An Open-Source Fenics Implementation of a Phase Field Fracture Model for Micropolar Continua

Abstract

A micropolar phase field fracture model is implemented in an open source library FEniCS. This implementation is based on the theoretical study in Suh, H.S., Sun, W., and O'Connor, D. (under review) in which the resultant phase field model exhibits the consistent micropolar size effect in both elastic and damage regions identifiable via inverse problems for micropolar continua. By leveraging the automatic code generation technique in FEniCS, we provide a documentation of the source code expressed in a language very close to the mathematical expressions without comprising significant efficiency. This combination of generality and interpretability therefore enables us to provide a detailed walk-through that connects the implementation with the regularized damage theory for micropolar materials. By making the source code open source, the paper will provide an efficient development and educational tool for third-party verification and validation, as well as for future development of other higher order continuum damage models.

Multi‐phase‐field microporomechanics model for simulating ice‐lens growth in frozen soil

“…To ensure  ≥ 0, as a simple remedy, we replace  with  * , which is defined as the pseudo-temporal maximum of normalized strain energy, while considering a critical value  crit that restricts the crack to initiate above a threshold strain energy 56,[100][101][102] :…”

“…Specifically, we decompose the elastic strain energy into two parts, that is, $$\psi ^{\prime }_{\text{int}} = \psi ^{\prime +}_{\text{int}} + \psi ^{\prime -}_{\text{int}}$$, $$\begin{equation} {\psi}_{\text{int}}^{\prime}=\frac{1}{2}K \langle {\varepsilon}^{\text{vol}}\rangle_{+}^{2}+G({\bm{\varepsilon}}^{\text{dev}}:{\bm{\varepsilon}}^{\text{dev}})\text{};\text{}{\psi}_{\text{int}}^{\prime}=\frac{1}{2}K \langle {\varepsilon}^{\text{vol}}\rangle_{-}^{2}, \end{equation}$$and only degrade the expansive volumetric and deviatoric parts, while $$\langle \bullet \rangle _{\pm } = (\bullet + | \bullet |)/2$$. To ensure $$\dot{\mathcal {H}} \ge 0$$, as a simple remedy, we replace $$\mathcal {H}$$ with $$\mathcal {H}^*$$, which is defined as the pseudo‐temporal maximum of normalized strain energy, while considering a critical value $$\mathcal {H}_{\text{crit}}$$ that restricts the crack to initiate above a threshold strain energy 56,100–102 : …”

An immersed phase field fracture model for microporomechanics with Darcy–Stokes flow

“…scitation.org/journal/phf smoothly from 0 in BD to 1 in BS. Specifically, we approximate the interfacial area A Γ * as A Γ * d , which can be expressed in terms of volume integration of the surface density functional Γ * d (d, ∇d) over B = BD ∪ BS (Miehe et al, 2010;Borden et al, 2012;Suh and Sun, 2019;and Suh et al, 2020),…”

An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition

“…Similar to [22], we attempt to employ a diffuse approximation for the sharp interface between two regions via implicit function. By adopting a phase field approach which is widely used in modeling fracture [3,14,23,24], we approximate the interfacial area as , which can be expressed in terms of volume integration of surface density over :…”