Modeling and Simulation of Thermomechanical Elasto-viscoplastic Material and Ductile Fracture with the Material Point Method
This dissertation focuses on applications and extensions of the Material Point Method(MPM) in simulating ductile fracture and thermomechanical material behavior for baking and cooking. We conclude the two major contributions as follows:
First, we present novel techniques for simulating and visualizing ductile fracture with MPM. We utilize traditional particle-based MPM [SZS95] as well as the Lagrangian energy formulation of [JSS15] that formulates the deformation gradient and potential energy through a tetrahedron mesh. We model failure and fracture via elasto-plasticity with damage. Material shows elastic behavior until the deformation exceeds a Rankine or von Mises yield criterion, at which point irreversible damage starts to occur. We introduce a softening model that shrinks the yield surface until a damage threshold is reached. Once damaged the material Lam� coefficients are modified to represent failure. We design visualization techniques for rendering the boundary of the material and its intersections with evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to represent crack surfaces. For traditional particle-based MPM we use an initial Delaunay tetrahedralization to connect randomly initialized MPM particles and form a reference mesh. Our visualization technique is a postprocess and can be run separately after the MPM simulation for efficiency. We demonstrate the strength of our method with a number of challenging simulations of ductile failure with considerable and persistent self contact.
Our second contribution is a Material Point Method for visual simulation of baking breads, cookies, pancakes and similar materials. We develop a novel thermomechanical model using mixture theory to resolve interactions between individual water, gas and solid species. Heat transfer with thermal expansion is used to model thermal variations in material properties. Water based mass transfer is resolved through the porous mixture. Gas represents carbon dioxide produced by leavening agents in the baking process, and the solid component is modeled as a visco-elastoplastic material to represent its varied and complex rheological properties. Water content in the mixture reduces during the baking process according to Fick’s Law which contributes to the drying and cracking of crust at the material boundary. Carbon dioxide gas produced by leavening agents during baking creates internal pressure that causes rising. The visco-elastoplastic model for the dough is temperature dependent and is used to model melting and solidification. We discretize the governing equations using a novel Material Point Method designed to track the solid phase of the mixture.