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The numerical manifold method (NMM) has been widely utilized to solve problems involving complicated boundaries, cracks, and interfaces. Recently, strain or gradient smoothing techniques have been incorporated into NMM to improve its performance. The resulting smoothed NMMs (SNMMs) normally possess enhanced numerical properties, for example, higher accuracy, convergence, and efficiency. A challenging issue rooted in NMM and other enhanced finite element methods using unfitted meshes is the ill‐conditioning induced by extremely small cut element. In this study, we investigate the behaviors of SNMMs in the case of small cut element. It is demonstrated that the cut‐induced ill‐conditionings also exist for two types of SNMMs, namely, edge‐based SNMM and physical‐patch‐based SNMM. Furthermore, a preconditioner based on the normalization of basis functions is proposed to resolve the ill‐conditioning. Several benchmark problems demonstrate the performances of SNMMs regarding accuracy, convergence, and stability. [ABSTRACT FROM AUTHOR]

Smoothed finite element method with the node‐based strain smoothing domains (NS‐FEM) is remarkable for the upper‐bound feature and insensitivity to the volumetric locking. As a mesh‐based methodology, its application is limited by the burdensome meshing for which elements align with the physical domain. We extend the strain smoothing in NS‐FEM to the numerical manifold method (NMM) with unfitted meshes, and propose a novel methodology named physical patch‐based smoothed NMM. Benchmark problems demonstrate the optimal convergence, stability in term of the condition number, upper‐bound property, suppression of the volumetric locking, as well as the stress stability. [ABSTRACT FROM AUTHOR]

As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini's element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff's thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM. [ABSTRACT FROM AUTHOR]

Zirconium alloys have been serving as primary structural materials for nuclear fuel claddings. Structural failure analysis under extreme conditions is critical to the assessment of the performance and safety of nuclear fuel claddings. This work focuses on simulating structural failure of Zircaloy tubes with multiple hydride defects through modeling explicit crack propagation in ductile media. First, we developed an integrated cladding failure model by taking into account both crack initiation induced by hydride/matrix interface separation and ligament tearing-off between activated hydride cracks. Second, to accommodate the initiation, propagation, and coalescence of multiple cracks in finite plastic media we incorporated this structural failure model into a coupled continuous/discontinuous Galerkin (DG) based finite element code, a traditionally preferred implicit numerical framework. Third, to improve the adaptive placement of DG interface elements for crack propagation and to identify potential coalescence of cracks due to the interaction between adjacent hydride cracks, we defined a special failure index for the assessment of potential failure zones using both true plastic strain developed and predicted failure strain based on the Johnson-Cook material failure criterion. Finally, by calibrating the proposed material failure model using a cluster of Zircaloy material experimental tests, we successfully simulated a complete failure process of a fuel cladding tube with multiple hydride cracks. [ABSTRACT FROM AUTHOR]

Summary: It is a challenge to achieve a complete simulation of fracture failure in ductile materials undergoing large plastic deformation within implicit finite element frameworks due to instability issues. Currently, traditional nodal force or crack surface traction release methods target the direct release of tractions on cracked surfaces within the current time/load step. An abrupt change from a system without cracks to another system with cracks may contribute to the instability issues. Specifically, because of broken meshes, discontinuous Galerkin (DG) methods have an advantage over traditional continuous elements in naturally accommodating crack openings along DG interfaces across elements. To improve the convergence in nonlinear iterations during crack openings, we propose a relaxation scheme for DG formulations to gradually recover the traction‐free condition on cracked surfaces. Furthermore, this DG‐based relaxation scheme for crack openings in finite plastic media has been consistently formulated within the incomplete interior penalty DG framework. Finally, we have demonstrated a good performance of the proposed implicit DG formulation along with the DG relaxation scheme by successfully solving a nuclear fuel rod structural failure problem with multiple hydride crack openings and the Sandia Fracture Challenge benchmark. [ABSTRACT FROM AUTHOR]

A fully implicit, fully coupled, and fully consistent finite element framework has been formulated in part I of this work for modeling reservoir compaction through linearizing coupled solid and flow field equations and constructing a local material integrator. In part II of this work, we focus on verification and performance analysis of our numerical formulation and computer implementation using several numerical examples. First, we design a cube problem in triaxial compression to verify our numerical formulation and computer code implementation especially for rock formation in compaction using cap plasticity models. The finite element prediction on stresses is compared with the analytical solution. The second problem we select is a strip footing problem popular in the geotechnical area where the evolution of soil consolidation degrees following the diffusion of pore pressure is the main interest. In this example, we demonstrate a good performance of the proposed numerical formulation on solving different shear and compaction-dominated deformation behaviors by varying the footing length. Importantly, an extremely sharp cap model based on real experimental data for Leda clays, a challenging cap model, is successfully applied in this footing problem. Our focus in this work is to model field reservoirs undergoing serious compaction. A reservoir with complex payzone geometries, multiple horizontal wells, and cap plasticity models with sharp cap surfaces has been successfully solved using our fully implicit formulation. The last example is to model a horizontal wellbore damage problem. Finally, the sensitivity of predicted subsidence to nonlinear flow model, cap hardening parameters, and Lode angles have been systemically investigated and documented in detail, which can provide a constructive guidance on how to successfully model field reservoir compaction problems with cap plasticity models. [ABSTRACT FROM AUTHOR]

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction. [ABSTRACT FROM AUTHOR]

Fractures have attracted the attention of computational scientists for several decades. The modeling and simulation of fractures have been a major motivation for developing enriched finite element methods (FEMs), such as the numerical manifold method (NMM). However, ill-conditioning has always haunted NMM and other enriched FEMs when they are utilized for linear elastic fracture problems. Generally, ill-conditioning for a fracture problem is caused by two main issues: the arbitrary cut of the mesh by the fracture path and linear dependence related to the crack-tip enrichments. It is significantly challenging to overcome these two types of ill-conditioning using a single technique. In this study, we employ a preconditioner based on global normalization and local Gram–Schmidt orthogonalization of bases to eliminate these two ill-conditioning issues in NMM entirely and simultaneously. Various numerical examples have demonstrated that the proposed preconditioning strategy is highly effective in reducing the condition number and iteration counts of a iterative solver. It is highly robust, stable, and efficient and can be incorporated into enriched FEM programs to significantly facilitate the analyses of linear elastic fractures. • Ill-conditioning due to mesh cut and crack-tip enrichment is explored. • Symmetric preconditioning overcomes ill-conditioning. • Stability and efficiency are significantly enhanced for linear elastic fractures. [ABSTRACT FROM AUTHOR]

We report terahertz metamaterial waveguides based on the concept of composite right/left-handed transmission-lines. The waveguides are implemented in a metal-insulator-metal geometry fabricated with spin-coated Benzocyclobutene and contact photolithography. Angle-resolved reflection spectroscopy shows strong resonant absorption features corresponding to both right-handed and left-handed (backward wave) propagating modes within the leaky-wave bandwidth. Tuning of the waveguide dispersion is achieved by varying the effective lumped element series capacitance. The experimental results are in good agreement with full-wave finite element method simulations as well as an intuitive transmission-line circuit model. [ABSTRACT FROM AUTHOR]

Fracture propagation coupled with fluid flow in porous media has very important applications in fracking in oil and gas reservoirs, corrosion in ceramics, and degradation of human bones. Modeling fracture failure in porous media governed by the coupled solid and fluid field equations is challenging and time-consuming. This paper extends discontinuous Galerkin (DG) finite element methods to model crack openings in porous media through exploiting an easy construction of interfaces for potential crack paths by locally breaking continuous elements. Consequently, a finite element mesh for fracture apertures is completely and gracefully constructed using DG interface objects as well as the definitions of jumps of displacements across the DG interfaces defined for bulk matrices. Furthermore, rigid cohesive laws often adopted for crack openings can be naturally implemented in DG formulations without introducing artificial stiffness, which may eventually improve the performance for implicit formulations in handling crack openings in porous media. In this work, we perform a consistent, fully implicit, and fully coupled hybrid DG/continuous finite element formulation for three field equations including the solid, bulk fluid, and fluid in fracture apertures resulting from crack openings. We verify our DG formulation and implementation using the Khristianovich-Geertsma-DeKlerk analytical solutions. Finally, we further demonstrate a good performance of the proposed DG method by modeling fracking in an oil reservoir containing two nature fractures. • A fully implicit and fully coupled hybrid IIPG/CG formulations. • Easy incorporatation of rigid cohesive laws in DG methods. • Verification of DG formulation using KGD benchmark. • A two-fracture propagation in porous media simulated. [ABSTRACT FROM AUTHOR]

• A new numerical manifold method is proposed based on the Hermitian interpolation and adoption of rectangular meshes. • C 1 continuity is obtained in the proposed Hermitian numerical manifold method, and the convergence, accuracy and efficiency are considerably improved. • Strains at mathematical nodes inside the physical domain are directly available without extra postprocessing. • The linear dependence problems in most high-order numerical manifold methods are circumvented. Numerous approaches have been proposed to enhance the accuracy and convergence of the numerical manifold method (NMM) in recent years, but most, if not all, of these approaches cannot ensure C 1 continuity. Hermitian interpolation is an effective approach for obtaining high-order approximations. However, the requirement of rectangular meshes hinders the application of this approach in the finite element method. Taking advantage of the freedom in meshing in NMM, Hermitian interpolation is incorporated into NMM to obtain the C 1 approximation. In contrast to the common high-order NMM, the Hermitian NMM (HNMM) improves the accuracy and convergence without causing the linear dependence problem. Moreover, the degrees of freedom (DOFs) of the mathematical nodes inside the physical domain have physical meanings, and the strains at nodes can be obtained directly without the need for extra postprocessing. The proposed HNMM is verified by solving numerous benchmark linear elastic problems, and the results are compared against those of linear and cubic Lagrangian NMMs. The numerical solutions for these examples confirm the remarkable superiority of the HNMM over the Lagrangian NMMs in terms of accuracy, convergence and efficiency. [ABSTRACT FROM AUTHOR]