极限荷载近场动力学建模英文文献和中文翻译(4)
EMU is currently in theresearch and development stage and is being licensed to a few users. The numerical method described in Section 3 does not use elements, and there are no geometricalobjects connecting the grid points. Hence, EMU is mesh free. There is no need for a mesh generatorwhen modeling complex structures. Only the generation of grid points is required.EMU is Lagrangian in the sense that each node contains a fixed amount of material. A body containsmultiple nodes and may fragment if bonds between nodes are broken. However, the mass in each noderemains constant.EMU uses explicit time integration to advance the solution in time as discussed in Section 3. Explicittime integration is a simple, reliable method. A stable time-step estimate was obtained by Silling andAskari [2005] for a linear PFF as given by (18). For nonlinear materials, a safety factor less than onemay be applied to this stable time step to account for possible nonlinear material response that wouldmake the estimated stable time step based on the linear analysis too large.Execution of an EMU simulation requires a computational grid and an input file containing datato control execution, provide information on the grid geometry, and specify material properties. (Anunpublished user’s manual is available to licensed users of EMU.)A computation grid in EMU can be defined in either of two ways, or any combination of the two.Figure 5 shows an EMU problem containing two internally generated material regions and one externallygenerated grid. Everything outside the material regions is empty space.For an internally generated grid, the code currently uses a lattice inside a rectangular box. The boxcontaining the lattice includes several material regions, each region with a given material. There arevarious options for defining the shapes of these regions. A lattice site that is inside one of the materialregions becomes a node. A lattice site that is not in any material region represents a void and is, in effect,not used during the calculation.For an externally generated grid, one typically writes a separate program to generate the grid pointcoordinates and material numbers and place them into files that are processed during EMU execution.A user writes an input file containing data to control execution, specify details of the grid geometry,and specify material properties. After the title on the first line of the input file, the input is keyword based.The keywords may be placed in any order. Any numerical input following a keyword is format-free andmay extend to multiple lines. SI units are recommended for all dimensional quantities. Data to control execution include time span or number of cycles for execution of a simulation, time-step safety factor,plot-dump frequency, and location of output files. Data to specify details of the grid geometry includegrid spacing, horizon, and volume of a node for each material.The details of the peridynamic material model are specified in the EMU input file. For each pro-portional, microelastic material, the user provides its density or total mass, yield strength, sound speed,and critical stretch. Alternately, material properties of microelastic materials may be specified by thepenetrability as measured by Young’s S-number [Young 1969]. Specific inputs give properties of fluids,gases, or explosive materials.Initial and boundary conditions may be specified in the input file. Boundary conditions include fixeddisplacement or velocity and applied force. They are applied somewhat differently in the peridynamicmethod than in the classical approach. In peridynamics, boundary conditions are prescribed within a layerof finite thickness at the surface of a body. This layer must include some nodes in the computationalgrid. Forces at the surface of a body are applied as body force density b in (1) within some layer underthe surface.In peridynamics as implemented in EMU, contact is treated using short-range repulsive forces thatprevent nodes from getting too close. These short-range forces are independent of the positions of thenodes in the reference configuration, so that contact is treated in a consistent way even under largedeformations. This approach is physical and avoids the need for defining contact surfaces as is requiredby many finite-element codes.EMU is parallelized using MPI and executes on parallel computers. Parallelization was performed byallowing each processor to be responsible for a fixed region of space. Figure 6 illustrates this processorpartitioning in two dimensions.Figure 6 shows a grid surrounded by a margin region, which is the light blue shaded area. Theregions of space owned by the eight processors in this example are separated by heavy red lines. Eachprocessor region owns the nodes within its domain and needs information from nodes a distance equalto the horizon δ surrounding its domain. As the body deforms, nodes are permitted to migrate betweenprocessors. After each time step, the updated variables for nodes within a distance δ of a given processorare passed using MPI subroutines to be used during the following cycle. This parallelization technique has the advantage of simplicity.