A Combined Particle-Element Method for Explicit Dynamic Computations

Abstract eng:
A combined particle-element method (CPEM) [1] is currently under development for explicit dynamic Lagrangian computations involving intense loading and very large deformations. The motivation is to improve upon the accuracy of existing methods for this class of problems. One prominent and robust existing method [2] converts individual finite elements of an initial mesh to meshfree GPA particles when a prescribed critical strain is exceeded. This conversion method therefore automatically uses the relatively expensive, variable-connectivity particles only when they are needed – to model highly deformed material – and otherwise uses the relatively inexpensive and accurate fixed-connectivity finite elements. The CPEM adopts this same automated partitioning of the computational domain, but it offers three potential advantages in accuracy over the conversion method. The first advantage is due to the compatibility of the finite-element and particles methods, which results in a relatively simple transition from element method to particle method. The particle method in CPEM evaluates the equations of motion at mass nodes, and the constitutive equations at stress points. These two sets of points are analogous to the nodes and integration points, respectively, of the finite-element method, and replace them one-for-one in the transition from element to particle. The transition is therefore implemented simply be replacing the finite-element shape functions (to compute the strain rates and internal forces) with moving least-squares (MLS) shape functions of the particle method. No variables are mapped. In contrast, the GPA of the conversion method solves the equations of motion and the constitutive equations on the same set of particles, so that nodal variables must be mapped to the particles, such as replacing an element’s mass contributions to each of its nodes with an equivalent resultant mass at the location of the new particle. The second CPEM advantage arises in maintaining a discrete approximation to the continuum across the interface between elements and particles. The GPA conversion method requires an algorithm to monitor and enforce the interfaces as they evolve. Numerical approximations in this algorithm effectively introduce small discontinuities, or cracks, that lead to premature material failure. In CPEM, the compatibility of the particle and element methods assures the continuum approximation, and precludes the need for an interface algorithm and its associated approximations. The third CPEM advantage is due to MLS shape functions that are derived from a full linear basis and therefore ensure consistency of the method with the governing equations. In addition, zero-energy modes of deformation are diminished by avoiding the co-location of mass nodes and stress points. This paper provides a description of the approach, and evaluations for a range of problems involving high-velocity impact and explosive-generated air blast. Advantages and disadvantages of CPEM are discussed, comparisons to other approaches are provided, and the longer-term potential of CPEM is presented.

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