Implementation and validation of finite element model of skull deformation and failure response during uniaxial compression.

Abstract

Numerical studies aimed at evaluating head injury due to externally applied loading can be made more biofidelic by incorporating nonlinear mechanism-based and microstructurally-inspired material models representing the mechanical response and fracture (failure or injury) of the human skull bone. Thus, incorporation of these mechanism-based models would increase the ability of simulations of mechanical impact to identify more realistic fracture-based injuries at clinical relevancy, such as linear (tensile), depressed (compressive), or penetration (shear). One of the challenges for accurate modeling of the mechanical response of the human skull is the intricate location dependent heterogeneous mesostructural arrangement of bone within the structure of the skull. Recently, a power-law relationship between the localized bone volume fraction (BVF) and modulus (E) within the human skull was developed based on quasi-static compression experiments. However, the parameters of the power-law were optimized and obtained using approximations which were not experimentally or computationally validated for the actual heterogeneous 3D bone structure. Here, a hybrid experimental-modeling-computational (HEMC) based concept was used to develop a microstructurally compatible detailed meso-scale finite element (FE) model of the heterogeneous microstructure of one of the human skull bone coupons previously used to derive the E-BVF relationship. Finite elements were mapped to the corresponding regions from microcomputed tomography images, and the BVF of each element was identified. Then, element-specific moduli were calculated from the E-BVF power relationship. The goal of the simulations was twofold: to assess the assumptions used to derive the E-BVF relationship from the linear regime of the experimental response, and also to model the subsequent deviation from linearity. Using the E-BVF relationship, the 3D simulation was able to match the experimentally measured global modulus to within 3%. After validating the E-BVF power law using the initial linear response, to develop and validate failure models, the following steps were completed. The subsequent deviation of the mechanical response from its initial linearity was assumed to be due to failure of elements either by compression or tension. Elemental microstructure-specific compressive and tensile failure thresholds (σf) for each element were modeled by BVF (fBV) power functional relationships of the form: [Formula: see text] MPa. The initial leading coefficients (σf,0) for compression and tension were derived from prior reported experimental work. Through incorporating element-level failure and then iterating the leading coefficients, the simulation was able to represent the nonlinearity of the stress-strain curve and its catastrophic failure in the experiment. Evolution of the measured non-uniform full-strain-fields on two surfaces of the coupon, showing the localized regions of failure, was compared between experiment and simulation, and was approximately similar, thus validating the developed HEMC procedure and failure models. The simulation methodology developed here allowed for identification of failure location within the skull coupon specimen, thereby providing a tool to predict the localized failure (fracture or injury) initiation within the human skull in FE simulations at larger length scales.