A generalized machine learning framework for brittle crack problems using transfer learning and graph neural networks

Despite their recent success, machine learning (ML) models such as graph neural networks (GNNs), suffer from drawbacks such as the need for large training datasets and poor performance for unseen cases. In this work, we use transfer learning (TL) approaches to circumvent the need for retraining with large datasets. We apply TL to an existing ML framework, trained to predict multiple crack propagation and stress evolution in brittle materials under Mode-I loading. The new framework, ACCelerated Universal fRAcTure Emulator (ACCURATE), is generalized to a variety of crack problems by using a sequence of TL update steps including (i) arbitrary crack lengths, (ii) arbitrary crack orientations, (iii) square domains, (iv) horizontal domains, and (v) shear loadings. We show that using small training datasets of 20 simulations for each TL update step, ACCURATE achieved high prediction accuracy in Mode-I and Mode-II stress intensity factors, and crack paths for these problems. %case studies (i) - (iv). We demonstrate ACCURATE's ability to predict crack growth and stress evolution with high accuracy for unseen cases involving the combination of new boundary dimensions with arbitrary crack lengths and crack orientations in both tensile and shear loading. We also demonstrate significantly accelerated simulation times of up to 2 orders of magnitude faster (200x) compared to an XFEM-based fracture model. The ACCURATE framework provides a universal computational fracture mechanics model that can be easily modified or extended in future work

Dynamic and adaptive mesh-based graph neural network framework for simulating displacement and crack fields in phase field models

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of crack propagation with AMR for different crack configurations. The developed framework - ADAPTive mesh-based graph neural network (ADAPT-GNN) - exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with high accuracy compared to conventional phase field fracture model. We also compute crack stress fields with high accuracy using the predicted displacements and phase field parameter. Finally, we observe speed up of 15-36x compared to serial execution of the phase field model

Investigating shock wave propagation, evolution, and anisotropy using a moving window concurrent atomistic-continuum framework

Despite their success in microscale modeling of materials, atomistic methods are still limited by short time scales, small domain sizes, and high strain rates. Multiscale formulations can capture the continuum-level response of solids over longer runtimes, but using such schemes to model highly dynamic, nonlinear phenomena is very challenging and an active area of research. In this work, we develop novel techniques within the concurrent atomistic-continuum multiscale framework to simulate shock wave propagation through a two-dimensional, single-crystal lattice. The technique is described in detail, and two moving window methods are incorporated to track the shock front through the domain and thus prevent spurious wave reflections at the atomistic-continuum interfaces. We compare our simulation results to analytical models as well as previous atomistic and CAC data and discuss the apparent effects of lattice orientation on the shock response of FCC crystals. We then use the moving window techniques to perform parametric studies which analyze the shock front's structure and planarity. Finally we compare the efficiency of our model to molecular dynamics simulations. This work showcases the power of using a moving window concurrent multiscale framework to simulate dynamic shock evolution over long runtimes and opens the door to more complex studies involving shock propagation through composites and high-entropy alloys

Shock Wave Propagation in Composites and Electro-Thermomechanical Coupling of Ferroelectric Materials

How is material behavior at the macro scale influenced by its properties and structure at the micro and meso-scales? How do heterogeneities influence the properties and the response of a material? How does nonlinear coupling of electro-thermo-mechanical properties influence the behavior of a ferroelectric material? How can design at the micro-scale be exploited to obtain selective response? These questions have been topics of significant interest in the materials and mechanics community. Recently, new materials like multifunctional composites and metamaterials have been developed, targeted at selective applications. These materials find applications in areas like energy harvesting, damage mitigation, biomedical devices, and various aerospace applications. The current thesis explores these questions with two major thrusts: (i) internal reflects of shocks in composite media and (ii) shocks in ferroelectric media. Under the application of high-pressure, high strain rate loading, such as during high velocity impact, shock waves are generated in the material. They can cause the material to achieve very high stress states, and if transmitted without mitigation, can lead to failure of key components. An important question here is 'Can we design materials which can successfully mitigate damage due to shocks?' In a heterogeneous material, like a layered composite, the traveling waves undergo scattering due to internal reflections. In order to understand internal reflections, an idealized problem that focuses on nonlinear shocks and ignores less important elastic waves was formulated and studied in detail. The problem is studied by classifying all possible interactions in the material and then solving corresponding Riemann problems. Using dynamic programming tools, a new algorithm is designed that uses these solutions to generate a complete picture of the impact process. Different laminate designs are explored to study optimal design, by varying individual layer properties and their arrangement. Phenomena like spallation and delamination are also investigated. Upon high strain rate loading, ferroelectric materials like lead zirconate titanate (PZT) undergo ferroelectric to anti-ferroelectric phase transition leading to large pulsed current output. These materials have thus found applications as pulsed power generators. The problem of shock induced depolarization and the associated electro-thermo-mechanical coupling of ferroelectric materials is studied in this thesis using theoretical and numerical methods. A large deformation dynamic analysis of such materials is conducted to study phase boundary propagation in the medium. The presence of high electrical fields can lead to formation of charges in the material, such as surface charge on the phase boundary. Using conservation laws and the second law of thermodynamics, a set of governing equations are formulated that dictate the phase boundary propagation in isothermal and adiabatic environments. Due to the possibility of surface charges on the phase boundary, the curvature of the phase boundary starts to play a role in the driving force acting on the phase boundary. The equations of motion and driving force see the contribution of nonlinear electro-thermomechanical coupling in the material. Using the equations derived, a canonical problem of impact on a ferroelectric material is studied. A new finite-volume, front-tracking method is developed to solve these equations. Finally, results from numerical simulations are compared to the experimental results.</p

Shock wave propagation through a model one dimensional heterogeneous medium

We study the problem of impact-induced shock wave propagation through a model one-dimensional heterogeneous medium. This medium is made of a model material with spatially varying parameters such that it is heterogeneous to shock waves but homogeneous to elastic waves. Using the jump conditions and maximal dissipation criteria, we obtain the exact solution to the shock propagation problem. We use it to study how the nature of the heterogeneity changes material response, the structure of the shock front and the dissipation