Machining is very common in industry, e.g. automotive industry and aerospace industry, which is a nonlinear dynamic problem including large deformations, large strain, large strain rates and high temperatures, that implies some difficulties for numerical methods such as Finite element method. One way to simulate such kind of problems is the Particle Finite Element Method (PFEM) which combines the advantages of continuum mechanics and discrete modeling techniques. In this work we introduce an improved PFEM called the Adaptive Particle Finite Element Method (A-PFEM). The A-PFEM introduces particles and removes wrong elements along the numerical simulation to improve accuracy, precision, decrease computing time and resolve the phenomena that take place in machining in multiple scales. At the end of this paper, some examples are present to show the performance of the A-PFEM.

In this work, the particle finite element method (PFEM) is extended to simulate additive manufacturing processes in a variety of different complicated geometries. A three-dimensional α-shape approach is used to carry out the material addition procedure. It overcomes the limitation of merely employing the traditional element birth and death technique and reduces the degrees of freedom compared to this technique. Furthermore, numerical examples are used to evaluate and demonstrate the applicability of the PFEM method for additive manufacturing within the framework of a weakly coupled thermoelasticity formulation. During additive manufacturing operations, deflections, stresses, and temperature are computed using a user defined implementation in FEniCS.

The particle finite element method (PFEM) combines the benefits of discrete modeling techniques and approaches based on continuum mechanics. It provides a convenient tool to deal with the problem of large configurational change, such as metal cutting, in which nonlinear plasticity plays a key role [1]. In this article we introduce a phenomenological plasticity model with the help of a multiplicative decomposition of the deformation gradient and an intermediate local configuration into the PFEM framework. Numerical examples of cutting simulations are presented to show the performance of the formulation.Continuum methods are suitable for modelling of complex material behaviour but are problematic for large configurational changes, whereas discrete models are appropriate for detecting configurational changes but are computational expensive for large dimensions and long time scales. The particle finite element method (PFEM) first introduced in [2] for problems with liquid solid interaction combines the benefits of the continuum based methods and the discrete modelling techniques, therefore is well suited for simulation of problems with large deformations and large configurational changes. The structural diagram of the PFEM is given in Fig. 1. A body is represented by an ensemble of particles, which carry the physical quantities such α-shape method mesh region transfer data from particles to Gau points to particles updated particle data detect boundary using initialize particle data transfer data from Gau points solve FEM problem Fig. 1: Outline of the PFEM algorithm as the deformation gradient and the hardening variable. To detect the boundary of the set of particles an α-shape method is employed [3]. After that the detected domain is meshed and a finite element problem along with boundary conditions will be solved. The particle coordinates are updated by using the result of the displacement and the physical quantities are transferred to the particles for the next PFEM step.