Theoretical and Numerical Framework for Extrusion-Based Additive Manufacturing Applications
Advisor: Professor Arif Masud
Abstract
The main objective of this work is to develop a theoretical and computational framework to model extrusion-based additive manufacturing (EB-AM) processes. The major components of this work are: (i) modeling materials with arbitrary compressibility, (ii) modeling the material addition in EB-AM, and (iii) modeling evolving materials under loading.
Commonly used materials in EB-AM, such as polymer and concrete, can feature a wide range of compressibilities. In the beginning of the curing process, the materials are nearly incompressible, but the compressibility increases as they cure. Therefore, it is desirable to have a unified formulation that applies to materials with arbitrary compressibility. Starting from a compressible model, a displacement-pressure formulation is derived via Legendre transform. Then, a stabilized finite element method based on variational multiscale method is developed to solve the resulting mixed initial-boundary-value problem. The stabilization allows for arbitrary combinations of shape functions for the displacement and pressure field. In addition, a novel time integration scheme is introduced to convert any explicit or implicit scheme into a stable scheme that preserves the determinant of the integrand.
In their initial stage, materials used in EB-AM have a relatively low stiffness, and the manufactured structure may undergo significant deformation or even failure due to self-weight. Therefore, the fabrication plan must allow enough time for the material to cure and gain stiffness. To simulate the effect of the process parameters, a method to model the material addition in EB-AM is proposed. The method is based on controlling material parameters at each integration point. The method's flexibility accommodates various type of formulations and can be easily implemented in existing finite element codes.
Another important aspect of EB-AM is to model the mechanical response of evolving materials under loading. In this work, it is shown that the second law of thermodynamics implies the existence of inelastic processes in material evolution due to curing. This finding is validated by comparison with experimental data. To model this behavior, an internal variable is introduced to model the inelastic strain associated with curing, and the corresponding evolution equation is derived.
The proposed framework is employed in various settings with elastic, viscoelastic and elastoplastic materials. It is also flexible enough to be used in contact-friction and thermo-chemo-mechanical problems. Applications of the framework to model concrete printing and frontal polymerization are presented
