A parallel algorithm for transient solid dynamics simulations with contact detection Page: 3 of 15
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Sandia's PRONTO3D code is a Lagrangian finite element program for the analysis of the
three-dimensional response of solid bodies subjected to transient dynamic loading. The pro-
gram includes nonlinear constitutive models and accurately analyzes large deformations that
may lead to geometric nonlinearities. PRONTO is a powerful tool for analyzing a wide variety
of problems, including classes of problems in impact dynamics, rock blasting, and accident
analyses. The algorithms within PRONTO3D were designed to be accurate, dependable, and to
The following is a summary of the technology within PRONTO3D: explicit mid-point time
integration; adaptive time-step control; eight-node brick elements and four-node shell ele-
ments; one-point element integration; Flanagan-Belytschko Hourglass control for hexahedral
elements; Assumed Strain hourglass control for hexahedral elements; objective material coor-
dinate system; and global contact (self-contact) with erosion of surfaces.
The structure of this paper is as follows: We review the components of an explicit time step
in PRONTO3D, then in preparation for describing the parallel contact algorithm, we review
some background material needed to understand aspects of the parallel algorithm. A description
of the parallel contact algorithm is followed by some examples that illustrate the performance
of the parallel algorithm.
2. Explicit time step integration
An outline of the computations performed every time step in the explicit time-step algo-
rithm in PRONTO3D is shown in Figure 1.
(1.1) Define/redefine contact surface
(1.2) Integrate the equations of motion
(1.3) Compute the strain rate based on the motion of the nodes
(1.4) Compute the stress rate based on the strain rate and the material models
(1.5) Compute internal forces acting on nodes
(1.6) Predict the locations of the nodes assuming no contacts
(1.7) Search for potential contacts between nodes and surfaces
(1.8) Perform detailed contact check to determine "best" contact surfaces.
(1.9) Enforce contacts by computing contact force required to remove overlap
FIGURE 1.Outline of explicit time step algorithm.
Steps (1.2) through (1.5) may be viewed as the finite element (FE) portion of the calcula-
tion, while the contact algorithm is composed of steps (1.7)-(1.9).
In explicit time-integration algorithms, contacts are usually processed with a predictor/cor-
rector method. Within a time step, the positions of nodes in the mesh are predicted assuming
that no contacts occur. A check for overlap and penetration is made, and these overlaps are cor-
rected by applying a contact force between the contact surfaces.
It is convenient to separate contact algorithms into a location phase and a restoration phase.
The location phase consists of a neighborhood identification, step (1.7), followed by a detailed
contact check, step (1.8). We define a set of nodes on the exterior of the mesh called contact
nodes and a set of surface patches on the exterior element faces called contact surfaces. For ef-
ficiency, the contact constraint is enforced only at the contact nodes. Thus, list of potential con-
tact pairs are built in the neighborhood identification phase, then each contact node is checked
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Attaway, S.; Hendrickson, B.; Plimpton, S.; Gardner, D.; Vaughan, C.; Heinstein, M. et al. A parallel algorithm for transient solid dynamics simulations with contact detection, article, June 1, 1996; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc668963/m1/3/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.