Auxetic materials are increasingly used in the field of sports, defense, bio-medicine, and acoustic-filtering due to their unconventional behavior of exhibiting a negative Poisson's effect. The prospective use of auxetics to mitigate shock and impact forces have proven the relevance of research on auxetics. It becomes of paramount importance to understand their behavior and mechanics of deformation, especially regarding their response to dynamic loading conditions. Although auxetics have caught attention from several researchers, a detailed overview of computational modeling of auxetics is still missing and the deformation behavior of auxetics subjected to different loading conditions is an unfolded topic in structural mechanics.

In this thesis, computational tools are developed and validated to investigate the effect of auxeticity in a linear elastic continuum and a re-entrant honeycomb structure under different static and dynamic loading conditions. The possibility to assess the global behavior of an assembly of re-entrant honeycomb unit cells by the analysis of an equivalent continuum model with the same global dimensions and homogenized mechanical properties has been examined. The dynamic analysis of a continuum model of an isotropic auxetic material presented the influence of auxeticity in increasing the ratio of shear wave velocity to dilatation wave velocity. The finite element analysis of a simply supported auxetic beam subjected to impact at mid-span affirmed the hypothesis that in auxetics, the material flows towards the point of impact, thus increasing the indentation resistance. Computational challenges in analyzing a beam impact problem are discussed through the comparison of results from the standard finite element analysis, modal analysis, and the B-Bar method. It is recommended to further develop the proposed models to have a more robust approach on analyzing the continuum beam impact problem.

The assembly of a re-entrant honeycomb structure used in the finite element simulations were modelled with different unit cells by the variation of the two dominant geometrical parameters of the unit cell members. The results highlighted the strong correlation between the effective mechanical properties and the geometrical parameters, therefore indicating the possibility of achieving the desired values of the Poisson's ratio by simply modifying the necessary geometrical parameters. The results also showed that it is possible to obtain a Poisson's ratio more negative than -1 which can be exploited to design a displacement amplifier especially suitable for defense applications. The close comparison of the analytical and the computational results provided a groundwork to extend the numerical study to geometrical nonlinear analysis and other loading conditions like bi-axial loading and bending at the structural level. The comparison of results obtained from the analysis of an assembled cellular structure and an equivalent continuum model subjected to bi-axial loading and bending demonstrated the possibility of assessing the global behavior of cellular structure using the continuum model.

Dynamic analyses of a re-entrant honeycomb structure revealed that the wave propagation phenomenon in a re-entrant honeycomb structure is a result of several reflections, transmissions, mode conversions and superposition of waves occurring at the connection of cell members. The proportion of reflection, transmission and mode conversion of incident wave when it passes the connection can be controlled by varying the re-entrant angle between the cell members. For the lower frequency regime, the speed of wave propagation in re-entrant structures can be estimated using the continuum approach.

Furthermore, in a secondary study, the influence of the geometrical parameters of a re-entrant honeycomb structure to exhibit the stop-pass band was examined. Recommendations are provided for the further development of computational tools to analyze the three-dimensional and disordered re-entrant structures. In addition, it is also suggested to investigate the beam impact problem in the cellular model, the effect of rigidity of connection of cell members and research the possibility of having an isotropic re-entrant honeycomb structure as the present model is orthotropic in nature.

Inclusion of safety formats method in nonlinear finite element analysis of a structure is beneficial to realize the safe and real behavior of structures. In addition, reliability analysis in combination with NLFEA results and safety assessments provide an insight into consistency of the safety assessments recommendations related to targeted safety. However, various complications arise regarding the appropriate constitutive model to be used in analysis, estimation and inclusion of modelling uncertainty in results from nonlinear finite element analysis, unavailability of a suitable function that defines the response of a structure when subjected to a certain load etc. In this additional thesis, a case study is performed to study the combination of structural safety assessment and reliability analysis using nonlinear finite element analysis. A wall specimen experimented by Lefas et. al is selected for the study [1]. Solution strategy is adopted based on the recommendations ofDutch guidelines with some deviations [2]. The nonlinear finite element analyses are performed inDIANA 10.1. Since only one solution strategy was used during the analysis of a single wall specimen, the modelling uncertainty parameters were estimated using results from previous studies[3]. The modelling uncertainty parameters were estimated to be, µm Æ 1.21 and Vµ Æ 6.88%. These parameters infer that the results obained from different solution strategies were close to each other but still had a considerable bias with respect to the structural capacity obtained from the experimental values. The NLFEA underestimated the capacity as compared to experimental results. Only 79.3 % of the experimental capacity was realized from NLFEA. Three different safety format methods suggested in [2] and a new safety format method by Schlune et al. [4] are used in NLFEA to estimate the design load capacity. The effect of inclusion of estimated model uncertainty parameters on design load capacity is observed too. The results of safety assessments indicated that the design load estimated by using ECOV and Schlune et al. safety format are comparatively higher than using Partial Safety Factor and Global Resistance Factor, but still conservative with respect to the experimental results. The reliability of the design load estimated by using different safety assessment methods is checked using response surface method and first order reliability methods. A response surface method together with FORM is used to obtain a quadratic limit state function that closely represents the response of the structural wall subjected to the design load value. The limit state function thus obtained is then used for FORM analysis, Importance sampling and/or Monte Carlo simulations to observe if the intended safety level is achieved. The study of acheived reliability index indicated that the design load values estimated by using three safety formats recommended in [2] are conservative, whereas the one estimated by using Schlune et al. format was found to be non-conservative. The additional thesis was carried out with various approximations and limitations. All limitations and approximations are explained in detail and justified where necessary and possible. The results and discussions of this additional thesis are dependent only on a single solution strategy adopted in a single wall specimen and in a single failure mode. Therefore, the results should instead be interpreted as an indication of need of further and extensive research and studies required in the field of reliability analysis and safety assessment using nonlinear finite element analysis.