Lagrangian finite element approaches are particularly suited for the description of free surface flows. The position of the fluid mesh nodes defines automatically the boundaries with no need for interface tracking algorithms. Unfortunately, the Lagrangian motion of the fluid nodes can lead to overly distorted meshes. The Particle Finite Element Method (PFEM) overcomes generating a new mesh when the current one gets too distorted using Delaunay Tassellation coupled with a distortion criterion.

The analysis of fluid–structure interaction (FSI) problems, in which the structure undergoes large deformations and the fluid motion is characterized by free surfaces and breaking waves, is of great relevance in many areas of engineering. A possibility to overcome the difficulties related to the tracking of the interfaces between fluids and solids is the use of a Lagrangian approach for both the fluid and the solid parts. We proposed a (FSI) approach in which the fluid si described with the Particle Finite Element Method (PFEM) and the structure with the Finite Element Method. Tha Lagrangian nature of the PFEM, toghether with its efficient mesh management allows for the automatic tracking of the free surfaces.

3D Concrete Printing (3DCP) is a rapidly evolving technology that allows for the efficient and accurate construction of complex concrete objects. In 3DCP a cementitious mortar is extruded through a digitally controlled nozzle and the targeted shape is progressively generated out of layers of material. Nonetheless, this technology is not ready yet for large-scale adoption, because of the technical issues still to be addressed and the many uncertainties linked to the extrusion process and its outcomes. The progress of numerical models is expected in time to cover this gap and to provide the designer with better knowledge and control of 3DCP.

The Virtual Element Method (VEM) is an innovative numerical technique designed for polygons in 2D and polyhedra in 3D. Avoiding the explicit definition of the shape functions and introducing an innovative construction of the stiffness matrixes, the method has important advantages with respect to standard Finite Element Method. Its mathematical foundations have been well established and it has been applied on numerous applications.

Landslides characterized by high velocities and long runout distances behave in a fluid-like manner. Modeling such fluidized material is important for the creation of maps of hazardous areas, to estimate the entity of the hazard and finally to design appropriate protective measures. The prediction of runout distances and velocities requires a complete mathematical modeling of the phenomenon. A Lagrangian approach with continuous remeshing, to account for the extremely large deformations and consequent mesh distortion, based on the particle finite-element method (PFEM) is here adopted.