Conforming To Interface Structured Adaptive Mesh Refinement Research Articles

Automated Reconstruction and Conforming Mesh Generation for Polycrystalline Microstructures from Imaging Data

A new algorithm named PolyCISAMR is introduced to automatically generate high-fidelity conforming finite element (FE) meshes for two-dimensional polycrystalline microstructures. PolyCISAMR extends the capabilities of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm, which transforms a structured grid overlaid on the domain geometry into a high-quality conforming mesh. The PolyCISAMR approach uses a segregated meshing strategy, where CISAMR is used to discretize each grain independently and the resulting matching meshes are merged to form the final FE model. In addition, this article presents a set of integrated algorithms for processing low-resolution images of a polycrystal, reconstructed using DREAM.3D software (Version 6.5.121), to generate NURBS characterizations for each grain prior to mesh generation. Example problems demonstrate the effectiveness of PolyCISAMR in creating high-quality meshes for various polycrystalline metallic microstructures along with corresponding crystal plasticity finite element (CPFE) simulations.

An automated mesh generation algorithm for simulating complex crack growth problems

In this manuscript, we expand the conforming to interface structured adaptive mesh refinement (CISAMR) algorithm for modeling complex two-dimensional (2D) crack growth problems involving contact/friction along the crack surface and interaction between multiple cracks. The CISAMR algorithm transforms a structured mesh into a high-quality conforming mesh non-iteratively, which is an attractive feature for modeling the evolution of the crack geometry with minimal changes to the underlying mesh structure. To model such problems, the mesh structure is first adaptively refined and updated near the crack tip to form a spider-web pattern of elements for the accurate approximation of the energy release rate and thereby predicting the new crack path. In each step of the crack advance simulation, a small subset of elements in the vicinity of the crack tip is detected using a tree data structure and then deleted/regenerated to simulate the crack growth. The construction of a high-quality mesh with appropriate element aspect ratios in the algorithm allows the use of an explicit dynamic solver, which is essential to simulate the nonlinear response of the problem caused by contact forces along crack faces. Several benchmark fracture problems are presented to study the accuracy of the proposed algorithm, as well as two more complex problems to demonstrate its ability for modeling interaction of multiple growing cracks with one another and with embedded heterogeneities in the domain.

Higher-order mesh generation using CISAMR: A case study on bias in presentation and interpretation of results

A modified version of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm is presented for the construction of higher-order Lagrangian and NURBS-enhanced (NE) finite element meshes. CISAMR non-iteratively transforms a structured grid into a conforming mesh with an upper bound of three on elements aspect ratio. In this work, we introduce new algorithmic aspects for generating higher-order Lagrangian and NE meshes using CISAMR. For each type of element, a comprehensive study is then provided on the performance of first, second, and third-order meshes for solving linear elastic problems with smooth and oscillatory curvilinear edges. Local gradient recovery error and computational cost are used as performance metrics in these examples. Outcomes are then used as a case study to elucidate common sources of bias in presenting and interpreting results. In particular, we show how bias, whether purposeful or not, could lead to misleading conclusions regarding the performance of a method.

Scalable parallel implementation of CISAMR: a non-iterative mesh generation algorithm

We present the parallel implementation of a non-iterative mesh generation algorithm, named conforming to interface structured adaptive mesh refinement (CISAMR). The partitioning phase is tightly integrated with a microstructure reconstruction algorithm to determine the optimized arrangement of partitions based on shapes/sizes of particles. Each processor then creates a structured sub-mesh with one layer of ghost elements for its designated partition. h-adaptivity and r-adaptivity phases of the CISAMR algorithm are also carried out independently in each sub-mesh. Processors then communicate to merge mesh/hanging nodes along faces shared between neighboring partitions. The final mesh is constructed by performing face-swapping and element subdivision phases, after which a minimal communication phase is required in 3D CISAMR to merge new nodes created on partition boundaries. Several example problems, together with scalability tests demonstrating a super-linear speedup, are provided to show the application of parallel CISAMR for generating massive conforming meshes.

Automated homogenization-based fracture analysis: Effects of SVE size and boundary condition

To model the sample-to-sample variations and the effect of microscale inhomogeneities on fracture response, statistical volume elements (SVEs) are employed to homogenize the elastic and fracture properties of ZrB2-SiC, a two-phase particulate composite often used as a thermal coating. In the mesoscale analysis, 2D finite element models are generated using a non-iterative, automated mesh generation algorithm named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR). The analysis of SVEs under mixed, traction, and minimal kinematic boundary conditions yields their angle-dependent tensile and shear fracture strengths and elastic stiffnesses. This study shows that homogenized fracture strengths are highly dependent on the SVE size and the particular geometric distribution of inclusions (even for similar volume ratios), whereas elastic properties are mainly a function of the volume fraction. Moreover, mean values of strength and bulk modulus, respectively, decrease and remain almost constant as the SVE size increases. For the macroscale analysis, an isotropic, inhomogeneous field of fracture strength is generated from the homogenization of SVEs. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is subsequently employed for fracture analysis under uniaxial tensile and thermal strain loadings.

Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation

A new non-iterative mesh generation algorithm named conforming to interface structured adaptive mesh refinement (CISAMR) is introduced for creating 3D finite element models of problems with complex geometries. CISAMR transforms a structured mesh composed of tetrahedral elements into a conforming mesh with low element aspect ratios. The construction of the mesh begins with the structured adaptive mesh refinement of elements in the vicinity of material interfaces. An r-adaptivity algorithm is then employed to relocate selected nodes of nonconforming elements, followed by face-swapping a small fraction of them to eliminate tetrahedrons with high aspect ratios. The final conforming mesh is constructed by sub-tetrahedralizing remaining nonconforming elements, as well as tetrahedrons with hanging nodes. In addition to studying the convergence and analyzing element-wise errors in meshes generated using CISAMR, several example problems are presented to show the ability of this method for modeling 3D problems with intricate morphologies.

A non-iterative local remeshing approach for simulating moving boundary transient diffusion problems

A computational framework relying on a non-iterative mesh generation algorithm is introduced for modeling moving boundary transient diffusion problems, with a special focus on its application for simulating corrosion phenomena. In this approach, the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is employed to adapt the finite element mesh to the evolving morphology of the problem. CISAMR combines customized h-adaptivity, r-adaptivity, and sub-triangulation algorithms to transform a simple structured mesh into a high quality hybrid conforming mesh composed of rectangular and triangular elements. A key advantage of this method for modeling moving boundary problems is that only the elements located along the moving boundary must be modified to regenerate a conforming mesh at each step. This feature not only facilitates the remeshing process but also reduces the error associated with projecting nodal values of the solution to the new mesh. After a convergence study, we verify the accuracy of CISAMR for modeling pitting corrosion problems by comparing results with analytical solutions and phase field simulations. Additional examples are also provided to show the application of CISAMR for simulating corrosion problems with intricate morphologies.

An integrated computational framework for simulating the failure response of carbon fiber reinforced polymer composites

A new computational framework is introduced for the automated finite element (FE) modeling of fiber reinforced composites and simulating their micromechanical behavior. The proposed methodology relies on a new microstructure reconstruction algorithm that implements the centroidal Voronoi tessellation (CVT) to generate an initial uniform distribution of fibers with desired volume fraction and size distribution in a repeating unit cell of the composite. The genetic algorithm (GA) is then employed to optimize locations of fibers such that they replicate the target spatial arrangement. We also use a non-iterative mesh generation algorithm, named conforming to interface structured adaptive mesh refinement (CISAMR), to create FE models of the CFRPC. The CVT–GA–CISAMR framework is then employed to investigate the appropriate size of the composite’s representative volume element. We also study the strength and failure mechanisms in the CFRPC subject to varying uniaxial and mixed-mode loadings.

Numerical quantification of the impact of microstructure on the mechanical behavior of particulate Al/SiC composites in 2D

The objectives of the current manuscript are twofold: (i) Introducing an automated computational framework for creating realistic finite element models of metal matrix composites (MMCs) microstructures; (ii) Implementing this technique to investigate the effect of microstructure on the mechanical behavior of an Al/SiC particulate MMC. A microstructure reconstruction algorithm is proposed, which relies on the Centroidal Voronoi tessellation, together with the erosion, random movement, and iterative elimination of the resulting Voronoi cells to create an initial periodic virtual microstructure. Non-Uniform Rational B-Splines are also employed to capture the realistic shapes of embedded particles. High fidelity finite element models of the composite microstructure are then created using a non-iterative Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique. This integrated numerical framework is employed to analyze the effect of an Al/SiC MMC microstructure on its mechanical behavior, considering the plastic deformation of the Al matrix and damage in the SiC particles.

Automated Quantification of the Impact of Defects on the Mechanical Behavior of Deoxyribonucleic acid Origami Nanoplates.

Deoxyribonucleic acid (DNA) origami is a method for the bottom-up self-assembly of complex nanostructures for applications, such as biosensing, drug delivery, nanopore technologies, and nanomechanical devices. Effective design of such nanostructures requires a good understanding of their mechanical behavior. While a number of studies have focused on the mechanical properties of DNA origami structures, considering defects arising from molecular self-assembly is largely unexplored. In this paper, we present an automated computational framework to analyze the impact of such defects on the structural integrity of a model DNA origami nanoplate. The proposed computational approach relies on a noniterative conforming to interface-structured adaptive mesh refinement (CISAMR) algorithm, which enables the automated transformation of a binary image of the nanoplate into a high fidelity finite element model. We implement this technique to quantify the impact of defects on the mechanical behavior of the nanoplate by performing multiple simulations taking into account varying numbers and spatial arrangements of missing DNA strands. The analyses are carried out for two types of loading: uniform tensile displacement applied on all the DNA strands and asymmetric tensile displacement applied to strands at diagonal corners of the nanoplate.

A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems

A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.

Conforming to interface structured adaptive mesh refinement: New technique for the automated modeling of materials with complex microstructures

This manuscript introduces a new method named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) for the automated finite element modeling of problems with complex morphologies. The CISAMR transforms a simple structured mesh of quadrilateral elements into a conforming hybrid mesh composed of quadrilateral and triangular elements with low aspect ratios using a non-iterative algorithm. The automated construction of the mesh begins with implementing a customized Structured Adaptive Mesh Refinement (SAMR) algorithm to achieve the desired element size along materials interfaces. A new r-adaptivity algorithm is then employed to move selected nodes of nonconforming elements to intersection points of their edges with the interface, followed by the diagonal sub-triangulation of all elements deformed during this process into conforming sub-triangles. CISAMR does not require relocating the nodes of the background mesh or creating any new node away from materials interfaces after the completion of the SAMR phase. Further, this method can easily handle special cases such as intersecting boundaries/interfaces, while ensuring that aspect ratios of resulting sub-elements are lower than three. A comprehensive discussion is provided on different aspects of the implementation of CISAMR, followed by several example problems to show its application for modeling materials with complex microstructures.