The curse of dimensionality confounds the comprehensive evaluation of computational structural mechanics problems. Adequately capturing complex material behavior and interacting physics phenomenon in models can lead to long run times and memory requirements resulting in the need for substantial computational resources to analyze one scenario for a single set of input parameters. The computational requirements are then compounded when considering the number and range of input parameters spanning material properties, loading, boundary conditions, and model geometry that must be evaluated to characterize behavior, identify dominant parameters, perform uncertainty quantification, and optimize performance. To reduce model dimensionality, global sensitivity analysis (GSA) enables the identification of dominant input parameters for a specific structural performance output. However, many distinct types of GSA methods are available, presenting a challenge when selecting the optimal approach for a specific problem. While substantial documentation is available in the literature providing details on the methodology and derivation of GSA methods, application-based case studies focus on fields such as finance, chemistry, and environmental science. To inform the selection and implementation of a GSA method for structural mechanics problems for a nonexpert user, this article investigates five of the most widespread GSA methods with commonly used structural mechanics methods and models of varying dimensionality and complexity. It is concluded that all methods can identify the most dominant parameters, although with significantly different computational costs and quantitative capabilities. Therefore, method selection is dependent on computational resources, information required from the GSA, and available data.

The evaluation of the on-ground casualty risk assessments due to a controlled or uncontrolled re-entry is highly sensitive to the accurate prediction of fragmentation events during an atmospheric re-entry. The main objective of this study is an investigation into the use of peridynamics (PD) to improve the analysis of fragmentation during atmospheric re-entry with respect to currently adopted semi-empirical approaches. The high temperatures characterising such scenarios may substantially impact fragmentation, which requires appropriate modelling of the damage process within the PD method. The damage models in PD require experimentally determined fracture mechanical properties that are unavailable as a function of temperature. This work proposes a numerical methodology to estimate the PD damage parameters changes with temperature to enable the study of fragmentation during atmospheric re-entry. Initially, tensile-testing simulation experiments are performed in peridynamics to calibrate material parameters for steel and aluminium alloys as a function of temperature. Then, a parametric study is carried out to evaluate the temperature-dependent damage model parameters for the same materials. The applicability of the proposed methodology is showcased using a re-entry test case scenario.

In this study, a peridynamic material model for a polycrystalline ice is utilised to investigate its fracture behaviour under dynamic loading condition. First, the material model was validated by considering a single grain, double grains and polycrystalline structure under tension loading condition. Peridynamic results are compared against finite element analysis results without allowing failure. After validating the material model, dynamic analysis of a polycrystalline ice material with two pre-existing cracks under tension loading is performed by considering weak and strong grain boundaries with respect to grain interiors. Numerical results show that the effect of microstructure is significant for weak grain boundaries. On the other hand, for strong grain boundaries, the effect of microstructure is insignificant. The evaluated results have demonstrated that peridynamics can be a very good alternative numerical tool for fracture analysis of polycrystalline ice material.

This paper introduces a new approach to calculate stress intensity factors based on a combination of Displacement Extrapolation Method and Peridynamic Theory. After obtaining the displacement field from Peridynamic Theory, by appropriately selecting nodes at the crack tip region and their displacements yield stress intensity factors at the crack tips. To demonstrate the capability of the proposed approach, three different benchmark problems are considered including plate with a central crack, plate with an edge crack and plate with a slanted crack. Results evaluated from the current approach are compared against analytical and finite element analysis results, and good agreement is obtained between three different approaches. This shows that coupled Displacement Extrapolation Method and Peridynamic Theory approach can be an alternative method to calculate stress intensity factors.

When dealing with ice structure interaction modeling, such as designs for offshore structures/icebreakers or predicting ice cover’s bearing capacity for transportation, it is essential to determine the most important failure modes of ice. Structural properties, ice material properties, ice-structure interaction processes, and ice sheet geometries have significant effect on failure modes. In this paper two most frequently observed failure modes are studied; splitting failure mode for in-plane failure of finite ice sheet and out-of-plane failure of semi-infinite ice sheet. Peridynamic theory was used to determine the load necessary for inplane failure of a finite ice sheet. Moreover, the relationship between radial crack initiation load and measured out-of-plane failure load for a semi-infinite ice sheet is established. To achieve this, two peridynamic models are developed. First model is a 2 dimensional bond based peridynamic model of a plate with initial crack used for the in-plane case. Second model is based on a Mindlin plate resting on a Winkler elastic foundation formulation for out-of-plane case. Numerical results obtained using peridynamics are compared against experimental results and a good agreement between the two approaches is obtained confirming capability of peridynamics for predicting in-plane and out-of-plane failure of ice sheets.

Nonlocal diffusion models involve integral equations that account for nonlocal interactions and do not explicitly employ differential operators in the space variables. Due to the nonlocality they might look different from classical partial differential equation (PDE) models, but their local limit reduces to partial differential equations. The effect of mesh element anisotropy mesh refinement and kernel functions on the conditioning of the stiffness matrix for a nonlocal diffusion model on 2D geometric domains is considered, and the results compared with those obtained from typical local PDE models. Numerical experiments show that the condition number is bounded by (where c is a constant) for an integrable kernel function, and is not affected by the choice of the basis function. In contrast to local PDE models, mesh anisotropy and refinement affect the condition number very little.

We investigate connections between nonlocal continuum models and molecular dynamics. A continuous upscaling of molecular dynamics models of the form of the embedded-atom model is presented, providing means for simulating molecular dynamics systems at greatly reduced cost. Results are presented for structured and structureless material models, supported by computational experiments. The nonlocal continuum models are shown to be instances of the state-based peridynamics theory. Connections relating multibody peridynamic models and upscaled nonlocal continuum models are derived.