References of "Computer Methods in Applied Mechanics and Engineering"
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See detailStructural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods
Chen, L.L.; Lian, Haojie UL; Chen, H.B. et al

in Computer Methods in Applied Mechanics and Engineering (2019), 355

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to ... [more ▼]

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD geometry directly without postprocessing steps. In the present paper, we apply the IGABEM to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis. We employ the Burton–Miller formulation to overcome fictitious frequency problems, in which hyper-singular integrals are evaluated explicitly. The gradient-based optimizer is adopted and shape sensitivity analysis is conducted with implicit differentiation methods. The design variables are set to be the positions of control points which directly determine the shape of structures. Finally, numerical examples are provided to verify the algorithm. [less ▲]

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See detailComputational chemo-thermo-mechanical coupling phase-field model for complex fracture induced by early-age shrinkage and hydration heat in cement-based materials
Nguyen, Thanh Tung UL; Waldmann, Danièle UL; Bui, T. Q.

in Computer Methods in Applied Mechanics and Engineering (2019), 348

In this paper, we present a new multi-physics computational framework that enables us to capture and investigate complex fracture behavior in cement-based materials at early-age. The present model ... [more ▼]

In this paper, we present a new multi-physics computational framework that enables us to capture and investigate complex fracture behavior in cement-based materials at early-age. The present model consists of coupling the most important chemo-thermo-mechanical processes to describe temperature evolution, variation of hydration degree, and mechanical behavior. The changes of material properties are expressed as a function of the hydration degree, to capture the age effects. Fracture analysis of these processes are then accommodated by a versatile phase field model in the framework of smeared crack models, addressing the influence of cracks on hydration and thermal transfer. We additionally describe a stable and robust numerical algorithm, which aims to solve coupled problems by using a staggered scheme. The developed approach is applied to study the fracture phenomena at both macroscopic and mesoscopic scales, in which all microstructural heterogeneities of sand and cement matrix are explicitly accounted. Nucleation, initiation, and propagation of complex crack network are simulated in an efficient way demonstrating the potential of the proposed approach to assess the early-age defects in concrete structures and materials. [less ▲]

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See detailA unified enrichment approach addressing blending and conditioning issues in enriched finite elements
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics and Engineering (2019), 349

We present a combination of techniques to improve the convergence and conditioning properties of partition of unity (PU) enriched finite element methods. By applying these techniques to different types of ... [more ▼]

We present a combination of techniques to improve the convergence and conditioning properties of partition of unity (PU) enriched finite element methods. By applying these techniques to different types of enrichment functions, namely polynomial, discontinuous and singular, higher order convergence rates can be obtained while keeping condition number growth rates similar to the ones corresponding to standard finite elements. [less ▲]

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See detailModel order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties
Ding, Chensen UL; Deokar, Rohit R.; Ding, Yanjun et al

in Computer Methods in Applied Mechanics and Engineering (2019), 349

Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially ... [more ▼]

Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially uncorrelated material uncertainties. They are not representative of realistic and practical engineering situations. In particular, it is more serious for composite structures comprised of dissimilar materials. Therefore, we propose a novel model order reduction via proper orthogonal decomposition accelerated Monte Carlo stochastic isogeometric method (IGA-POD-MCS) for stochastic analysis of exactly represented (composite) structures. This approach particularly enables high-dimensional material uncertainties wherein the characteristics of each element are independent. And the novelties include: (1) the structural geometry is exactly modeled thanks to isogeometric analysis (IGA), as well as providing more accurate deterministic and stochastic solutions, (2) we innovatively consider high-dimensional and independent material uncertainties by separating the stochastic mesh from the IGA mesh, and modeling different stochastic elements to have different (independent) uncertainty behaviors, (3) the classical Monte Carlo simulation (MCS) is employed to universally solve the high-dimensional uncertainty problem. However, to circumvent its computational expense, we employ model order reduction via proper orthogonal decomposition (POD) into the IGA coupled MCS stochastic analysis. In particular, we observe that this work decouples all IGA elements and hence permits independent uncertainty models easily, thereby the engineering problem is modeled to be more realistic and authentic. Several illustrative numerical examples verify the proposed IGA-POD-MCS approach is effective and efficient; and the larger the scale of the problem is, the more advantageous the method will become. [less ▲]

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See detailA simple and robust computational homogenization approach for heterogeneous particulate composites
Bansal, Manik; Singh, I.V.; Patil, R.U. et al

in Computer Methods in Applied Mechanics and Engineering (2019), 349

In this article, a computationally efficient multi-split MsXFEM is proposed to evaluate the elastic properties of heterogeneous materials. The multi-split MsXFEM is the combination of multi-split XFEM ... [more ▼]

In this article, a computationally efficient multi-split MsXFEM is proposed to evaluate the elastic properties of heterogeneous materials. The multi-split MsXFEM is the combination of multi-split XFEM with multiscale finite element methods (MsFEM). The multi-split XFEM is capable to model multiple discontinuities in a single element which leads to reduction in the number of mesh elements, whereas MsFEM helps in reducing the computational time. Strain energy based homogenization has been implemented on an RVE (having volume fraction of heterogeneities up to 50%) for evaluating the elastic properties. From macro-element size analysis, we estimate that the RVE edge length must be 5 times the edge length of the macro-element. The directional analysis has been performed to verify the isotropic behavior of the material, whereas contrast analysis has been done to check the numerical accuracy of the proposed scheme. A level set correction (LSC) based on higher order shape functions has been proposed to reduce mapping errors of level set values. It is also observed that multi-split MsXFEM is about 16 times computationally more efficient than MsXFEM for 50% volume of heterogeneities. [less ▲]

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See detailFracture modeling with the adaptive XIGA based on locally refined B-splines
Gu, Jiming; Yu, Tiantang; Le, Van Lich et al

in Computer Methods in Applied Mechanics and Engineering (2019), 354

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See detailCorotational cut finite element method for real-time surgical simulation: Application to needle insertion simulation
Bui, Huu Phuoc UL; Tomar, Satyendra UL; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics and Engineering (2018), 345

We present the corotational cut Finite Element Method (FEM) for real-time surgical simulation. The only requirement of the proposed method is a background mesh, which is not necessarily conforming to the ... [more ▼]

We present the corotational cut Finite Element Method (FEM) for real-time surgical simulation. The only requirement of the proposed method is a background mesh, which is not necessarily conforming to the boundaries/interfaces of the simulated object. The details of the surface, which can be directly obtained from binary images, are taken into account by a multilevel embedding algorithm which is applied to elements of the background mesh that are cut by the surface. Dirichlet boundary conditions can be implicitly imposed on the surface using Lagrange multipliers, whereas traction or Neumann boundary conditions, which is/are applied on parts of the surface, can be distributed to the background nodes using shape functions. The implementation is verified by convergences studies, of the geometry and of numerical solutions, which exhibit optimal rates. To verify the reliability of the method, it is applied to various needle insertion simulations (e.g. for biopsy or brachytherapy) into brain and liver models. The numerical results show that, while retaining the accuracy of the standard FEM, the proposed method can (1) make the discretisation independent from geometric description, (2) avoid the complexity of mesh generation for complex geometries, and (3) provide computational speed suitable for real-time simulations. Thereby, the proposed method is very suitable for patient-specific simulations as it improves the simulation accuracy by automatically, and properly, taking the simulated geometry into account, while keeping the low computational cost. [less ▲]

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See detailImproving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization
Agathos, Konstantinos; Bordas, Stéphane UL; Chatzi, Eleni

in Computer Methods in Applied Mechanics and Engineering (2018)

Partition of unity enrichment is known to significantly enhance the accuracy of the finite element method by allowing the incorporation of known characteristics of the solution in the approximation space ... [more ▼]

Partition of unity enrichment is known to significantly enhance the accuracy of the finite element method by allowing the incorporation of known characteristics of the solution in the approximation space. However, in several cases it can further cause conditioning problems for which a number of remedies have been proposed in the framework of the extended/generalized finite element method (XFEM/GFEM). Those solutions often involve significant modifications to the initial method and result in increased implementation complexity. In the present work, a simple procedure for the local near-orthogonalization of enrichment functions is introduced, which significantly improves the conditioning of the resulting system matrices, while requiring only minor modifications to the initial method. Although application to different types of enrichment functions is possible, the resulting scheme is specialized for the singular enrichment functions used in linear elastic fracture mechanics and tested through benchmark problems. [less ▲]

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See detailAdaptive multi-patch isogeometric analysis based on locally refined B-splines
Gu, J.; Yu, T. T.; Le, V. L. et al

in Computer Methods in Applied Mechanics and Engineering (2018), 339

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See detailSkew-symmetric Nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact
Hu, Qingyuan; Chouly, Franz; Hu, Ping et al

in Computer Methods in Applied Mechanics and Engineering (2018), 341

A simple skew-symmetric Nitsche’s formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions ... [more ▼]

A simple skew-symmetric Nitsche’s formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as Signorini contact conditions. For linear boundary or interface conditions, the skew-symmetric formulation is parameter-free. For contact conditions, it remains stable and accurate for a wide range of the stabilization parameter. Several numerical tests are performed to illustrate its accuracy, stability and convergence performance. We investigate particularly the effects introduced by Nitsche’s coupling, including the convergence performance and condition numbers in statics as well as the extra “outlier” frequencies and corresponding eigenmodes in structural dynamics. We present the Hertz test, the block test, and a 3D self-contact example showing that the skew-symmetric Nitsche’s formulation is a suitable approach to simulate contact problems in IGA. [less ▲]

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See detailA parallel and efficient multi-split XFEM for 3-D analysis of heterogeneous materials
Bansal, Manik; Singh, I.V.; Mishra, B.K. et al

in Computer Methods in Applied Mechanics and Engineering (2018)

We propose a parallel and computationally efficient multi-split XFEM approach for 3-D analysis of heterogeneous materials. In this approach, multiple discontinuities (pores and reinforcement particles ... [more ▼]

We propose a parallel and computationally efficient multi-split XFEM approach for 3-D analysis of heterogeneous materials. In this approach, multiple discontinuities (pores and reinforcement particles) may intersect any given element (we call those elements multi-split elements). These discontinuities are modeled by imposing additional degrees of freedom at the nodes. The main advantage of the proposed scheme is that the mesh size remains independent of the relative distance among the heterogeneities/discontinuities. The pores and reinforcement particles are assumed to be spherical. The simulations are performed for uniform and non-uniform heterogeneity distribution. The Young’s modulus of the heterogeneous material is evaluated for different amount of pores and reinforcement particles. To demonstrate the computational efficiency of the multi-split XFEM, elastic damage analysis is performed for the unit cell with 5% pores and 5% reinforcement particles under uniaxial tensile loading. These simulations show that the Young’s modulus decreases linearly with the increase in the volume fraction of the pores and increases linearly with the increase in volume fraction of reinforcement particles. The multi-split XFEM is found to be at least 1.8 times computationally efficient than standard XFEM and at least 6.7 times computationally efficient than FEM. [less ▲]

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See detailAdaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimation
Yu, Peng; Anitescu, Cosmin; Tomar, Satyendra UL et al

in Computer Methods in Applied Mechanics and Engineering (2018), 342

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed ... [more ▼]

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field approximaTion (GIFT) framework, which may be seen as a generalization of the Iso-Geometric Analysis (IGA).Within the GIFT framework, we describe the geometry of the structure exactly with NURBS (Non-Uniform Rational B-Splines), whilst independently employing Polynomial splines over Hierarchical T-meshes (PHT)-splines to represent the solution field. The proposed strategy of local adaptivity, wherein a posteriori error estimators are computed based on inexpensive hierarchical h-refinement, aims to control the discretization error within a frequency band. The approach sweeps from lower to higher frequencies, refining the mesh appropriately so that each of the free vibration mode within the targeted frequency band is sufficiently resolved. Through several numerical examples, we show that the GIFT framework is a powerful and versatile tool to perform local adaptivity in structural dynamics. We also show that the proposed adaptive local h-refinement scheme allows us to achieve significantly faster convergence rates than a uniform h-refinement. [less ▲]

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See detailA phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography
Nguyen, Thanh Tung UL; Yvonnet, J.; Zhu, Q.-Z. et al

in Computer Methods in Applied Mechanics and Engineering (2016), 312

Detailed reference viewed: 48 (2 UL)