Eulerian-Lagrangian Coupling in Finite Element Calculations With Applications to Machining

Multi-material Eulerian finite element methods are attractive for problems in solid mechanics where new free surfaces are created, e.g., the formation of chips in machining. One weakness associated with the Eulerian finite element formulation, however, is the interaction of materials at the contact interface. The standard mixture theories effectively bond the materials together, and prohibit the relative slip between the materials that is crucial for an accurate machining simulation. In this paper, we compare the results of a machining calculation performed using an Eulerian formulation with a contact mixture theory and a coupled Eulerian-Lagrangian calculation, where the workpiece is Eulerian, and the tool is Lagrangian.

First-Principles Equation of State for an Energetic Intermetallic Mixture

The thermodynamically complete equation of state P=P(ρ,T) for a intermetallic mixture of nickel and aluminum is obtained via first principle calculations for pressures up to 300GPa and temperatures up to 1000K. The calculations for the static-lattice EOS are carried out in the framework of the density functional theory (DFT), using generalized gradient approximations and ultrasoft psuedopotentials. The phonon modes are calculated by using the density functional perturbation theory (DFPT). First, the EOS for each species is obtained based on ab initio prediction of the electron ground state and thermal excitations. Then, the mixture theories are utilized to obtain the EOS for the mixture. Two mixture theories are proposed, which correspond to the two limiting cases. The nature of the real mixture is intermediate to those of the two idealized mixtures and hence can be modeled as a weighted combination of the two cases. The Comparisons of the EOS for nickel and aluminum obtained from existing shock Hugoniot data show good agreement with the theoretical results.

On bulk growth mechanics of solid-fluid mixtures

This work aims at investigating the possibility to account for the volumetric growth of a binary solid-uid mixture, within the context of biomechanical perspectives in rational mixture theories. Growth phenomena are coarsely taken into account by describing the time evolution of the solid stress-free configuration, whose introduction contributes a part of the constitutive information to the resulting dynamics, while enriching the kinematical description of the mixture. The issue of invariance requirements under changes in observer is also addressed, and some relevant constitutive implications are briey outlined. .