add LDLNucleationMicroForce with tests in surfing (#159)

* Add LDLNucleationMicroForce * Modify surfing tutorial close #158 --------- Co-authored-by: Gary Hu <[email protected]>
hugary1995 · Apr 24, 2024 · 202c2a7 · 202c2a7
1 parent 1e3a38e
commit 202c2a7
Show file tree

Hide file tree

Showing 18 changed files with 402 additions and 215 deletions.
diff --git a/doc/content/bib/raccoon.bib b/doc/content/bib/raccoon.bib
@@ -8,7 +8,7 @@ @article{bourdin2007numerical
   year={2007}
 }
 
-@Article{Kumar2022,
+@Article{Kumar2022,
 author={Kumar, A.
 and Ravi-Chandar, K.
 and Lopez-Pamies, O.},
@@ -53,3 +53,11 @@ @article{Drucker-Prager
  volume = {10},
  year = {1952}
 }
+
+@article{larsen2024,
+  title={A variational formulation of Griffith phase-field fracture with material strength}, 
+  author={C. J. Larsen and J. E. Dolbow and O. Lopez-Pamies},
+  journal = {Arxiv},
+  year={2024},
+  url={https://arxiv.org/abs/2401.13938},
+}
diff --git a/...rce/materials/KLBFNucleationMicroForce.md → ...eation_models/KLBFNucleationMicroForce.md b/...rce/materials/KLBFNucleationMicroForce.md → ...eation_models/KLBFNucleationMicroForce.md
@@ -8,7 +8,7 @@ In general, model KLR published in [!cite](Kumar2022) is recommended over model
 
 ### KLR (Kumar, Lopez, Ravi-Chandar) Model 2022
 
-Please see [KLRNucleationMicroForce](source/materials/KLRNucleationMicroForce.md)
+Please see [KLRNucleationMicroForce](nucleation_models/KLRNucleationMicroForce.md)
 
 ### KLBF (Kumar, Lopez, Bourdin, Francfort) Model 2020
 

diff --git a/...urce/materials/KLRNucleationMicroForce.md → ...leation_models/KLRNucleationMicroForce.md b/...urce/materials/KLRNucleationMicroForce.md → ...leation_models/KLRNucleationMicroForce.md
@@ -74,13 +74,9 @@ l_e = \frac{l_0}{\sqrt{1+\delta}},\quad (\delta > -1)
 
 could deviate from $\ell$. The mesh should be able to resolve $l_e$ as well.
 
-Here is an example input deck
-
-!listing /tutorials/surfing_boundary_problem/fracture.i block=Materials/kumar_material
-
 ### KLBF (Kumar, Lopez, Bourdin, Francfort) Model 2020
 
-See [KLBFNucleationMicroForce](source/materials/KLBFNucleationMicroForce.md)
+See [KLBFNucleationMicroForce](nucleation_models/KLBFNucleationMicroForce.md)
 
 ## Example Input File Syntax
 

diff --git a/doc/content/source/materials/nucleation_models/LDLNucleationMicroForce.md b/doc/content/source/materials/nucleation_models/LDLNucleationMicroForce.md
@@ -0,0 +1,82 @@
+# LDLNucleationMicroForce
+
+!syntax description /Materials/LDLNucleationMicroForce
+
+See *A variational formulation of Griffith phase-field fracture with material strength* by [!cite](larsen2024)
+
+This is a variational recast of the phase-field fracture formulation put forth by Kumar, Francfort and Lopez-Pamies (2018), where $\delta$ is explicitly evaluated.
+
+## Overview
+
+### LDL (Larsen, Dolbow, Lopez) Model 2024
+
+The fracture functional reads
+
+\begin{equation}
+\mathcal{E}_f^l(\boldsymbol{u}, d):= \int_\Omega g(d) \psi_e(\boldsymbol{\varepsilon}(\boldsymbol{u})) \;\mathrm{dV} + \frac{\delta^l G_c}{c_0}\int_\Omega\left(\frac{\alpha(d)}{l} + l\nabla d\cdot \nabla d\right) \;\mathrm{dV} + \int_\Omega\left(\int_0^1 g(d) \;\mathrm{dd}\right)\widehat{c_e}(\boldsymbol{\varepsilon}(\boldsymbol{u})) \;\mathrm{dV}.
+\end{equation}
+
+The governing equation for fracture is
+\begin{equation}
+-\nabla\cdot \dfrac{2 G_c l \delta^l}{c_0}\nabla d + \dfrac{\partial}{\partial d}\left( \alpha \dfrac{\delta^l G_c}{c_0 l} - g(d)\psi_e\right) - g(d)\widehat{c_e} \ge 0.
+\end{equation}
+
+Note that the following derivation follows settings of `AT-1`, i.e., $\alpha(d)=d$ and $c_0=\dfrac{8}{3}$. In this model, the strict irreversibility condition for $d$ is adopted.
+
+The "undamaged" nucleation driving force is defined as
+\begin{equation}
+\widehat{c_e}(\boldsymbol{\varepsilon}(\boldsymbol{u}))= \alpha_2 \sqrt{J_2} +  \alpha_1 I_1 - (1-d)\left(1 - \dfrac{\sqrt{I_1^2}}{I_1}\right)\psi_e.
+\end{equation}
+
+In this recast, $\delta^l$ is evaluated explicitly as
+\begin{equation}
+\text{without h correction:}\quad\delta^l=\left(\frac{\sigma_{ts}+ (1+2\sqrt{3})\sigma_{hs}}{(8+3\sqrt{3})\sigma_{hs}}\right)\frac{3G_c}{16 \psi_{ts} l} + \frac{3}{8},
+\end{equation}
+
+\begin{equation}
+\text{with h correction:}\quad\delta^l=\left(1+\frac{3 h}{8 l}\right)^{-2}\left(\frac{\sigma_{ts}+(1+2\sqrt{3})\sigma_{hs}}{(8+3\sqrt{3})\sigma_{hs}}\right)\frac{3G_c}{16 \psi_{ts} l} + \left(1 + \frac{3h}{8l}\right)^{-1}\frac{2}{5},
+\end{equation}
+
+where
+\begin{equation}
+\alpha_1 = - \frac{1}{\sigma_{hs}}\delta^l \frac{G_c}{8l} + \frac{2\psi_{hs}}{3\sigma_{hs}}, \qquad \alpha_2= - \frac{\sqrt{3}(3\sigma_{hs} - \sigma_{ts})}{\sigma_{hs}\sigma_{ts}}\delta^l \frac{G_c}{8l} - \frac{2\psi_{hs}}{\sqrt{3}\sigma_{hs}} + \frac{2\sqrt{3}\psi_{ts}}{\sigma_{ts}},
+\end{equation}
+
+with
+\begin{equation}
+\psi_{ts}=\frac{\sigma^2_{ts}}{2E}, \quad \psi_{hs}=\frac{\sigma^2_{hs}}{2\kappa}.
+\end{equation}
+
+The material properties used are the bulk modulus $\kappa$ and Young's modulus $E$ and the shear modulus $\mu$.
+
+The strength surface is presented with uniaxial tensile $\sigma_{ts}$ and hydrostatic strength $\sigma_{hs}$, where $\sigma_{hs}=\dfrac{2}{3} \dfrac{\sigma_{ts}\sigma_{cs}}{\sigma_{cs} - \sigma_{ts}}$.
+
+### KLR (Kumar, Lopez, Ravi-Chandar) Model 2022
+
+Please see [KLRNucleationMicroForce](nucleation_models/KLRNucleationMicroForce.md)
+
+### KLBF (Kumar, Lopez, Bourdin, Francfort) Model 2020
+
+Please see [KLBFNucleationMicroForce](nucleation_models/KLBFNucleationMicroForce.md)
+
+## Example Input File Syntax
+
+```
+[Materials]
+  [micro_force]
+    type = LDLNucleationMicroForce
+    regularization_length = l
+    normalization_constant = c0
+    tensile_strength = sigma_ts
+    hydrostatic_strength = sigma_hs
+    external_driving_force_name = ce
+    h_correction = true
+  []
+[]
+```
+
+!syntax parameters /Materials/LDLNucleationMicroForce
+
+!syntax inputs /Materials/LDLNucleationMicroForce
+
+!syntax children /Materials/LDLNucleationMicroForce
diff --git a/include/materials/KLRNucleationMicroForce.h b/include/materials/KLRNucleationMicroForce.h
diff --git a/include/materials/nucleation_models/KLBFNucleationMicroForce.h b/include/materials/nucleation_models/KLBFNucleationMicroForce.h
@@ -0,0 +1,31 @@
+//* This file is part of the RACCOON application
+//* being developed at Dolbow lab at Duke University
+//* http://dolbow.pratt.duke.edu
+
+#pragma once
+
+#include "NucleationMicroForceBase.h"
+
+/**
+ * The class implements the external driving force to recover a Drucker-Prager
+ * strength envelope. See Kumar et. al. https://doi.org/10.1016/j.jmps.2020.104027 for model 2020.
+ */
+class KLBFNucleationMicroForce : public NucleationMicroForceBase
+{
+public:
+  static InputParameters validParams();
+
+  KLBFNucleationMicroForce(const InputParameters & parameters);
+
+protected:
+  virtual void computeQpProperties() override;
+
+  /// The critical tensile strength
+  const ADMaterialProperty<Real> & _sigma_ts;
+
+  /// The critical compressive strength
+  const ADMaterialProperty<Real> & _sigma_cs;
+
+  /// The materiel and model dependent parameter
+  const ADMaterialProperty<Real> & _delta;
+};
diff --git a/include/materials/nucleation_models/KLRNucleationMicroForce.h b/include/materials/nucleation_models/KLRNucleationMicroForce.h
@@ -0,0 +1,37 @@
+//* This file is part of the RACCOON application
+//* being developed at Dolbow lab at Duke University
+//* http://dolbow.pratt.duke.edu
+
+#pragma once
+
+#include "NucleationMicroForceBase.h"
+
+/**
+ * The class implements the external driving force to recover a Drucker-Prager
+ * strength envelope developed by Kumar et al. in 2022. See Kumar, A., Ravi-Chandar, K. &
+ * Lopez-Pamies, O. The revisited phase-field approach to brittle fracture: application to
+ * indentation and notch problems. Int J Fract 237, 83–100 (2022).
+ * https://doi.org/10.1007/s10704-022-00653-z.
+ */
+class KLRNucleationMicroForce : public NucleationMicroForceBase
+{
+public:
+  static InputParameters validParams();
+
+  KLRNucleationMicroForce(const InputParameters & parameters);
+
+protected:
+  virtual void computeQpProperties() override;
+
+  /// The critical tensile strength
+  const ADMaterialProperty<Real> & _sigma_ts;
+
+  /// The critical compressive strength
+  const ADMaterialProperty<Real> & _sigma_cs;
+
+  /// The materiel and model dependent parameter
+  const ADMaterialProperty<Real> & _delta;
+
+  /// Quantifying how far is the stress state from Drucker Prager
+  ADMaterialProperty<Real> & _druck_prager_balance;
+};
diff --git a/include/materials/nucleation_models/LDLNucleationMicroForce.h b/include/materials/nucleation_models/LDLNucleationMicroForce.h
@@ -0,0 +1,35 @@
+//* This file is part of the RACCOON application
+//* being developed at Dolbow lab at Duke University
+//* http://dolbow.pratt.duke.edu
+
+#pragma once
+
+#include "NucleationMicroForceBase.h"
+
+/**
+ * The class implements the external driving force to recover a Drucker-Prager
+ * strength envelope. See Larsen et. al. https://doi.org/10.48550/arXiv.2401.13938 for model 2024.
+ */
+
+class LDLNucleationMicroForce : public NucleationMicroForceBase
+{
+public:
+  static InputParameters validParams();
+
+  LDLNucleationMicroForce(const InputParameters & parameters);
+
+protected:
+  virtual void computeQpProperties() override;
+
+  /// The critical tensile strength
+  const ADMaterialProperty<Real> & _sigma_ts;
+
+  /// The critical hydrostatic strength
+  const ADMaterialProperty<Real> & _sigma_hs;
+
+  /// The materiel and model dependent parameter
+  ADMaterialProperty<Real> & _delta;
+
+  /// Whether to use h correction formula for delta
+  bool _h_correction;
+};
diff --git a/include/materials/KLBFNucleationMicroForce.h → ...leation_models/NucleationMicroForceBase.h b/include/materials/KLBFNucleationMicroForce.h → ...leation_models/NucleationMicroForceBase.h
@@ -8,30 +8,16 @@
 #include "BaseNameInterface.h"
 #include "DerivativeMaterialPropertyNameInterface.h"
 
-/**
- * The class implements the external driving force to recover a Drucker-Prager
- * strength envelope. See Kumar et. al. https://doi.org/10.1016/j.jmps.2020.104027 for model 2020.
- * all parameters are required to be Material type, not double type
- */
-class KLBFNucleationMicroForce : public Material,
+class NucleationMicroForceBase : public Material,
                                  public BaseNameInterface,
                                  public DerivativeMaterialPropertyNameInterface
 {
 public:
   static InputParameters validParams();
-
-  KLBFNucleationMicroForce(const InputParameters & parameters);
+  NucleationMicroForceBase(const InputParameters & parameters);
 
 protected:
-  virtual void computeQpProperties() override;
-
-  /// Name of the external driving force
-  const MaterialPropertyName _ex_driving_name;
-
-  /// The external driving force
-  ADMaterialProperty<Real> & _ex_driving;
-
-  ///@{ Phase field properties
+  ///@{ fracture properties
   /// The fracture toughness
   const ADMaterialProperty<Real> & _Gc;
   /// The normalization constant
@@ -45,20 +31,22 @@ class KLBFNucleationMicroForce : public Material,
   /// The shear modulus
   const ADMaterialProperty<Real> & _mu;
 
-  /// The critical tensile strength
-  const ADMaterialProperty<Real> & _sigma_ts;
-
-  /// The critical compressive strength
-  const ADMaterialProperty<Real> & _sigma_cs;
-
-  /// The materiel and model dependent parameter
-  const ADMaterialProperty<Real> & _delta;
-
   /// The stress tensor
   const ADMaterialProperty<RankTwoTensor> & _stress;
-
   /// Name of the stress space balance
   const MaterialPropertyName _stress_balance_name;
   /// Quantifying how far is the stress state from stress surface
   ADMaterialProperty<Real> & _stress_balance;
+
+  /// Name of the external driving force
+  const MaterialPropertyName _ex_driving_name;
+  /// The external nucleation driving force
+  ADMaterialProperty<Real> & _ex_driving;
+
+  /// @{ The degradation function and its derivative w/r/t damage
+  const VariableName _d_name;
+  const MaterialPropertyName _g_name;
+  const ADMaterialProperty<Real> & _g;
+  const ADMaterialProperty<Real> & _dg_dd;
+  /// @}
 };