Resumen:

There are several problems in physics that involve the presence of interfaces between different phases and the evolution of these interfaces with time. These problems include phase transformation, solidification, fracture, Li-ion transport in batteries, etc.
In this work, the phenomenon of fracture within diffuse interphase approaches (continuous framework) will be studied, specifically the well-known phase-field fracture. The origins and motivations of this method are presented, starting from Griffith’s theory.
To prevent the appearance of cracks due to compressive stresses, a series of formulations that make the distinction between compressive and tensile stresses will be taken into account, analyzing the advantages and disadvantages of each of them.
The phase field-fracture model presents a system of coupled partial differential equations; for its resolution, a Newton Raphson solver is used with a staggered scheme, making use of the finite element method.
Finally, a series of widely known simulations in the fracture mechanics community will be carried out, verifying and obtaining conclusions from the implementation done