Michael A. Puso

A highly efficient enhanced assumed strain physically stabilized hexahedral element

A method which combines the incompatible modes method with the physical stabilization method is developed to provide a highly efficient formulation for the single point eight-node hexahedral element. The resulting element is compared to well-known enhanced elements in standard benchmark type problems. It is seen that this single-point element is nearly as coarse mesh accurate as the fully integrated EAS elements. A key feature is the novel enhanced strain fields which do not require any matrix inversions to solve for the internal element degrees of freedom. This, combined with the reduction of hourglass stresses to four hourglass forces, produces an element that is only 6.5 per cent slower than the perturbation stabilized single-point brick element commonly used in many explicit finite element codes. Copyright

Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity

Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a lockingfree small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum

Mesh tying on curved interfaces in 3D

In this work, a mortar method is implemented for tying arbitrary dissimilar 3D meshes, i.e. 3D meshes with curved, non‐matching interfaces. The 3D method requires approximations to the surface integrals specified by the projection of the displacement jump across the interface onto the Lagrange multiplier space. The numerical integration scheme is presented and several Lagrange multiplier interpolation schemes are considered. Furthermore, some implementational issues such as how to handle boundary conditions will be described such that stability is retained. Finally, the implementation will be demonstrated in numerical simulations and comparison of different formulations will be made.

Strain Smoothing for Stabilization and Regularization of Galerkin Meshfree Methods

In this paper we introduce various forms of strain smoothing for stabilization and regularization of two types of instability: (1) numerical instability resulting from nodal domain integration of weak form, and (2) material instability due to material strain softening and localization behavior. For numerical spatial instability, we show that the conforming strain smoothing in stabilized conforming nodal integration only suppresses zero energy modes resulting from nodal domain integration. When the spurious nonzero energy modes are excited, additional stabilization is proposed. For problems involving strain softening and localization, regularization of the ill-posed problem is needed. We show that the gradient type regularization method for strain softening and localization can be formulated implicitly by introducing a gradient reproducing kernel strain smoothing. It is also demonstrated that the gradient reproducing kernel strain smoothing also provides a stabilization to the nodally integrated stiffness matrix. For application to modeling of fragment penetration processes, a nonconforming strain smoothing as a simplification of conforming strain smoothing is also introduced.

A New Stabilized Nodal Integration Approach

A new stabilized nodal integration scheme is proposed and implemented. In this work, focus is on the natural neighbor meshless interpolation schemes. The approach is a modification of the stabilized conforming nodal integration (SCNI) scheme and is shown to perform well in several benchmark problems.

Accomplishments and Challenges in Code Development for Parallel and Multimechanics Simulations

The Methods Development Group at Lawrence Livermore National Laboratory has historically developed and supported software for engineering simulations, with a focus on nonlinear structural mechanics and heat transfer. The quality, quantity and complexity of engineering analyses have continued to increase over time as advances in chip speed and multiprocessing computers have empowered this simulation software. As such, the evolution of simulation software has seen a greater focus on multimechanics and the incorporation of more sophisticated algorithms to improve accuracy, robustness and usability. This paper will give an overview of the latest code technologies developed by the Methods Development group in the areas of large deformation transient analysis and implicit coupled codes. Applications were run on the state of the art hardware available at the national laboratories.