SPH (Smoothed Particle Hydrodynamics)is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. In the present study, the SPH algorithm has been subjected to detailed testing and analysis to determine its applicability in the field of solid dynamics. An important result of the work is a rigorous von Neumann stability analysis which provides a simple criterion for the stability or instability of the method in terms of the stress state and the second • derivative of the kernel function. Instability, which typically occurs only for solids in tension, results not from the numerical time integration algorithm, but because tt_e SPH algorithm creates an effective stress with a negative modulus. The analysis

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A method for modeling the initiation and growth of discrete delaminations in shell-like composite structures is presented, The laminate is divided into two or more sublaminates, with each sublaminate modeled with four-noded quadrilateral shell elements. A special, eight-noded hex constraint element connects opposing sublaminate shell elements. It supplies the nodal forces and moments needed to make the two opposing shell elements act as a single shell element until a prescribed failure criterion is satisfied. Once the failure criterion is attained, the connection is broken, creating or growing a discrete delamination. This approach has been implemented in a threedimensional finite element code. This code uses explicit time integration, and can analyze shelllike structures subjected to large deformations and complex contact conditions. The shell elements can use existing composite material models that include in-plane laminate failure modes. This analysis capability was developed to perform crashworthiness studies of composite structures, and is useful whenever there is a need to estimate peak loads, energy absorption, or the final shape of a highly deformed composite structure. This paper describes the eight-noded hex constraint element used to model the initiation and growth of a delamination, and discusses associated implementation issues. Particular attention is focused on the delamination growth criterion, and it is verified that calculated results do not depend on element size. In addition, results for double cantilever beam and end notched flexure specimens are presented and compared to measured data to assess the ability of the present approach to model a growing delamination.

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A method for modeling the initiation and growth of discrete delaminations in shell-like composite structures is presented. The laminate is divided into two or more sublaminates, with each sublaminate modeled with four-noded quadrilateral shell elements. A special, eight-noded hex constraint element connects opposing sublaminate shell elements, and makes the two opposing shell elements act as a single shell element until a prescribed failure criterion is satisfied. Once the failure criterion is met, the connection is broken, and a discrete delamination initiates or grows. This approach has been implemented in a three-dimensional finite element code. This code uses explicit time integration, and can analyze shell-like structures subjected to large deformations and complex contact conditions. Tensile, compressive, and shear laminate failures are also modeled. This paper describes the eight-noded hex constraint element used to model the initiation and growth of a delamination, and discusses associated implementation issues. In addition, calculated results for double cantilever beam and end notched flexure specimens are presented and compared to measure data to assess the ability of the present approach to model a growing delamination. Results are also presented for a diametrally compressed ring to demonstrate the capability for analyzing progressive failure in a highly deformed composite structure.