Computational Methods for Fatigue and Fracture

The development of modern numerical methods has led to significant advances in the field of fatigue and fracture, which are pivotal issues in structural integrity. Because of the permanent tendency to shorten time-to-market periods and the development cost, the use of the finite element method, extended finite element method, peridynamics, or meshless methods, among others, has represented a viable alternative to experimental methods. This Special Issue aims to focus on the new trends in computational methods to address fatigue and fracture problems. Research on innovative and successful industrial applications as well as on nonconventional numerical approaches is also addressed

A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semi-analytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygons to represent arbitrary geometric shapes leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility. © 2017 Elsevier Lt

Linear elastic fracture mechanics via the Material Point Method: a phase field approach

Fracture is one of the main failure mechanisms of materials and structural components. During the past thirty years, various methods have been introduced to simulate crack initiation and growth. These include the introduction of Element Deletion Method and re-meshing strategies within the standard Finite Element Method (FEM), cohesion based Finite Element strategies and the extended Finite Element Method. Very recently, a new method for crack propagation, namely the phase field method has been introduced; phase field models have been proven very robust in accurately predicting complex crack behavior while at the same time avoiding standard re-meshing or enriching techniques. To this point, phase field modelling has extensively been applied within a Finite Element framework while very little research and applications have been demonstrated with particle methods. However, treating the crack propagation problem using a grid based method is a challenging and computationally taxing task. The reliability and robustness of the Finite Element Method and in general mesh-based methods depends on the quality of the mesh itself. In this work, the phase field method is re-formulated and treated using an attractive Particle-In-Cell (PIC) scheme, namely the Material Point Method (MPM). In this approach, the coupled continuum/phase field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, i.e. non-deforming, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying Finite Element mesh and relieved from corresponding mesh distortion errors. This framework is then generalized for the case of anisotropic brittle fracture by introducing an anisotropic crack density functional. The anisotropic crack density functional gives rise to a family of phase field models, both second and fourth order, able to address brittle fracture simulation in anisotropic media. The proposed method is further extended into dynamic brittle fracture using both isotropic and anisotropic phase field models. Frictional contact problems involving phase field fracture are also examined and their post-fracture contact response is investigated. On the proposed model, the local contact features are naturally handled using the Eulerian mesh and the damage evolution emerges without the need to numerically track discontinuities in the displacement field e.g. with jump and tip enrichment functions as well as complex crack paths can be obtained without any additional ad hoc rules. These advantages make the derived model a robust computational tool when arbitrary crack paths occur at impact-fracture problems. Following, the proposed model is used to efficiently simulate crack paths induced from rocking response. The accuracy of the method is examined and verified based on existing analytical rocking response models; the method is then further extended into rocking system dynamics involving phase field fracture. Merits and drawbacks of the proposed formulation are examined using a set of benchmark tests. The influence of impact velocity, phase field and material point parameters on induced crack path is also examined. Validation based on experimental observations is also performed

Linear elastic fracture mechanics via the Material Point Method: a phase field approach

Fracture is one of the main failure mechanisms of materials and structural components. During the past thirty years, various methods have been introduced to simulate crack initiation and growth. These include the introduction of Element Deletion Method and re-meshing strategies within the standard Finite Element Method (FEM), cohesion based Finite Element strategies and the extended Finite Element Method. Very recently, a new method for crack propagation, namely the phase field method has been introduced; phase field models have been proven very robust in accurately predicting complex crack behavior while at the same time avoiding standard re-meshing or enriching techniques. To this point, phase field modelling has extensively been applied within a Finite Element framework while very little research and applications have been demonstrated with particle methods. However, treating the crack propagation problem using a grid based method is a challenging and computationally taxing task. The reliability and robustness of the Finite Element Method and in general mesh-based methods depends on the quality of the mesh itself. In this work, the phase field method is re-formulated and treated using an attractive Particle-In-Cell (PIC) scheme, namely the Material Point Method (MPM). In this approach, the coupled continuum/phase field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, i.e. non-deforming, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying Finite Element mesh and relieved from corresponding mesh distortion errors. This framework is then generalized for the case of anisotropic brittle fracture by introducing an anisotropic crack density functional. The anisotropic crack density functional gives rise to a family of phase field models, both second and fourth order, able to address brittle fracture simulation in anisotropic media. The proposed method is further extended into dynamic brittle fracture using both isotropic and anisotropic phase field models. Frictional contact problems involving phase field fracture are also examined and their post-fracture contact response is investigated. On the proposed model, the local contact features are naturally handled using the Eulerian mesh and the damage evolution emerges without the need to numerically track discontinuities in the displacement field e.g. with jump and tip enrichment functions as well as complex crack paths can be obtained without any additional ad hoc rules. These advantages make the derived model a robust computational tool when arbitrary crack paths occur at impact-fracture problems. Following, the proposed model is used to efficiently simulate crack paths induced from rocking response. The accuracy of the method is examined and verified based on existing analytical rocking response models; the method is then further extended into rocking system dynamics involving phase field fracture. Merits and drawbacks of the proposed formulation are examined using a set of benchmark tests. The influence of impact velocity, phase field and material point parameters on induced crack path is also examined. Validation based on experimental observations is also performed

Damage modelling in fibre-reinforced composite laminates using phase field approach

Thin unidirectional-tape and woven fabric-reinforced composites are widely utilized in the aerospace and automotive industries due to their enhanced fatigue life and impact damage resistance. The increasing industrial applications of such composites warrants a need for high-fidelity computational models to assess their structural integrity and ensure robust and reliable designs. Damage detection and modelling is an important aspect of overall design and manufacturing lifecycle of composite structures. In particular, in thin-ply composites, the damage evolves as a result of coupled in-plane (membrane) and out-of-plane (bending) deformations that often arise during critical events, e.g., bird strike/ hail impact or under in-flight service loads. Contrary to metallic structures, failure in composites involves complex and mutually interacting damage patterns, e.g., fibre breakage/ pullout/ bridging, matrix cracking, debonding and delamination. Providing high-fidelity simulations of intra-laminar damage is a challenging task both from a physics and a computational perspective, due to their complex and largely quasi-brittle fracture response. This is manifested by matrix cracking and fibre breakage, which result in a sudden loss of strength with minimum crack openings; subsequent fibre pull-outs result in a further, although gradual, strength loss. To effectively model this response, it is necessary to account for the cohesive forces evolving within the fracture process zone. Furthermore, the interaction of the failure mechanisms pertinent to both the fibres and the matrix necessitate the definition of anisotropic damage models. In addition, the failure in composites extends across multiple scales; it initiates at the fibre/ matrix-level (micro-scale) and accumulates into larger cracks at the component/ structural level (macro-scale). From a simulation standpoint, accurate prediction of the structure’s critical load bearing capacity and its associated damage thresholds becomes a challenging task; accuracy necessitates a fine level of resolution, which renders the corresponding numerical model computationally expensive. To this point, most damage models are applied at the meso-scale based on local stress-strain estimates, and considering material heterogeneity. Such damage models are often computationally expensive and practically inefficient to simulate the failure behaviour in real-life composite structures. Moreover at the macro-scale, the effect of local stresses is largely minimised, which necessitates definition of a homogenised failure criterion based on global macro-scale stresses. This thesis presents a phase field based MITC4+ (Mixed Interpolation of Tensorial Components) shell element formulation to simulate fracture propagation in thin shell structures under coupled membrane and bending deformations. The employed MITC4+ approach renders the element shear- and membrane- locking free, hence providing high-fidelity fracture simulations in planar and curved topologies. To capture the mechanical response under bending-dominated fracture, a crack-driving force description based on the maximum strain energy density through the shell-thickness is considered. Several numerical examples simulating fracture in flat and curved shell structures which display significant transverse shear and membrane locking are presented. The accuracy of the proposed formulation is examined by comparing the predicted critical fracture loads against analytical estimates. To simulate diverse intra-laminar fracture modes in fibre reinforced composites, an anisotropic cohesive phase field model is proposed. The damage anisotropy is captured via distinct energetic crack driving forces, which are defined for each pertinent composite damage mode together with a structural tensor that accounts for material orientation dependent fracture properties. Distinct 3-parameter quasi-quadratic degradation functions based on fracture properties pertinent to each failure mode are used, which result in delaying or suppressing pre-mature failure initiation in all modes simultaneously. The degradation functions can be calibrated to experimentally derived strain softening curves corresponding to relevant failure modes. The proposed damage model is implemented in Abaqus and is validated against experimental results for woven fabric-reinforced and unidirectional composite laminates. Furthermore, a dynamic explicit cohesive phase field model is proposed to capture the significantly nonlinear damage evolution behaviour pertinent to impact scenarios. A strategy is presented to combine the phase field and the cohesive zone models to perform full composite-laminate simulations involving both intra-laminar and inter-laminar damage modes. Finally, the developed phase field model is employed within the framework of a multiscale surrogate modelling technique. The latter is proposed to perform fast and efficient damage simulation involving different inherent scales in composites. The technique is based on a multiscale FE2 (Finite Element squared) homogenisation approach, however the computationally expensive procedure of solving the meso- and macro-scale models simultaneously is avoided by using a robust surrogate model. The meso-scale is defined as a unit-cell representative volume element (RVE) model, which is analysed under a large number of statistically randomised mixed-mode macro-strains, applied with periodic boundary conditions. The complex damage mechanisms occurring at the meso-scale are captured using the anisotropic cohesive phase field model, and the homogenised stress-strain responses post-damage evolution are obtained. These anisotropic meso-scale fracture responses are used to train the Polynomial Chaos Expansion (PCE) and Artificial Neural Network (ANN) based surrogate models, which are interrogated at the macro-scale using arbitrary macro-strain combinations. The accuracy of the surrogate model is validated against high-fidelity phase field simulations for a set of benchmarks

Damage modelling in fibre-reinforced composite laminates using phase field approach

Thin unidirectional-tape and woven fabric-reinforced composites are widely utilized in the aerospace and automotive industries due to their enhanced fatigue life and impact damage resistance. The increasing industrial applications of such composites warrants a need for high-fidelity computational models to assess their structural integrity and ensure robust and reliable designs. Damage detection and modelling is an important aspect of overall design and manufacturing lifecycle of composite structures. In particular, in thin-ply composites, the damage evolves as a result of coupled in-plane (membrane) and out-of-plane (bending) deformations that often arise during critical events, e.g., bird strike/ hail impact or under in-flight service loads. Contrary to metallic structures, failure in composites involves complex and mutually interacting damage patterns, e.g., fibre breakage/ pullout/ bridging, matrix cracking, debonding and delamination. Providing high-fidelity simulations of intra-laminar damage is a challenging task both from a physics and a computational perspective, due to their complex and largely quasi-brittle fracture response. This is manifested by matrix cracking and fibre breakage, which result in a sudden loss of strength with minimum crack openings; subsequent fibre pull-outs result in a further, although gradual, strength loss. To effectively model this response, it is necessary to account for the cohesive forces evolving within the fracture process zone. Furthermore, the interaction of the failure mechanisms pertinent to both the fibres and the matrix necessitate the definition of anisotropic damage models. In addition, the failure in composites extends across multiple scales; it initiates at the fibre/ matrix-level (micro-scale) and accumulates into larger cracks at the component/ structural level (macro-scale). From a simulation standpoint, accurate prediction of the structure’s critical load bearing capacity and its associated damage thresholds becomes a challenging task; accuracy necessitates a fine level of resolution, which renders the corresponding numerical model computationally expensive. To this point, most damage models are applied at the meso-scale based on local stress-strain estimates, and considering material heterogeneity. Such damage models are often computationally expensive and practically inefficient to simulate the failure behaviour in real-life composite structures. Moreover at the macro-scale, the effect of local stresses is largely minimised, which necessitates definition of a homogenised failure criterion based on global macro-scale stresses. This thesis presents a phase field based MITC4+ (Mixed Interpolation of Tensorial Components) shell element formulation to simulate fracture propagation in thin shell structures under coupled membrane and bending deformations. The employed MITC4+ approach renders the element shear- and membrane- locking free, hence providing high-fidelity fracture simulations in planar and curved topologies. To capture the mechanical response under bending-dominated fracture, a crack-driving force description based on the maximum strain energy density through the shell-thickness is considered. Several numerical examples simulating fracture in flat and curved shell structures which display significant transverse shear and membrane locking are presented. The accuracy of the proposed formulation is examined by comparing the predicted critical fracture loads against analytical estimates. To simulate diverse intra-laminar fracture modes in fibre reinforced composites, an anisotropic cohesive phase field model is proposed. The damage anisotropy is captured via distinct energetic crack driving forces, which are defined for each pertinent composite damage mode together with a structural tensor that accounts for material orientation dependent fracture properties. Distinct 3-parameter quasi-quadratic degradation functions based on fracture properties pertinent to each failure mode are used, which result in delaying or suppressing pre-mature failure initiation in all modes simultaneously. The degradation functions can be calibrated to experimentally derived strain softening curves corresponding to relevant failure modes. The proposed damage model is implemented in Abaqus and is validated against experimental results for woven fabric-reinforced and unidirectional composite laminates. Furthermore, a dynamic explicit cohesive phase field model is proposed to capture the significantly nonlinear damage evolution behaviour pertinent to impact scenarios. A strategy is presented to combine the phase field and the cohesive zone models to perform full composite-laminate simulations involving both intra-laminar and inter-laminar damage modes. Finally, the developed phase field model is employed within the framework of a multiscale surrogate modelling technique. The latter is proposed to perform fast and efficient damage simulation involving different inherent scales in composites. The technique is based on a multiscale FE2 (Finite Element squared) homogenisation approach, however the computationally expensive procedure of solving the meso- and macro-scale models simultaneously is avoided by using a robust surrogate model. The meso-scale is defined as a unit-cell representative volume element (RVE) model, which is analysed under a large number of statistically randomised mixed-mode macro-strains, applied with periodic boundary conditions. The complex damage mechanisms occurring at the meso-scale are captured using the anisotropic cohesive phase field model, and the homogenised stress-strain responses post-damage evolution are obtained. These anisotropic meso-scale fracture responses are used to train the Polynomial Chaos Expansion (PCE) and Artificial Neural Network (ANN) based surrogate models, which are interrogated at the macro-scale using arbitrary macro-strain combinations. The accuracy of the surrogate model is validated against high-fidelity phase field simulations for a set of benchmarks

Deep learned Electrical Resistance Tomography Applications in Structural Health Monitoring

In recent studies, electrical resistance tomography (ERT) has been explored as a non-destructive testing imaging modality in conjunction with structural health monitoring (SHM). This imaging modality has been shown to be able to locate cracks in cement-based materials as well as reconstruct strain and stress distributions in nano-composite materials. However, due to the ill-conditioned nature of the ERT inverse problem, the computational cost of solving such problems can be high. In order to reduce the overall computational cost of solving the ERT inverse problem in practical applications, we propose using a deep learning approach to address this challenge. The deep-learned ERT frameworks have been successfully implemented and validated using simulation and experimental data for various materials relevant to SHM. The results indicate that the deep-learned ERT frameworks are feasible for implementation in SHM applications