Phase-field model for fracture using MPI and AMR

Phase_field_fracture_model_in_3D/CMakeLists.txt

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+##
+#  CMake script for the step-854 tutorial program:
+##
+
+# Set the name of the project and target:
+SET(TARGET "phase_field")
+
+# Declare all source files the target consists of. Here, this is only
+# the one step-X.cc file, but as you expand your project you may wish
+# to add other source files as well. If your project becomes much larger,
+# you may want to either replace the following statement by something like
+#    FILE(GLOB_RECURSE TARGET_SRC  "source/*.cc")
+#    FILE(GLOB_RECURSE TARGET_INC  "include/*.h")
+#    SET(TARGET_SRC ${TARGET_SRC}  ${TARGET_INC})
+# or switch altogether to the large project CMakeLists.txt file discussed
+# in the "CMake in user projects" page accessible from the "User info"
+# page of the documentation.
+SET(TARGET_SRC
+  ${TARGET}.cc
+  )
+
+# Usually, you will not need to modify anything beyond this point...
+
+CMAKE_MINIMUM_REQUIRED(VERSION 3.3.0)
+
+FIND_PACKAGE(deal.II 9.4.0
+  HINTS ${deal.II_DIR} ${DEAL_II_DIR} ../ ../../ $ENV{DEAL_II_DIR}
+  )
+IF(NOT ${deal.II_FOUND})
+  MESSAGE(FATAL_ERROR "\n"
+    "*** Could not locate a (sufficiently recent) version of deal.II. ***\n\n"
+    "You may want to either pass a flag -DDEAL_II_DIR=/path/to/deal.II to cmake\n"
+    "or set an environment variable \"DEAL_II_DIR\" that contains this path."
+    )
+ENDIF()
+
+DEAL_II_INITIALIZE_CACHED_VARIABLES()
+PROJECT(${TARGET})
+DEAL_II_INVOKE_AUTOPILOT()

Phase_field_fracture_model_in_3D/README.md

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+# Phase-field Fracture in 3D
+
+## Motivation
+This program implements the hybrid phase-field model of Ambati et al. [1] in deal.II using adaptive mesh refinement and parallel computing capabilities.
+Phase-field models have been proven to be effective in modeling complicated fractures because of their ability to model crack branching, merging, and fragmentation.
+Despite this, these models are mostly limited to 2D because of the high computational cost, as these models require very fine meshes to resolve the diffused representation of the crack.
+This code explores the use of parallel computing and adaptive mesh refinement to model fracture propagation using the hybrid phase-field model.
+
+## Governing equations
+
+The model this program solves is that of Ambati et al. [1], see there for more information. In short,
+the model describes the growth of a crack as an object is successively strained. The deformation
+of the solid is described by the usual force balance appropriate for quasi-static deformation:
+
+@f{align*}{
+\nabla\cdot\boldsymbol{\sigma}
+(\boldsymbol{\varepsilon}(\boldsymbol{u}),d) = \mathbf{0}
+@f}
+with Dirichlet boundary conditions
+@f{align*}{
+\boldsymbol{u} = \boldsymbol{u}_D \text{ on  } \Gamma_D
+@f}
+
+The crack is tracked by a "damage field" $d$ that is a smoothed version of a history field $\mathcal{H}^{+}$
+that corresponds to accumulated strain at a quadrature point:
+@f{align*}{
+-l^2 \nabla^2 d+d=\frac{2 l}{G_c}(1-d) \mathcal{H}^{+}
+@f} with the boundary condition
+@f{align*}{
+\left(G_{c} l\right) \nabla d \cdot \boldsymbol{n}=\mathbf{0}.
+@f}
+Here, $\boldsymbol{u}, d$ represent the displacement and damage(crack) fields, $l$ is the length scale parameter, $G_c$ is the critical energy release rate and $\mathcal{H}^{+}$ is the history field variable.
+
+## To run the Code
+After running `cmake .`, run `make release` or `make debug` to switch between `release` and `debug`mode. Compile using `make`.
+Run the executable by using `make run` on the command line.
+
+## Numerical example
+The program currently models fracture propagation in a 3-layered material subjected to equibiaxial loading along $+x$ and $+y$ directions. The problem setup is shown in the following picture:
+![Setup](./doc/polyhedral_setup.png)
+Results are compared for two different initial meshes, the finer $80\times80\times40$ mesh and the coarser $20\times20\times10$ mesh. The following picture shows results for the fracture patterns and the load-displacement curves for the 2 meshes:
+![Load displacement curves](./doc/load_displacement_curves.png)
+
+An animation of how the crack system in this setup evolves can be found as `./doc/polyhedral_cracks.mp4` in the code gallery source directory (left: coarse mesh; right: fine mesh).
+
+
+## References
+[1]
+```
+@article{Ambati2015,
+  title={A review on phase-field models of brittle fracture and a new fast hybrid formulation},
+  author={Ambati, Marreddy and Gerasimov, Tymofiy and De Lorenzis, Laura},
+  journal={Computational Mechanics},
+  volume={55},
+  pages={383--405},
+  year={2015},
+  publisher={Springer}
+}
+```

Phase_field_fracture_model_in_3D/doc/author

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+Wasim Niyaz Munshi <[email protected]>
+Chandrasekhar Annavarapu <[email protected]>
+Wolfgang Bangerth <[email protected]>
+Marc Fehling <[email protected]>

Phase_field_fracture_model_in_3D/doc/builds-on

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+step-8 step-40

Phase_field_fracture_model_in_3D/doc/dependencies

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+DEAL_II_WITH_TRILINOS DEAL_II_WITH_MPI

Phase_field_fracture_model_in_3D/doc/entry-name

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+Phase-field fracture model in 3D

Phase_field_fracture_model_in_3D/doc/tooltip

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+Phase-field fracture model in 3D with adaptive mesh refinement and a parallel solver