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result(s) for
"Fracture mechanics Mathematics."
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Fracture mechanics of electromagnetic materials
Fracture Mechanics of Electromagnetic Materials provides a comprehensive overview of fracture mechanics of conservative and dissipative materials, as well as a general formulation of nonlinear field theory of fracture mechanics and a rigorous treatment of dynamic crack problems involving coupled magnetic, electric, thermal and mechanical field quantities.
eBook
Extended finite element method for crack propagation
Novel techniques for modeling 3D cracks and their evolution in solids are presented.Cracks are modeled in terms of signed distance functions (level sets).Stress, strain and displacement field are determined using the extended finite elements method (X-FEM).
eBook
A review on phase-field models of brittle fracture and a new fast hybrid formulation
In this contribution we address the issue of efficient finite element treatment for phase-field modeling of brittle fracture. We start by providing an overview of the existing quasi-static and dynamic phase-field fracture formulations from the physics and the mechanics communities. Within the formulations stemming from Griffith’s theory, we focus on quasi-static models featuring a tension-compression split, which prevent cracking in compression and interpenetration of the crack faces upon closure, and on the staggered algorithmic implementation due to its proved robustness. In this paper, we establish an appropriate stopping criterion for the staggered scheme. Moreover, we propose and test the so-called hybrid formulation, which leads within a staggered implementation to an incrementally linear problem. This enables a significant reduction of computational cost—about one order of magnitude—with respect to the available (non-linear) models. The conceptual and structural similarities of the hybrid formulation to gradient-enhanced continuum damage mechanics are outlined as well. Several benchmark problems are solved, including one with own experimental verification.
Journal Article
Robust, strong form mechanics on an adaptive structured grid: efficiently solving variable-geometry near-singular problems with diffuse interfaces
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries and constant remeshing. The purpose of this work is to present a comprehensive strategy for efficiently solving such problems on an adaptive structured grid, while expositing some of the basic yet important nuances associated with solving near-singular problems in strong form. We employ a robust smooth boundary method (SBM) that represents complex geometry implicitly, in a larger and simpler computational domain, as the support of a smooth indicator function. We present the resulting semidefinite equations for mechanical equilibrium, in which inhomogeneous boundary conditions are replaced by source terms. In this work, we present a computational strategy for efficiently solving near-singular SBM-based solid mechanics problems. We use the block-structured adaptive mesh refinement method, coupled with a geometric multigrid solver for an efficient solution of mechanical equilibrium. We discuss some of the practical numerical strategies for implementing this method, notably including the importance of grid versus node-centered fields. We demonstrate the solver’s accuracy and performance for three representative examples: (a) plastic strain evolution around a void, (b) crack nucleation and propagation in brittle materials, and (c) structural topology optimization. In each case, we show that very good convergence of the solver is achieved, even with large near-singular areas, and that any convergence issues arise from other complexities, such as stress concentrations.
Journal Article
A general phase-field model for fatigue failure in brittle and ductile solids
In this work, the phase-field approach to fracture is extended to model fatigue failure in high- and low-cycle regime. The fracture energy degradation due to the repeated externally applied loads is introduced as a function of a local energy accumulation variable, which takes the structural loading history into account. To this end, a novel definition of the energy accumulation variable is proposed, allowing the fracture analysis at monotonic loading without the interference of the fatigue extension, thus making the framework generalised. Moreover, this definition includes the mean load influence of implicitly. The elastoplastic material model with the combined nonlinear isotropic and nonlinear kinematic hardening is introduced to account for cyclic plasticity. The ability of the proposed phenomenological approach to naturally recover main features of fatigue, including Paris law and Wöhler curve under different load ratios is presented through numerical examples and compared with experimental data from the author’s previous work. Physical interpretation of additional fatigue material parameter is explored through the parametric study.
Journal Article
A comparative review of peridynamics and phase-field models for engineering fracture mechanics
Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.
Journal Article
A phase-field model of thermo-elastic coupled brittle fracture with explicit time integration
The phase-field method is a very effective way to simulate arbitrary crack nucleation, propagation, bifurcation, and the formation of complex crack networks. The diffusion-based method is suitable for multi-field coupling fracture problems. In this paper, a parallel algorithm of the thermo-elastic coupled phase-field model is implemented in commercial finite element code Abaqus/Explicit. The algorithm is applied to simulate the dynamic and quasi-static brittle fracture of thermo-elastic materials. Further, it is adopted on a structured mesh combined with first-order explicit integrators. Several examples of the quasi-static and dynamic cases of single crack, as well as multi-crack initiation and propagation under thermal shock, are given to demonstrate the robustness of the algorithm. The source code and tutorials provide an effective way to simulate crack nucleation and propagation in multi-field coupling problems.
Journal Article
Phase-field modeling of ductile fracture
Phase-field modeling of
brittle
fracture in elastic solids is a well-established framework that overcomes the limitations of the classical Griffith theory in the prediction of crack nucleation and in the identification of complicated crack paths including branching and merging. We propose a novel phase-field model for
ductile
fracture of elasto-plastic solids in the quasi-static kinematically linear regime. The formulation is shown to capture the entire range of behavior of a ductile material exhibiting
J
2
-plasticity, encompassing plasticization, crack initiation, propagation and failure. Several examples demonstrate the ability of the model to reproduce some important phenomenological features of ductile fracture as reported in the experimental literature.
Journal Article
Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture
Efficient implementation of the element-free Galerkin (EFG) method for a phase-field model of linear elastic fracture mechanics is presented, in which the convenience of the meshfree method to construct high order approximation functions and to implement h-adaptivity is fully exploited. A second-order moving-least squares approximation for both displacement and phase field is employed. Domain integration of the weak forms is evaluated by the quadratically consistent 3-point integration scheme. The refinement criterion using maximum residual strain energy history is proposed and the insertion of nodes is based on the background mesh. Numerical results show that the developed method is more efficient than the standard finite element method (3-node triangle element) due to the proposed h-adaptivity. In comparison with the standard EFG method, the proposed consistent EFG method significantly improves the computational efficiency and accuracy. The advantage of the quadratic approximation is also demonstrated. In addition, the feasibility of extending the proposed method to 3D is validated by the modeling of a twisting crack.
Journal Article