, the build-up of volcanic and sedimentary rocks, of ice structures, the formation of planets, etc. Examples in technological applications are additive manufacturing (3D printing), metal solidification, the build-up of concrete structures in successive layers, and the deposition of thin films. The goal of this research program is to formulate the nonlinear coupled diffusion-thermo-mechanics of elastic bodies that grow as a result of addition of new material on their boundary while deforming at the same time. There are four immediate questions that any mechanical/mathematical model of accretion should be able to answer: i) What is the state of deformation and stresses during a process of accretion? ii) At the end of the accretion process and after removing the external loads, what is the state of internal stresses (residual stresses) in the body? iii) Now this accreted structure is put under service loads. How can one analyze such a structure? iv) How should an accretion process be designed in order to build structures with the desired distribution of residual stresses, and the optimum stiffness under service loads? The research program aims to formulate a nonlinear theory of accretion mechanics that would enable one to answer these questions. In this project, a new theory of accretion will be developed that accounts for finite strains without any symmetry assumptions using a differential geometry approach.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.