The simulation of manufacturing processes represents one of the relevant areas of applications of the PFEM. The capability of the method to deal with large deformations, complex contact interaction, and constitutive models, explains the large number of PFEM works on manufacturing processes. Furthermore, typically, these problems also include coupled thermal effects that can be easily handled with the PFEM [11].

Cold Massive Forge. Coining, metal working of a copper piece considering deformable dies and thermo-mechanical contact [12,6,4]

Manufacturing processes have been approached with the PFEM using both solid and fluid mechanics formulations. In [2], a PFEM-solid formulation was used to reproduce industrial metal forging, machining, or powder filling problems. PFEM can be also efficiently used to simulate cutting processes in which phenomena of friction, adiabatic shear bands, excessive heating, large strains, and high strain rates are involved.

Hot bending of a steel plate. Steel plate at 800 K is bent by two deformable tool dies. [12,6]

Reference [3] showed examples of extrusion of steel plates, forging of metal pieces and cutting of metals. Other examples of manufacturing processes can be found in [6, 7, 10] which are focused on the simulation of the segmental chips generated during metal cutting processes.

Non-orthogonal machining of a metal piece using a deformable tool [12]

Some manufacturing processes involve so large deformation of the contours that are more conveniently approached in a fluid dynamics framework than in a solid one. In mold filling and casting problems, fluid dynamics approaches are generally preferred. Some applications of PFEM to these problems can be found in [1] and [4].

Machining of a metal piece. Rigid tool generating a segmental chip from a metal piece [13]

Cold shearing of a steel plate. Cutting of the plate by a punch [3,4,6]

Manufacturing processes in the context of glass forming were considered in [5], where the heat equation is coupled to the mechanical model through a temperature-dependent viscosity. An axisymmetric PFEM formulation was proposed in [8] to simulate the forming of glass bottles.

Modeling the counter blow process (bottle manufacturing) using PFEM [5]

[1] Oñate E, Rojek J, Idelsohn S, Pin FD, Aubry R (2006) Advances in stabilized finite element and particle methods for bulk forming processes. Comput Methods Appl Mech Eng 195(48–49):6750–6777 
[2] Oliver J, Cante J, Weyler R, González C, Hernández J (2007) Particle finite element methods in solid mechanics problems. In: Oñate E, Owen R (eds) Computational plasticity. Springer, Berlin
[3] Carbonell JM, Oñate E, Suarez B (2010) Modeling Ground Excavation with the Particle Finite-Element Method. Journal of Engineering Mechanics. ASCE. 136-4, pp.455-463
[4] Oñate E, Franci A, Carbonell JM (2014) A particle finite element method for analysis of industrial forming processes. Comput Mech 54(1):85–107 
[5] Ryzhakov P, Garcia J, Oñate E (2016) Lagrangian finite element model for the 3D simulation of glass forming processes. Comput Struct 177:126–140 
[6] Rodriguez J, Carbonell JM, Cante J, Oliver J (2016) The particle finite element method (PFEM) in thermo-mechanical problems. Int J Numer Methods Eng 107(9):733–785 
[7] Rodríguez J, Carbonell JM, Cante J, Oliver J (2017) Continuous chip formation in metal cutting processes using the particle finite element method (PFEM). Int J Solids Struct 120:81–102 
[8] Ryzhakov P (2017) An axisymmetric PFEM formulation for bottle forming simulation. Comput Part Mech 4(1):3–12
[9] Rodriguez J, Carbonell JM, Cante J, Oliver J; Jonsén. P (2018). Generation of segmental chips in metal cutting modeled with the PFEM Computational Mechanics. Springer. 61-6, pp.639-655. 
[10] Rodríguez J, Jonsén P, Svoboda A (2019) Simulation of metal cutting using the particle finite-element method and a physically based plasticity model. Comput Part Mech 4(1):35–51
[11] Cremonesi M, Franci A, Idelsohn SR, Oñate E (2020) A state of the art review of the Particle Finite Element Method (PFEM). Archives of Computational Methods in Engineering, 17, 1709-1735
[12] Rodríguez J, Carbonell JM, Jonsén P (2020) Numerical methods for the modelling of chip formation processes, Archives of computational methods in engineering. 27, 387-412
[13] Carbonell JM, Rodríguez J, Oñate E (2020) Modelling 3D metal cutting rpoblems with the particle finite element method, Comput Mech 66-3, 603-624