Finite element modeling of mechanical properties of bone and bioinspired composites with stiff and soft continuous compared to discontinuous phases

In this dissertation, the aim is to understand better mechanical properties and arrangement of phases in bone as biological composite material and study the effect of the topology of phases on mechanical properties of 3D-printed bio-inspired composites as well as scale and size effects. In the first part of this dissertation, bone is modeled at the mesoscale (trabecular bone) to shed light on which constitutive law can better describe the behavior of bone at this scale. Finite element models were built from micro-computed tomography images of trabecular bone that allow a precise realization of the geometry. The effect of using different plasticity formulations at the tissue level on the overall mechanical behavior was studied as well as the local response. Also, the effect of volume fraction of bone tissue on the mechanical response of trabecular bone was investigated. Simulations of trabecular bone are highly challenging due to its complex structure. Several types of nonlinearities in the problem result in the need for using an explicit solver instead of an implicit solver for some cases. Although both implicit and explicit methods have been used in the literature, a comparative study on both methods' outcomes is of high interest for the bone modeling community. Thus, a comparison of the effect of using implicit and explicit solvers on the results of modeling trabecular bone has been performed. In the second part, the influence of geometrical arrangements of phases on the overall mechanical properties of bio-inspired composites was investigated. Two-phase composites with stiff and soft phases and different phase geometries, including an interpenetrating phase composite with two continuous phases, a matrix-inclusion composite with a continuous and a discontinuous phase, and a discontinuous phase composite where both phases are discontinuous, were studied. These different types of composites were 3D printed using two polymers: VeroClear (stiff) and TangoBlackPlus (soft). Their mechanical performance was studied both experimentally, using compression testing and digital image correlation, and numerically by a finite element analysis. These composite types were also simulated using properties of bone constituents (collagen and hydroxyapatite) to better understand the nanostructure of bone and its mechanical properties. Scale and size effects were also investigated in these composites, and the results from mechanical testing were compared with finite element modeling results

Finite element modelling of infant head impacts for use in forensic reconstructions

When a child is admitted to an Accident and Emergency department with head injuries considered to be suspicious, the parent or guardian often explains the history of the injury as resulting from a fall or similar accident. However, depending on the nature and seriousness of the injuries, medical professionals may suspect the injuries resulted from non-accidental causes. Without the history being corroborated by a second, reliable, witness, it can be difficult for any prosecution to prove beyond reasonable doubt that a child’s injuries were a result of abusive head trauma. One method that has the potential to help improve the chances of a successful prosecution is finite element (FE) modelling. A FE model of an infant head can be used to reconstruct a case to determine whether the observed injuries are likely to have resulted from the history provided. However, infant head FE modelling is a developing field and cannot yet be used accurately, reliably and efficiently in forensic cases. In this thesis, an extensive review of the existing literature was conducted to determine what is required to further develop infant head FE models. It was found that the greatest limitation was the lack of accurate material property data for the infant head tissues. This was followed by a lack of validation of local parameters (stress and strain), as well as a lack of investigation on the effects of drop height and different impact surfaces. From these findings, a sensitivity analysis was carried out on the material model parameters of the tissues used in infant head FE models. This was to investigate which material model parameters had the greatest influence on the response of the model, allowing for guidance on future experimental work that will best make use of scarce human infant head tissues. The baseline FE model used in the sensitivity analysis was of a three-month-old infant occipital head impact with an impact speed of 2.4 ms-1. An isotropic elastic material model was used to represent the behaviour of the cranial bones, while Ogden hyperelastic models were used for the scalp, suture and brain. The elastic modulus of the skull was found to have the greatest influence and it is recommended that future experimental work should prioritise increasing the data set for this parameter. The brain hyperelastic constants were found to be important for determining the local response of the brain tissue, while the scalp and suture hyperelastic constants had some influence over the global response. It is recommended that a further sensitivity analysis be conducted to investigate which material parameters are important for accurate prediction of tissue failure. This will be important for relating modelling results to forensic data. Based on the findings from the sensitivity analysis, three-point bend testing of child cranial bone was conducted to improve the elastic modulus data. Due to the prompt brittle fracture and limitations of the high-speed cameras, elastic moduli data was not obtained; rather, preliminary observations were made on the behaviour of the failure of child cranial bone at loading rates of 5.65 ms-1 (previous experimental work has only investigated up to 2.81 ms-1). It was found that the failure mode in specimens aged two to 18 years was prompt brittle fracture, while bending before fracture occurred in the three-week-old specimens. Impact force ranged from 200 to 6000 N and was higher in the occipital bone than in the parietal or frontal bones. The energy absorbed to failure increased with age and thickness, with the occipital bone having a greater energy absorbing capacity due to its greater thickness. Drop heights ranging from 0.05 to 1.8 m and impact surfaces consisting of carpet and a combination of carpet and underlay were investigated to determine the effect on the response of the FE model. Peak head acceleration increased, while impact duration decreased as drop height increased. While the softer surfaces of carpet and the carpet and underlay combination increased the impact duration, the peak head acceleration was not significantly affected by the addition of a softer surface. As these investigations did not consider tissue failure, a method of predicting skull fracture was also investigated. It was found that the method of element erosion can predict skull fracture based on where it would be expected to occur due to the maximum principal stress. However, it has limitations, including being dependent on mesh density, as refinement of the FE mesh resulted in a different fracture pattern. The FE models used for each of these analyses, as well as in the sensitivity analysis, all used simplifying assumptions to make the computational time of the baseline model tractable. These assumptions mostly included neglecting various thin head tissue layers due to an increase in the mesh density required, and the associated increase in computational time. The baseline model consisted of a single layer scalp, cranial bones, suture brain and bonded contact at all tissue interfaces. To assess the validity of these assumptions, the neglected tissues were included in several variants of a higher fidelity FE model. Compared to the baseline model, the addition of each tissue resulted in an increase in the global stiffness due to the limitations associated with a bonded contact condition at the tissue interfaces. A model consisting of all tissues (a dual layered scalp, cranial bones, suture, dura, cerebrospinal fluid (CSF) and brain) and using frictional contact at the dura-CSF and CSF-brain interfaces resulted in a 1.7% and 3% increase in the peak head acceleration and impact duration respectively over the baseline model, but had a 70% greater computational time. Overall, using FE models of the infant head to accurately reconstruct the injury patterns in forensic cases requires high-fidelity models. However, this comes at a significant computational cost. Standard professional grade computers are inadequate and high-performance computers have significant financial cost. Therefore, trade-offs with the computational cost and model fidelity are required to make forensic reconstructions tractable. This thesis investigated what is required to further develop infant head FE models. Some of these requirements have been addressed in this thesis, or preliminary research undertaken to provide guidance for future work. As the field of infant head FE modelling develops, and computational power becomes more cost effective, the accuracy of such models and the financial cost will improve. This will allow forensic reconstructions of suspected abusive head trauma to be more easily investigated, bringing justice for those children who have been fatally injured from such trauma or protect survivors from future abuse