An efficient procedure for concrete fracture analysis based on mesh refinement ergodicity - Chacón, G.; Rivarola, F. L.; van Huyssteen, Daniel; Steinmann, Paul; Etse, G. (Computational Mechanics, 2024)
In this paper a new procedure for modeling brittle fracture processes in concrete components is proposed in the framework of the so-called discrete crack approach and exploiting ergodic behaviour with respect to the refinement of the mesh. The complexity in controlling localized crack development in quasi-brittle materials like concrete usually necessitates very fine meshes that are associated with a very high computational cost. In this work, a method is proposed that exploits the ergodic behavior with respect to mesh refinement/density observed in simulations performed on randomly generated meshes. The proposed method is framed in the discrete crack concept, which avoids or minimizes mesh dependence. It considers the interaction between elastic solids or aggregates and nonlinear interfaces, where the fractures are described based on the relative displacements at the joints where energy dissipation occurs. To allow significant geometric flexibility in the modeling of elastic aggregates, Voronoi discretizations of virtual elements are used in combination with nonlinear interface elements. Numerical simulations of benchmark problems demonstrate that the proposed procedure accurately predicts failure behavior in brittle materials. Specifically, the peak load, crack path, and load–displacement relationship obtained from the averaged behavior of coarse-mesh simulations closely match those from very fine-mesh simulations. The results demonstrate that by taking advantage of both the well-known mesh flexibility of virtual element method and the observed ergodic behavior with respect to mesh density, the proposed procedure represents an efficient and accurate tool for modeling failure behavior in quasi-brittle materials such as concrete.
CRIS-Team Scopus Importer:2024-06-21
Keywords: Interface element; Mesh refinement ergodicity; Virtual element method

On adaptive mesh coarsening procedures for the virtual element method for two-dimensional elastic problems - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2024)
In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries, and the seamless permission of ‘hanging’ nodes, have inspired many works concerning error estimation and adaptivity. However, these works have primarily focused on adaptive refinement techniques with little attention paid to adaptive coarsening (i.e. de-refinement) techniques that are required for the development of fully adaptive remeshing procedures. In this work novel indicators are proposed for the identification of patches/clusters of elements to be coarsened, along with a novel procedure to perform the coarsening. The indicators are computed over prospective patches of elements rather than on individual elements to identify the most suitable combinations of elements to coarsen. The coarsening procedure is robust and suitable for meshes of structured and unstructured/Voronoi elements. Numerical results demonstrate the high degree of efficacy of the proposed coarsening procedures and sensible mesh evolution during the coarsening process. It is demonstrated that critical mesh geometries, such as non-convex corners and holes, are preserved during coarsening, and that meshes remain fine in regions of interest to engineers, such as near singularities.
CRIS-Team Scopus Importer:2023-10-20
Keywords: De-refinement; Elasticity; Mesh adaptivity; Mesh coarsening; Virtual element method; Voronoi meshes

On mesh refinement procedures for polygonal virtual elements - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Applications in Engineering Science, 2025)
This work concerns the application of adaptive refinement procedures to meshes of unstructured polygonal virtual elements. Adaptive refinement indicators previously proposed by the authors, and investigated for meshes of structured quadrilateral elements, are studied in more general applications. Specifically, the performance of the indicators is studied on unstructured polygonal meshes, and for cases of compressible and nearly-incompressible materials. Localized refinement of unstructured meshes is a non-trivial task as the algorithm must be robust, and must accommodate a wide variety of geometric possibilities. To this end, an element refinement algorithm is presented based on strategic seeding of Voronoi tessellations and is suitable for both structured and unstructured meshes. Furthermore, it is not known apriori whether the previously proposed refinement indicators will be reliable or effective in the presence of unstructured mesh geometries and nearly-incompressible materials. Thus, the performance of the refinement procedures is studied through a broad numerical campaign. The results demonstrate that the high degree of efficacy and efficiency previously exhibited by the adaptive procedures is also achieved in the cases of irregular unstructured/Voronoi meshes and near-incompressibility.
CRIS-Team Scopus Importer:2025-05-23
Keywords: Elasticity; Mesh adaptivity; Mesh refinement; Near-incompressibility; Virtual element method; Voronoi meshes

On mesh refinement procedures for the virtual element method for two-dimensional elastic problems - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2022)
The virtual element method is an extension of the finite element method permitting arbitrary polygonal/polyhedral element geometry. The method's mesh flexibility is well-known and is beginning to be exploited in the context of mesh adaptivity. In this work a variety of novel approaches to the computation of isotropic and anisotropic mesh refinement indicators suited to the VEM are presented and comparatively assessed for the case of two-dimensional linear elasticity on structured meshes. Additionally, a novel investigation of the contributions of the two distinctive terms of the VE matrix, the consistency and stabilization terms, in the context of mesh adaptivity is performed. The results demonstrate that the best performance is achieved using combination of refinement procedures based on the displacement and strain fields. Furthermore, the results indicate that the stabilization term can be exploited to enhance adaptive refinement procedures.
CRIS-Team Scopus Importer:2022-04-08
Keywords: Anisotropic adaptivity; Elasticity; Mesh adaptivity; Mesh refinement procedure; Refinement indicators; Virtual element method

Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2025)
The mesh flexibility offered by the virtual element method has made it increasingly popular in the context of adaptive remeshing. There exists a healthy literature concerning error estimation and adaptive refinement techniques for virtual elements while the topic of adaptive coarsening (i.e. de-refinement) is in its infancy. The notion of a quasi-optimal mesh is based on the principle of quasi-even error distribution over the elements which inherently relies on localized refinement and coarsening techniques. Thus, necessitating a fully adaptive remeshing procedure. In this work a novel fully adaptive non-hierarchical remeshing procedure for the virtual element method is presented for two-dimensional elastic problems. Additionally, novel procedures are proposed for the identification of elements qualifying for refinement or coarsening based on user-defined targets. Specifically, a target percentage error, target number of elements, or target number of nodes can be selected. Numerical results demonstrate that the adaptive remeshing procedure can meet any prescribed target while creating a quasi-optimal mesh. The proposed fully adaptive procedure is of particular interest in engineering applications requiring an efficient simulation of a given accuracy, or desiring a simulation with the maximum possible accuracy for a given computational constraint. Numerical results additionally demonstrate the suitability of the fully adaptive procedure for dynamic problems.
CRIS-Team Scopus Importer:2025-02-17
Keywords: Adaptivity; Coarsening; Hierarchy-free; Quasi-optimal mesh; Refinement; Virtual element method