Energetic materials have widespread applicability in various fields of engineering as propellants, explosives, and pyrotechnics. The Netherlands Organisation for Applied Scientific Research (TNO) is investigating additive manufacturing of solid propellants. As part of this investigation, TNO developed a new polymer binder mix for solid propellants. The thermomechanical behavior of the solid propellants is not well understood yet. Therefore, TNO is interested in developing computational modelling schemes for characterizing their behavior. Computational schemes based on the finite element method (FEM) are developed in this thesis. They are calibrated with matrix-only and solid propellant uniaxial tension experiments provided by TNO. The developed schemes are compared with the experiments to better understand the materials behavior and improve the computational models.

The macro-structural behavior of solid propellants is significantly affected by the behavior of the micro-structure. It is computationally unfeasible to directly consider the micro-structure in macro-structural FEM. Therefore, computational homogenization (CH) is employed for idealizing the micro-structure with representative volume elements (RVEs) at a finite number of macroscopic locations. Micro-structural behavior consists of numerous nonlinear thermomechanical processes. This thesis focuses in characterizing micro-structural matrix viscoelasticity, continuum matrix damage, and debonding. The brittle and rate dependent behavior of the matrix and the solid propellants is described with these thermomechanical processes. Other relevant processes such as temperature effects, nonlinear elasticity, anisotropy, and large strains are not considered.

The experiments exhibit a clear rate dependence throughout the entire loading process, and viscoelasticity is hypothesized to play a major role in this dependence. The experimental samples experience a brittle failure that is believed to be caused by matrix micro-crack damage. Particle debonding is observed in the failure planes of the solid propellants and is hypothesized to significantly affect their behavior.

Matrix-only and solid propellant computational results confirm that viscoelasticity is a major source of rate dependence and that (continuum) matrix micro-crack damage causes brittle failure. They also suggest that continuum matrix damage is a significant source of rate dependence in the post-damage regime, and matrix-only experiments agree. Comparing the results for perfectly bonded solid propellants to the results for solid propellants with debonding and to the solid propellant experiments, it is clear that debonding indeed has a large effect in reducing the ultimate strength of the material. The full CH damage-debonding-viscoelastic scheme shows promise as a first step towards full characterization. Future work can improve the scheme by addressing the issue of free surface propagation and can build on it by including relevant thermomechanical processes that are not yet implemented. Recommendations on how to achieve this are given in the final chapter.

In recent times, composite materials are widely applied in the construction industry because of their superior properties compared to traditional materials like steel and concrete. The use of composite materials in defense and infrastructure protective applications to resist high rate dynamic loading conditions has been gaining the interest of a lot of researchers over the previous decade. The limitations involved in studying the behavior of composites when subjected to high rate dynamic loads experimentally generated a need for numerical models that could simulate such complex material behavior. These numerical models are also highly useful in situations where it is difficult to perform direct measurements in experiments. The idea of this thesis originated from an aim to study the behavior of a TNO developed composite laminate with alternate 0-degree and 90-degree ply layup when subjected to out of plane blast loads. Considering the complexities involved in such a loading situation, a simplified test setup that can approximately replicate stress conditions in the composite laminate due to out of plane blast load has been proposed to be designed. This simplified test setup is prepared by performing an angled cut from the composite laminate, thus making the plies off-axis with respect to the global coordinate system of its cross-section. The motivation behind choosing such a test setup is that the interface/s can be loaded by a combination of compressive and shear stresses with axial loading on the specimen. The behavior of the simplified test setup with off-axis angles 30-degree, 45-degree, and 60-degree, when subjected to dynamic compression loads with different rates ranging from quasi-static to high is analyzed in this thesis using the finite element method. The initial parts of the study focus on analyzing the quasi-static failure behavior of the off-axis angled composite specimens with a single critical interface at the center modelled using the rate-independent cohesive law coupled with friction. The later parts of the study focus on analyzing the dynamic failure behavior of the composite specimens. The rate-independent cohesive law with friction is improved by adding a rate-dependency feature based on a Johnson-Cook law. Finally, the dynamic behavior of different off-axis angled composite specimens with critical interface/s modelled using the rate-independent and the rate-dependent cohesive laws with friction when subjected to compression loads with different rates is analyzed. The results obtained from the quasi-static analyses indicate that an increase in the mode-II cohesive strength, mode-II cohesive fracture energy, and interface friction coefficient lead to an increase in the peak load carried by the laminates. An increase in the thickness of the plies of an off-axis angled composite specimen results in a decrease in its peak load and changes its governing failure mechanism. There will be a dominant contribution of local inertia and wave propagation effects in dictating the failure behaviors of the specimens when subjected to compression loads with higher rates. The rate-dependent cohesive law with friction developed in this thesis seemingly captured the rate effects in the off-axis angled composite specimens when loaded in compression at different rates. Finally, it is suggested to design the simplified test setup by performing a 45-degree cut from the original composite laminate to simulate delamination due to compression loads of different rates effectively. But all three simplified setups have to be tested to derive the unique set of interface parameters that dictate the failure behaviors of the specimens.

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.