Nonlinear Thermomechanics of Accretion

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

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.