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The Smoothed Particle Finite Element Method (SPFEM) has gained popularity as an effective numerical method for modelling geotechnical problems involving large deformations. To promote the research and application of SPFEM in geotechnical engineering, we present ESPFEM2D, an open-source two-dimensional SPFEM solver developed using MATLAB. ESPFEM2D discretizes the problem domain into computable particle clouds and generates the finite element mesh using Delaunay triangulation and the α -shape technique to resolve mesh distortion issues. Additionally, it incorporates a nodal integration technique based on strain smoothing, effectively eliminating defects associated with the state variable mapping after remeshing. Furthermore, the solver adopts a simple yet robust approach to prevent the rank-deficiency problem due to under-integration by using only nodes as integration points. The Drucker-Prager model is adopted to describe the soil's constitutive behavior as a demonstration. Implemented in MATLAB, this open-source solver ensures easy accessibility and readability for researchers interested in utilizing SPFEM. ESPFEM2D can be easily extended and effectively coupled with other existing codes, enabling its application to simulate a wide range of large geomechanical deformation problems. Through rigorous validation using four numerical examples, namely the oscillation of an elastic cantilever beam, non-cohesive soil collapse, cohesive soil collapse, and slope stability analysis, the accuracy, effectiveness and stability of this open-source solver have been thoroughly confirmed. [ABSTRACT FROM AUTHOR]

Simulation of melt pool dynamics is of crucial importance to understand and improve metal-based additive manufacturing processes. However, the task is challenging due to the complex physical phenomena that must be captured in the numerical models. Challenges include phase change due to solidification, melting and vaporization, and capillary and Marangoni effects from surface tension. Moreover, these highly transient phenomena take place along an evolving and moving surface, demanding accurate boundary detection algorithms. In this work, simulation of melt pool dynamics and the corresponding challenges are addressed with the particle finite element method. The advantage of PFEM over other numerical methods that can be cited is that PFEM allows for an automatic tracking of the melt pool’s free surface, because of the Lagrangian nature of the method and its efficient remeshing process. In addition to presenting the physical models in a comprehensive manner, this work incorporates new remeshing strategies that have recently been proposed in the PFEM literature of fluid flows. Several 2D examples are reported and compared with the literature to demonstrate the huge potential of PFEM to capture complex physical phenomena in melt pools. [ABSTRACT FROM AUTHOR]

The Particle Finite Element Method (PFEM) is attractive for the simulation of large deformation problems, e.g. in free-surface fluid flows, fluid–structure interaction and in solid mechanics for geotechnical engineering and production processes. During cutting, forming or melting of metal, quasi-incompressible material behaviour is often considered. To circumvent the associated volumetric locking in finite element simulations, different approaches have been proposed in the literature and a stabilised low-order mixed formulation (P1P1) is state-of-the-art. The present paper compares the established mixed formulation with a higher order pure displacement element (TRI6) under 2d plane strain conditions. The TRI6 element requires specialized handling, involving the deletion and re-addition of edge-mid-nodes during triangulation remeshing. The robustness of both element formulations is analysed along with different state-variable transfer schemes, which are not yet widely discussed in the literature. The influence of the stabilisation factor in the P1P1 element formulation is investigated, and an equation linking this factor to the Poisson ratio for hyperelastic materials is proposed. [ABSTRACT FROM AUTHOR]

The ability to model complex three dimensional geometries undergoing large deformations is frequently required in finite element simulations of industrial problems. As a result of the large deformations, finite elements may become excessively distorted and consequently unreliable from the numerical point of view. Remeshing must be used in order to preserve a good quality of the discretisation. An important aspect of remeshing is the transfer of history data from one mesh to another. Errors and numerical instabilities caused by this transfer can be minimised by using a consistent methodology. We concentrate here on this issue for finite-strain elasto-plasticity with and without nonlocal damage. A low-order tetrahedral element specially developed for this material behavior and free from locking and pressure oscillations is used for this purpose. The transfer strategy proposed by Mediavilla et al. (Comput Struct 84:604-623, ) for a conventional element is taken as a basis and is extended for the 3D bubble enriched element. It is shown that by consistently transferring a minimum and carefully selected set of variables the simulation remains stable with minimal inconsistencies and deviations. [ABSTRACT FROM AUTHOR]

We present the space-time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called 'DSD/SST-VMST' method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this 'ST/NURBS Mesh Update Method (STNMUM).' The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion. [ABSTRACT FROM AUTHOR]

We present the special space-time computational techniques we have introduced recently for computational aerodynamics modeling of flapping wings of an actual locust. These techniques have been designed to be used with the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, which is the core computational technique. The DSD/SST formulation was developed for flow problems with moving interfaces and was elevated to newer versions over the years, including the space-time version of the residual-based variational multiscale (VMS) method, which is called 'DSD/SST-VMST' and used in the computations reported here. The special space-time techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the locust wings. The motion and deformation data is extracted from the high-speed, multi-camera video recordings of a locust in a wind tunnel. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. These ingredients provide an accurate and efficient way of dealing with the wind tunnel data and the mesh. The computations demonstrate the effectiveness of the core and special space-time techniques in modeling the aerodynamics of flapping wings, with the wing motion and deformation coming from an actual locust. [ABSTRACT FROM AUTHOR]