The particle finite element method (PFEM) in thermo‐mechanical problems

Abstract

The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo-mechanical problems. In particular the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes and thermal effects.The framework of the numerical scheme is based on the Particle Finite Element Method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (α−shape method), in this work the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function.The description of the thermo-mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u-p mixed formulation, with a stabilization of the pressure term via the Polynomial Pressure Projection (PPP), is proposed.One of the novelties of this work is the use of a combination between the isothermal split (Simo and Miehe [79]) and the so-called IMPL-EX hybrid integration technique (proposed by Oliver, Huespe and Cante [53]) to enhance the robustness and reduce the typical iteration number of the fully implicit NewtonRaphson solution algorithm. * Universitat Politècnica de Catalunya (UPC), Campus Terrassa, C/Colom 11, 08222 Terrassa, Spain.† International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, Gran Capitán, s/n., 08034 Barcelona, Spain. E-mail: cpuigbo@cimne.upc.edu.‡ Escola Tècnica Superior d'Enginyeries Industrial i Aeronàutica de Terrassa, Rambla de Sant Nebridi 22, 08222 Terrassa, Spain.§ International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, Gran Capitán, s/n., 08034 Barcelona, Spain. 2The new set of numerical tools implemented in the PFEM algorithm -including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points-allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo-mechanical problems.Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking free element type and different time integration schemes for thermo-mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example.

A 3D Numerical Approach to Assess the Temporal Evolution of Settlement Damage to Buildings on Cavities Subject to Weathering

“…Microscopic weakening processes: a saturation-induced short-term debonding of depositional bonds; b, c dissolutiondriven long-term debonding and grain dissolution process (Ciantia et al 2015a) chemical enhanced crack propagation (Hueckel et al 2017) and strain localization cannot be captured by GHM and the adopted constitutive model, the definition and use of the BDI(t) would remain unchanged even if more advanced numerical methods such as FDEM (Geomechanica Inc 2016) or P-FEM (Rodriguez et al 2016) were to be used. Note that in the latter case a coupled constitutive relationship would still be required.…”

Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

“…The polynomial pressure projection (PPP) stabilization method has been originally developed to stabilize Stokes equations() and has also been applied to stabilize the u − p mixed formulation of solid mechanics and the simplified u − p w formulation in soil mechanics. () The technique has two main ingredients: A mixed equal order interpolation of the scalar and vector fields. A L 2 projection of the scalar variables. …”

Generation of segmental chips in metal cutting modeled with the PFEM

“…Thermoelastic trial state: The definition of the variables that appear in this box are explained in [21,27,29]. Tables 1 and 2.…”

“…In summary, the isothermal split solves the mechanical problem with a predicted value of temperature equal to the temperature of the last converged time step and, then, solves the thermal problem using the configuration obtained as a solution of the mechanical problem. A full Newton-Raphson scheme is used for the solution of the non-linear system; the necessary linearization of the constitutive law has been presented in see [21,29]. The details of the linearization of the weak form of the momentum and energy equation can be seen in [2,3].…”