Wolfram Computation Meets Knowledge

Wolfram Summer School


Luca Di Stasio

Summer School

Class of 2012


In 2010, Luca received a BSc in aerospace engineering from Politecnico di Milano, Italy, and he is currently enrolled in the double degree program EAGLES (Engineers as Global Leaders for Energy Sustainability). In this framework he received in 2012 a MSc in mechanical engineering from Drexel University majoring in advanced dynamics and robust control systems, and next fall he will be hosted at Universidad Politecnica de Madrid, Spain, to write his master thesis to complete the requirements for the MSc in space engineering, granted by Politecnico di Milano, Italy. Luca is deeply interested in mathematics, physics, and engineering and in general in theoretical and applied sciences; he is a lover of literature, architecture, art, and music, and he studied cello for about ten years. His main research interest is the study of multiscale and multiphysics problems such as turbulence, combustion, crack formation and propagation, fluid-structure interaction, bio-mechanics, and development of new methods to more accurately model and understand such complex phenomena. At Drexel, he has recently taken part into a project focusing on the study of the talus morphology and into a second research regarding the design of a nanoscale magnetomechanical resonator.

Project: Modeling Complex Patterns of Crack Propagation: Branching and Merging Mechanisms


The development of accurate models and simulations is becoming increasingly important in fault detection and prevention techniques applied to a wide variety of engineered systems. The recent advances in measurement devices technology has provided the designer an incredible amount of data related to acoustic, thermal, and optic behavior of the material subject to crack generation and propagation mechanisms. The lack of a reliable model prevents a correct interpretation of these data and makes predictions of future evolution difficult to be performed. The aim of this project is to propose an alternative approach to the development of a model for crack propagation by applying the NKS method. The problem firstly addressed is the simulation of mechanisms of crack branching and merging in 2D using a set of simple rules; the features of the resulting pattern are then considered and boundaries’ shapes, crack diffusion properties, and frequencies of branching and merging are studied. Finally, a method to relate the obtained model to the experimental observations is suggested.

Modeling assumptions

The phenomenon of crack generation and propagation is strictly related to the meso- and micro-structure of the material considered, as the experimental observations retrievable from the literature have shown. Although still far from a comprehensive understanding of the underlying mechanisms, studies conducted over the last 150 years have agreed on the presence of common features and basic functional principles driving the crack growth in different materials—mainly, its dependence on the elastic and plastic properties of the material and its relationships with the energy state of the system. On this ground, a variety of methods has been developed and proposed in which calculus of variations, partial differential equations, and integro-differential methods are the fundamental tools for modeling the problem; starting from such analytical models, numerical simulations have been shaped usually with the use of finite element methods, extended finite element methods, and finite difference methods. The focus has usually been on the dynamic and energetic behavior of the system, obtaining the crack shape as a final result. In this project, a different approach is considered: the kinematic behavior is addressed under the assumption that the crack shape can be reconstructed through the application of a suitable and known set of deterministic rule. The micro-/meso-structure is assumed to be known in the form of a digital image, either from some sort of experimental observation or as a reconstructed pattern simulated by another program, and it constitutes the background on which the designed program for crack propagation runs, giving as output the crack shape. The micro-/meso-structure and, similarly, the pattern adopted to represent it are assumed to be unaffected by the presence of the crack: the latter propagates in the structure causing only the breaking of the material, and no other effect or change is produced in the neighboring structure neither in the short nor in the long range. A quasi-1D geometry is considered: the crack is assumed to propagate in a thin plate moving from the top toward the bottom, and thus the vertical linear dimension coincides with the time dimension. From the kinematic point of view, the crack is considered to be in general capable of branching, merging, moving either to the right or to the left, going straight, or dying out in its evolution. The actual behavior is determined by the particular set of rules adopted each time.

Favorite Four-Color, Four State Turing Machine

RRule 143605065095165251237134