Modeling fracture formation on growing surfaces

This thesis describes a framework for modeling fracture formation on differentially growing, bi-layered surfaces, with applications to drying mud and tree bark. Two different, physically based approaches for modeling fractures are discussed. First, an approach based on networks of masses and springs is described. Two important shortcomings of the mass-spring approach are then identified: a tendency of the fractures to align themselves to the underlying mesh, and an unclear relationship between the simulation parameters and the real material properties. The rest of the thesis is focused on the second approach to modeling fractures, based on solid mechanics and finite element method, which effectively addresses the shortcomings of the mass-spring based approach. Two types of growth are investigated: isogonic and uniform anisotropic. The growth is then incorporated within the framework of finite element methods, implemented using velocity vector fields. The growth tensor is used to verify the properties of the growth. A number of efficiency and quality enhancing techniques are also described for the finite element based approach. An adaptive mesh refinement around fracture tips is introduced, which reduces the total number of elements required. Construction of a temporary, local multi-resolution mesh around the fracture tips is described, which is used to calculate stresses at fracture tips with increased accuracy but without introducing any additional elements permanently into the model. Further, a general method for efficient recalculation of an equilibrium state is presented, which can be employed after localized changes are made to the model. Finally, an adaptive time step control is described, which automatically and efficiently determines the next optimal time step during simulation.