7 research outputs found
A micromechanics-informed phase field model for brittle fracture accounting for the unilateral constraint
We propose a new direction-dependent model for the unilateral constraint
involved in the phase field approach to fracture and also in the continuous
damage mechanics models. The construction of this phase field model is informed
by micromechanical modeling through the homogenization theory, where the
representative volume element (RVE) has a planar crack in the center. The
proposed model is made closely match the response of the RVE, including the
frictionless self-contact condition. This homogenization approach allows to
identify a direction-dependent phase field model with the tension-compression
split obtained from cracked microstructures. One important feature of the
proposed model is that unlike most other models, the material degradation is
consistently determined without artificial assumptions or ad hoc parameters
with no physical interpretation, thus, a more realistic modeling is resulted.
With standard tests such as uniaxial loadings, three-point bending, simple
shear, and through-crack tests, the proposed model predicts reasonable crack
paths. Moreover, with the RVE response as a benchmark, the proposed model gives
rise to an accurate stress-strain curve under shear loads, more accurate than
most existing models
Orthogonal decomposition of anisotropic constitutive models for the phase field approach to fracture
We propose a decomposition of constitutive relations into crack-driving and
persistent portions, specifically designed for materials with
anisotropic/orthotropic behavior in the phase field approach to fracture to
account for the tension-compression asymmetry. This decomposition follows a
variational framework, satisfying the orthogonality condition for anisotropic
materials. This implies that the present model can be applied to arbitrary
anisotropic elastic behavior in a three-dimensional setting. On this basis, we
generalize two existing models for tension-compression asymmetry in isotropic
materials, namely the volumetric-deviatoric model and the no-tension model,
towards materials with anisotropic nature. Two benchmark problems, single
notched tensile shear tests, are used to study the performance of the present
model. The results can retain the anisotropic constitutive behavior and the
tension-compression asymmetry in the crack response, and are qualitatively in
accordance with the expected behavior for orthotropic materials. Furthermore,
to study the direction of maximum energy dissipation, we modify the surface
integral based energy release computation, , to account only for the
crack-driving energy. The computed energies with our proposed modifications
predict the fracture propagation direction correctly compared with the standard
G-theta method
Phase field approach to fracture : massive parallelization and crack identification
The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length parameter, which in turns restricts the maximum element size that can be used in a finite element mesh. In this work, we developed a massively parallel algorithm on the graphical processing unit (GPU) to alleviate this difficulty in the case of dynamic brittle fracture. In particular, we adopted the standard finite element method on an unstructured mesh combined with second order explicit integrators.
As the explicit methods fit nicely with the GPU paradigm especially in terms of thread and memory hierarchy, we solve an elastodynamic problem when the phase field update is based on a gradient flow, so that a fully explicit implementation is feasible. To ensure stability, we designed a time adaptivity strategy to account for the decreasing critical time step during the evolution of the fields.
We demonstrated the performance of the GPU-implemented phase field models by means of representative numerical examples, with which we studied the effect of the artificial viscosity, an artificial parameter to be input, and compared the crack path branching predictions from three popular phase field models. Moreover, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom.
One of the main ideas of the phase field method is to employ a smeared representation of discrete cracks. However, in some applications it is still convenient to have the explicit crack path available, or even to develop a mechanism to introduce crack paths to partially replace a smeared crack propagation model.
In this work, we presents a variational method to identify the crack path from phase field approaches to fracture. The method is proven to be successful not only for a simple curved crack but also for multiple and branched cracks. The algorithm employs the non-maximum suppression technique, a procedure borrowed from the image processing field, to detect a bounding area which covers the ridge of the phase field profile. After that, it is continued with the step to determine a cubic spline to represent the crack path and to improve it via a constrained optimization process. To demonstrate the performance of our method, we provide the results with three sets of representative examples. The developed algorithm can be combined with one on crack opening, for more elaborate interpretation of phase field simulations. This is the topic of the next part of the work.
In this dissertation, we also provide a variational way to calculate the crack opening from phase field approaches to fracture. We also demonstrate the performance of our method with three sets of representative examples, and verify the results with a proper benchmark.
Having the crack geometry available from a phase field approach can provide more elaborate interpretation of the phase field simulations. It may also offer a possibility of developing less expensive numerical schemes for a fluid-driven crack propagation of impermeable solids. This will be the topic of our future work.El método de phase field ha demostrado ser una herramienta importante en la mecánica de fractura computacional el cual no requiere el seguimiento complicado de una fractura y es capaz de predecir la nucleación y la ramificación. Sin embargo, el coste computacional de un método de este tipo es alto debido a un pequeño parámetro de regularización de longitud, que a su vez limita el tamaño del elemento máximo que se puede utilizar en una malla de los elementos finitos. En esta disertación, hemos desarrollado un algoritmo paralelo de forma masiva en la unidad de procesamiento gráfico (GPU) para aliviar esta dificultad en el caso de rotura frágil dinámica. En particular, hemos adoptado el método de los elementos finitos en una malla no estructurada combinada con integradores explÃcitos de segundo orden. A medida que los métodos explÃcitos encajan adecuadamente con el paradigma de la GPU especialmente en términos de hilo y la jerarquÃa de memoria, se resuelve un problema de elastodinámica cuando la actualización de phase field se basa en un flujo de gradiente, de modo que una implementación totalmente explÃcita es factible. Para asegurar la estabilidad, se diseñó una estrategia adaptativa de tiempo para tener en cuenta la disminución del paso de tiempo crÃtico durante la evolución de los campos. Hemos demostrado el rendimiento de los modelos de phase field GPU-implementado por medio de ejemplos numéricos representativos, con los que se estudió el efecto de la viscosidad artificial, un parámetro artificial que sirva como entrada, y se compara las predicciones de la trayectoria ramificada de la grieta a partir de tres modelos de phase field populares. Por otra parte, se verificó el método de convergencia con los estudios y se realizó un estudio para demostrar la escala lineal deseada del programa en términos del tiempo de reloj de pared por el tiempo fÃsico en función del número de grados de libertad. Una de las ideas principales del método de phase field es emplear una representación distribuida de una grieta discreta. Sin embargo, en algunas aplicaciones todavÃa es conveniente tener la ruta de grieta explÃcita disponible, o incluso desarrollar un mecanismo para introducir caminos de crack con el objetivo de sustituir en parte un modelo de fisura distribuida de propagación. En esta disertación, se presenta un método variacional para identificar la ruta de grietas en los enfoques de phase field en problemas de fractura. El método ha demostrado ser un éxito no sólo por una simple grieta curvada, sino también por múltiples grietas y ramificadas. El algoritmo emplea la técnica de supresión no máxima, un procedimiento tomado del campo de procesamiento de imágenes, para detectar un área de delimitación que cubre la cresta del perfil de phase field. A continuación, se continúa con la etapa de determinar un spline cúbico para representar la trayectoria de la grieta y mejorarlo a través de un proceso de optimización restringida. Para demostrar la eficacia de nuestro método, proporcionamos los resultados con tres conjuntos de ejemplos representativos. El algoritmo desarrollado se puede combinar con uno en apertura crack, para la interpretación más elaborada de simulaciones de phase field. Este es el tema de la siguiente parte de la tesis. En esta tesis, también ofrecemos una forma variacional para calcular la apertura de grietas de los enfoques de phase field a la fractura. También demostramos el rendimiento de nuestro método con tres conjuntos de ejemplos representativos, y verificar los resultados con un valor de referencia apropiado. Tener la geometrÃa grieta disponible a partir de un enfoque de phase field puede proporcionar una interpretación más elaborada de las simulaciones de phase field. También puede ofrecer una posibilidad de desarrollar esquemas numéricos con menos costes para una propagación de la grieta de accionamiento hidráulico de sólidos impermeables. Este será el tema de nuestro futuro trabajo