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 (${\sigma }_f)$ for each element were modeled by BVF ($f_{BV})$ power functional relationships of the form: ${\sigma }_f={\sigma }_{f,0}{(f_{BV})}^2$ MPa. The initial leading coefficients (${\sigma }_{f,0}$) 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.

通过结合基于非线性机制和微观结构启发的材料模型（代表人类颅骨的机械反应和骨折（断裂或损伤）），旨在评估由于外部施加的载荷而导致的头部损伤的数值研究可以变得更加生物逼真。因此，结合这些基于机制的模型将提高机械冲击模拟的能力，以在临床相关性时识别更现实的基于骨折的损伤，例如线性（拉伸），压迫（压缩）或穿透（剪切）。对人类头骨的机械反应进行精确建模的挑战之一是头骨结构内骨骼的位置依赖性复杂的异质介观结构排列。最近，基于准静态压缩实验，建立了人类颅骨局部骨体积分数（BVF）与模量（E）之间的幂律关系。但是，幂定律的参数是使用近似值进行优化和获取的，而这些近似值并未针对实际的异质3D骨骼结构进行实验或计算验证。在这里，基于混合实验模型计算（HEMC）的概念被用于开发以前用于导出E-的人头骨骨试样之一的异质微观结构的微观结构兼容的细观中尺度有限元（FE）模型。 BVF关系。从微计算机断层扫描图像将有限元素映射到相应区域，并确定每个元素的BVF。然后，根据E-BVF功率关系计算元素特定的模量。模拟的目的是双重的：评估用于从实验响应的线性机制中得出E-BVF关系的假设，并为随后的线性偏差建模。使用E-BVF关系，3D仿真能够将实验测量的整体模量匹配到3％以内。在使用初始线性响应验证E-BVF幂律之后，开发并验证故障模型，完成以下步骤。机械响应与其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（模拟的目的是双重的：评估用于从实验响应的线性机制中得出E-BVF关系的假设，并为随后的线性偏差建模。使用E-BVF关系，3D仿真能够将实验测量的整体模量匹配到3％以内。在使用初始线性响应验证E-BVF幂律之后，开发并验证故障模型，完成以下步骤。机械响应从其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（模拟的目的是双重的：评估用于从实验响应的线性机制中得出E-BVF关系的假设，并为随后的线性偏差建模。使用E-BVF关系，3D仿真能够将实验测量的整体模量匹配到3％以内。在使用初始线性响应验证E-BVF功率定律后，开发并验证故障模型，完成以下步骤。机械响应与其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（并为随后的线性偏差建模。使用E-BVF关系，3D仿真能够将实验测量的整体模量匹配到3％以内。在使用初始线性响应验证E-BVF幂律之后，开发并验证故障模型，完成以下步骤。机械响应与其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（并为随后的线性偏差建模。使用E-BVF关系，3D仿真能够将实验测量的整体模量匹配到3％以内。在使用初始线性响应验证E-BVF幂律之后，开发并验证故障模型，完成以下步骤。机械响应与其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（完成以下步骤。机械响应与其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（完成以下步骤。机械响应与其初始线性的后续偏差被认为是由于元件由于压缩或拉伸而失效。特定于元素微结构的压缩和拉伸破坏阈值（${\sigma }_F）$ 每个元素都由BVF建模（$F_{乙V}）$ 形式的幂函数关系： ${\sigma }_F={\sigma }_{F，0}{（F_{乙V}）}^2$MPa。初始前导系数（${\sigma }_{F，0}$压缩和拉伸力来自先前报道的实验工作。通过合并单元级故障，然后迭代前导系数，该仿真能够表示实验中应力应变曲线的非线性及其灾难性故障。在实验和仿真之间比较了试样两个表面上测得的非均匀全应变场的演变，显示出局部失效区域，并且近似相似，从而验证了已开发的HEMC程序和失效模型。此处开发的模拟方法可以识别出颅骨试样样本中的失效位置，从而提供了一种工具，可以在较大长度尺度的有限元模拟中预测人类颅骨内的局部失效（断裂或损伤）引发。