Adaptive modelling of dynamic brittle fracture - a combined phase field regularized cohesive zone model and scaled boundary finite element approach

Based on the error indicator computed from the scaled boundary equations, a quadtree based adaptive phase-field method is proposed for dynamic brittle fracture problems in isotropic material using the scaled boundary finite element method (SBFEM). The use of SBFEM alleviates the need for additional: (a) constraints to handle hanging nodes resulting from adaptive refinement and (b) post-processing techniques. Three representative examples are solved to demonstrate the efficiency of the proposed approach. From the numerical study, it is opined that the proposed approach requires an order of magnitude fewer degrees of freedom when compared to uniform refinement and can capture the crack morphology under dynamic loading conditions without compromising accuracy. © 2022, The Author(s), under exclusive licence to Springer Nature B.V

Transient thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method

To model fracture in functionally graded materials (FGMs), the scaled boundary finite element method (SBFEM) is extended to examine the effects of fully coupled transient thermoelasticity. Previously developed SBFEM supplementary shape functions are utilized to model thermal stresses. The spatial variation of thermal and mechanical properties of FGMs are approximated by polynomial functions facilitating the semi-analytical evaluation of coefficient matrices. The dynamic stress intensity factors (SIFs) are also evaluated semi-analytically from their definitions without the need for additional post-processing. Scaled boundary polygon elements are employed to facilitate the meshing of complex crack geometries. Both isotropic and orthotropic materials with different material gradation functions are considered. To study the transient effects of thermoelasticity on fracture parameters, several numerical examples with different crack configurations and boundary conditions are considered. The current approach is validated by comparing the results of dynamic SIFs with available reference solutions. © 2023 Elsevier Lt

A comparative study of numerical approaches for the computation of effective properties of micro‐heterogeneous materials

The paper presents a comparative study of the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for the numerical evaluation of the volume‐averaged stress of composites. Two‐dimensional meso‐scale models of concrete represented by digital images and discretized using an automatic mesh generation algorithm are considered. The different computational approaches are discussed and compared with respect to accuracy and efficiency for both scenarios

Thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method

The scaled boundary finite element method is extended to model fracture in functionally graded materials (FGM) under coupled thermo-mechanical loads. The governing equations of coupled thermo-mechanical equilibrium are discretized using scaled boundary shape functions enriched with the thermal load terms. The material gradient is modeled as a series of power functions, and the stiffness matrix is calculated semi-analytically. Stress intensity factors and T−stress are directly calculated from their definition without any need for additional post-processing techniques. Arbitrary-sided polygon elements are employed for flexible mesh generation. Several numerical examples for isotropic and orthotropic FGMs are presented to validate the proposed technique. © 2022 Elsevier Lt

Modelling karst vadose zone hydrology and its relevance for paleoclimate reconstruction

Understanding past climatic changes allows us to better understand how our planet will evolve in the future. One important source of information on paleoclimate is the analysis of speleothems that develop in karst caves and conduits due to the dissolution and precipitation of calcite. However, there are many uncertainties in paleoclimatic reconstruction with speleothems; one of them being hydrological variability. Up to now only few studies have considered the impact of hydrological variability on speleothem formation and composition. This review paper will provide an introduction to hydrological processes that have the potential to affect speleothem composition and the hydrological modelling approaches that are able to account for them. It presents the current state of knowledge on paleoclimatic reconstruction using speleothems and shows that many important flow and transport processes have not yet been included in the interpretation of these archives, mostly due to a lack of field information to parametrize them. Possible directions of future research efforts therefore include a better exploration of karst vadose zone processes and new approaches to incorporate this information into simulation models. Finally, we foresee the exciting advances in reconstructing paleohydrology using karst hydrology models combined with speleothem growth rate and geochemical composition to understand how past climate changes affected the hydrological cycle and water availability