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Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

SUMMARYNodal integration can be applied to the Galerkin weak form to yield a particle-type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions. This particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods. To a lesser degree, nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods. In this work, aspects regarding stability, consistency, efficiency and explicit time integration are explored within the context of nodal integration. Both small and large deformation numerical examples are provided.

SUMMARYA stabilized, nodally integrated linear tetrahedral is formulated and analysed. It is well known that linear tetrahedral elements perform poorly in problems with plasticity, nearly incompressible materials, and acute bending. For a variety of reasons, low-order tetrahedral elements are preferable to quadratic tetrahedral elements; particularly for nonlinear problems. But the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems. On the other hand, automatic mesh generation is often not feasible for building many 3D hexahedral meshes. A stabilized, nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity, nearly incompressible materials and acute bending. The formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u ∈ C 2 ∩ (H 1 ) 3 . Future work may extend the formulation to the incompressible regime and relax the regularity requirements; nonetheless, the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks. Published in

SUMMARYA version of the mortar method is developed for tying arbitrary dissimilar 3D meshes with a focus on issues related to large deformation solid mechanics. Issues regarding momentum conservation, large deformations, computational e ciency and bending are considered. In particular, a mortar method formulation that is invariant to rigid body rotations is introduced. A scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3D curved dissimilar interfaces. Here, integration need only be performed at problem initialization such that coe cients can be stored and used throughout a quasi-static time stepping process even for large deformation problems. A degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without Lagrange multipliers is proposed. This provided a signiÿcant reduction in factorization times. Example problems which touch on the aforementioned solid mechanics related issues are presented. Published in

The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasilinear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament-tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

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SUMMARYDual mortar method formulations have shown to be a very effective and efficient way for interfacing (e.g. tying, contacting) dissimilar meshes. On the other hand, we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications. A new modified two-dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem. Furthermore, mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method.