ProductsAbaqus/ExplicitAbaqus/CAE ALE adaptive mesh constraints on Eulerian boundariesALE adaptive mesh constraints should be applied normal to an Eulerian boundary region; otherwise, the motion of the mesh on the boundary is ambiguous. If no mesh constraints are applied normal to the boundary, Abaqus/Explicit will treat the region as if it were sliding, and the mesh will follow the material normal to the boundary. Although there are no restrictions on specifying adaptive mesh constraints at nodes on an Eulerian boundary region, the following guidelines should be followed in most cases:
Loads and boundary conditions on Eulerian boundaries act on the material that instantaneously coincides with the mesh at the surface. When used in combination with spatial adaptive mesh constraints, physically meaningful Eulerian flow conditions can be defined. Defining inflow Eulerian boundariesThe material flowing into an adaptive mesh domain through an Eulerian boundary will have the same stress and material state as the material in the elements immediately adjacent to the boundary. Therefore, it is important to maintain the stress and material state in those elements at the desired values (which in many cases will be zero, to simulate stressfree material entering the Eulerian domain). To accomplish this goal:
To be physically meaningful, the size and shape of the inflow boundary region must be maintained. For example, applying sufficient constraints is crucial for steadystate process simulations where the crosssection of the workpiece entering the adaptive mesh domain is known and affects the response downstream. The types of constraints appropriate for an inflow boundary depend on whether the precise location of the inflow boundary region is known or whether it is part of the solution. Known inflow boundary locationIn many problems the area, shape, and position of the inflow boundary are known a priori. For example, in the steadystate analysis of a forward extrusion process, an inflow Eulerian boundary can be used to model the flow of material into the adaptive mesh domain. The size of the inflow boundary is based on the known billet crosssection, and the location of the inflow boundary is fixed because of the confined conditions on the material. When the area, shape, and location of the inflow boundary are known, both material and mesh constraints should be applied. Figure 1 shows a typical model setup for a twodimensional forward extrusion problem where either a prescribed mass flow rate or a prescribed uniform pressure is applied to a known inflow boundary. Apply boundary conditions at all nodes on the inflow boundary region to prescribe material constraints in the directions tangential to the boundary surface. Preventing motion of the material tangential to the inflow boundary helps to maintain the stress and material state of the elements adjacent to the Eulerian boundary. Figure 1. Known inflow boundary.
Apply adaptive mesh constraints in the normal direction at all nodes on the inflow boundary. In addition, apply mesh constraints in all tangential directions at the edges and corners surrounding the Eulerian boundary region. These constraints fix the location and size of the crosssectional area at the inflow boundary. If a nonuniform boundary condition or load is applied to the material at the inflow boundary or if the initial material state in the elements adjacent to the boundary is nonuniform in the tangential direction, apply tangential mesh constraints to the nodes strictly in the interior of the Eulerian boundary region. Although the application of mesh and material constraints tangential to and along the edges and corners of an inflow Eulerian boundary may appear to be redundant, they are actually independent. For example, consider a long billet with a variable crosssection, as shown in Figure 2. Figure 2. Modeling a billet with a variable crosssection.
The adaptive mesh domain, with its inflow and outflow Eulerian boundary regions, is assumed to represent a portion of the billet along its length. The entire billet moves with a rigid body velocity along its length (xdirection) so that material flows into one Eulerian boundary and out the other. Boundary conditions are applied to the material at the inflow boundary to maintain this velocity. Mesh constraints are applied normal to the inflow and outflow boundary regions. The mesh constraint applied in the ydirection at node N is used to prescribe the known variable incoming crosssection of the material. The motion of this node does not affect the velocity field of the material entering the domain. Unknown inflow boundary locationSometimes, the location of the inflow boundary region is known only approximately; its precise location will be determined from the solution. For these problems, apply adaptive mesh constraints only in the direction normal to the Eulerian boundary region. In the absence of tangential mesh constraints at the edges and corners of the Eulerian boundary region, Abaqus/Explicit will move these edges and corners with the material in the tangential direction but with the mesh constraints in the normal direction. Therefore, material constraints should be applied using multipoint constraints (see General multipoint constraints) or linear constraint equations (see Linear constraint equations) to preserve the crosssectional area of the inflow boundary. For example, consider a steadystate rolling simulation with multiple rollers in an asymmetric configuration, as shown in Figure 3. Figure 3. Unknown inflow boundary location.
It may be impractical to extend the analysis domain as far as the guides on the upstream side, but spatially fixing the inflow boundary at an arbitrary position in the y and zdirections may cause unrealistic stress on the workpiece as it finds an equilibrium position between the rollers. Mesh constraints are applied normal to the Eulerian boundary region to fix the position of the inflow boundary relative to the rollers in the xdirection. Material constraints (applied with a PIN MPC) are used to ensure that material enters the domain at a uniform velocity and that the crosssection does not rotate. The material constraints will maintain the crosssectional shape of the section while allowing it to move laterally to the correct equilibrium position. Since tangential mesh constraints are not used, the mesh will follow the material in the directions tangential to the Eulerian boundary region. Defining outflow Eulerian boundariesTypically, adaptive mesh constraints should be applied only in the direction normal to the surface on an Eulerian boundary region that acts as an outflow boundary. No tangential mesh constraints should be applied to the edges or corners of an outflow boundary adjacent to a Lagrangian (or sliding) boundary region acting as a free surface. In contrast to inflow boundaries, the crosssection of an outflow boundary adjacent to a free surface is determined by the solution in the domain. At the edge or corner where an Eulerian boundary region meets a Lagrangian or sliding boundary region, Abaqus/Explicit will satisfy the applied mesh constraint normal to the Eulerian boundary region and the inherent mesh constraint normal to the Lagrangian or sliding boundary region simultaneously, thus correctly handling the evolution of the free surface adjacent to the outflow boundary. Figure 4 shows the evolution of an outflow boundary from ${t}_{0}$ to ${t}_{1}$, where material continues to flow through the outflow boundary. Figure 4. Abaqus/Explicit will respect the free surface at an Eulerian outflow boundary.
The mesh constraint normal to the Eulerian outflow boundary is applied by moving node N along the free surface of the material, so that the outflow boundary “expands” with the material arriving from upstream. Although not shown in the figure, mesh smoothing causes all other nodes on the outflow boundary, with the exception of the node on the symmetry plane, to move up toward node N as the boundary expands. No special material boundary conditions are required at outflow Eulerian boundaries. Boundary conditions tangential to the outflow boundary are recommended only if they are the same as those defined upstream (e.g., a symmetry plane running along the length of an Eulerian domain). However, to improve convergence to the steadystate solution in steadystate process simulations, it is often useful to constrain the material velocity to be uniform normal to the outflow boundary using multipoint constraints or linear constraint equations. Defining Eulerian boundary regions that act as both inflow and outflow boundariesAlthough it is rarely appropriate, an Eulerian boundary region can act as both an inflow and an outflow boundary at different times during the same analysis step. Adaptive mesh constraints and material boundary conditions at such a boundary should be chosen to be physically meaningful for both inflow and outflow situations. For each node on the edges and corners of an Eulerian boundary region that does not have mesh constraints tangential to the boundary surface, Abaqus/Explicit will determine in each adaptive mesh increment whether the boundary at the node is acting as an inflow or an outflow boundary. If an inflow condition is detected, the node will move with the material in the tangential direction but with the mesh constraints in the normal direction. If an outflow condition is detected, the movement of the node will both follow the adjacent Lagrangian boundary region and satisfy the mesh constraint normal to the Eulerian boundary region. Lagrangian versus sliding boundary regions on Eulerian domainsMany applications using Eulerian adaptive mesh domains, including the simulation of steadystate processes, have a primary direction of material flow and use a control volume approach to model the process zone. These problems usually include two Eulerian boundary regions, representing an inflow boundary and outflow boundary. The remaining surfaces between the Eulerian boundaries can be either Lagrangian or sliding boundary regions. Determining which type of boundary region to use between the two Eulerian boundary regions depends on the type of load or boundary condition that is required:
