Damage mechanics challenge: predictions based on the phase field fracture model

In this work, we describe our contribution to the Purdue-SANDIA-LLNL Damage Mechanics Challenge. The phase field fracture model is adopted to blindly estimate the failure characteristics of the challenge test, an unconventional three-point bending experiment on an additively manufactured rock resembling a type of gypsum. The model is formulated in a variationally consistent fashion, incorporating a volumetric–deviatoric strain energy decomposition, and the numerical implementation adopts a monolithic unconditionally stable solution scheme. Our focus is on providing an efficient and simple yet rigorous approach capable of delivering accurate predictions based solely on physical parameters. Model inputs are Young’s modulus , Poisson’s ratio , toughness and strength (as determined by the choice of phase field length scale ℓ). We show that a single mode I three-point bending test is sufficient to calibrate the model, and that the calibrated model can then reliably predict the force versus displacement responses, crack paths and surface crack morphologies of more intricate three-point bending experiments that are inherently mixed-mode. Importantly, our peak load, crack trajectory and crack surface morphology predictions for the challenge test, submitted before the experimental data was released, show a remarkable agreement with experiments. The characteristics of the challenge, and how changes in these can impact the predictive abilities of phase field fracture models, are also discussed

Simulating the processes controlling ice-shelf rift paths using damage mechanics

Rifts are full-thickness fractures that propagate laterally across an ice shelf. They cause ice-shelf weakening and calving of tabular icebergs, and control the initial size of calved icebergs. Here, we present a joint inverse and forward computational modeling framework to capture rifting by combining the vertically integrated momentum balance and anisotropic continuum damage mechanics formulations. We incorporate rift–flank boundary processes to investigate how the rift path is influenced by the pressure on rift–flank walls from seawater, contact between flanks, and ice mélange that may also transmit stress between flanks. To illustrate the viability of the framework, we simulate the final 2 years of rift propagation associated with the calving of tabular iceberg A68 in 2017. We find that the rift path can change with varying ice mélange conditions and the extent of contact between rift flanks. Combinations of parameters associated with slower rift widening rates yield simulated rift paths that best match observations. Our modeling framework lays the foundation for robust simulation of rifting and tabular calving processes, which can enable future studies on ice-sheet–climate interactions, and the effects of ice-shelf buttressing on land ice flow

An hp-adaptive discontinuous Galerkin method for phase field fracture

The phase field method is becoming the de facto choice for the numerical analysis of complex problems that involve multiple initiating, propagating, interacting, branching and merging fractures. However, within the context of finite element modelling, the method requires a fine mesh in regions where fractures will propagate, in order to capture sharp variations in the phase field representing the fractured/damaged regions. This means that the method can become computationally expensive when the fracture propagation paths are not known a priori. This paper presents a 2D -adaptive discontinuous Galerkin finite element method for phase field fracture that includes a posteriori error estimators for both the elasticity and phase field equations, which drive mesh adaptivity for static and propagating fractures. This combination means that it is possible to be reliably and efficiently solve phase field fracture problems with arbitrary initial meshes, irrespective of the initial geometry or loading conditions. This ability is demonstrated on several example problems, which are solved using a light-BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm. The examples highlight the importance of driving mesh adaptivity using both the elasticity and phase field errors for physically meaningful, yet computationally tractable, results. They also reveal the importance of including -refinement, which is typically not included in existing phase field literature. The above features provide a powerful and general tool for modelling fracture propagation with controlled errors and degree-of-freedom optimised meshes

Coupled Eulerian–Lagrangian extended finite element approach to simulating the mechanics and growth of biofilm, cells, and tissues

Simulating the mechanics and growth of soft biological and biomimetic materials (e.g., hydrogels, fibroblast-ECM system, biofilm evolution, cell protrusion, spreading of a cell nucleus) requires coupling large deformation solid mechanics with fluid mechanics, advective-diffusive transport, growth, and the evolution of embedded phase/material interfaces. The standard Lagrangian finite element approach suffers from numerical issues due to excessive mesh distortion and mesh-moving/remeshing algorithms can be cumbersome; therefore, there is a need for more robust and efficient numerical approaches. An Eulerian finite element approach that allows the material to move against the numerical mesh does not suffer from mesh distortion issues; so, it may be advantageous; however, specialized techniques are required for capturing the evolution of the phase interfaces or domain boundaries. In this presentation, we first present a Lagrangian solid mechanics formulation for studying the mechanics of a linear elastic biofilm to motivate the need for the proposed Eulerian approach. Next, we briefly describe the coupled Eulerian–Lagrangian extended finite element method (XFEM) for modeling the moving interface problem associated with finite deformation of isotropic hyperelastic materials. This formulation is based on the Eulerian description of motion and on the updated Lagrangian description for the transport of the isochoric part of the deformation gradient and of the Jacobian determinant, separately. The XFEM is used to discretize the equilibrium and transport equations in a two-phase medium. A mixed interpolation scheme (biquadratic for velocity and bilinear for Jacobian determinant and the isochoric part of the deformation gradient) is adopted to improve the stability and accuracy of the numerical formulation. A variational multiscale residual-based approach is employed to stabilize the formulation for flow problems. The two-phase interface is represented by the level set function and is evolved using the grid based particle method. The performance of the scheme is explored in two dimensions in the compressible and nearly incompressible regime. Our numerical results for benchmark examples involving: (i) uniaxial tension and simple shear flow are in agreement with theoretical results; and (ii) indentation of a rectangular block is in agreement with those from a Lagrangian finite element implementation in Abaqus. We believe the method can be used to better characterize biological materials and to explain physical mechanisms in conjunction with experiments

Modelling post-failure behaviour of chalk cliffs with the Material Point Method

This work evaluates the use of the Material Point Method (MPM) with continuum damage plasticity to model fracture for the use of a combined pre- and post-failure simulation. MPM is used to allow for large deformations and geometry changes without mesh distortion and damage diffusion. An integral non-local continuum damage model is used to model brittle fracture, which avoids the mesh dependency issues exhibited by local models. The modelling approach is demonstrated on chalk cliff collapse problems, where the final state of the rock formation after the failure is of importance and critically linked to further failure processes