Bone is a complex hierarchical structural material whose organ-level response is highly influenced by its constitutive behavior at the microstructural level, which can dictate the inelastic nonlinear deformation and fracture within the organ. In the current study, a combined experimental-computational approach was sought to first obtain the local constitutive properties. Later, a multiscale modeling framework utilizing a novel rate-dependent nonlinear viscoelastic cohesive zone (NVCZ) model was used to explore the fracture behavior at the microstructure of the bone and its influence on the global scale (organ-level) response. Toward this end, nanoindentation testing was conducted within the cross-section of a rat femur bone specimen. An inverse optimization process was used to identify the isotropic linear viscoelastic (LVE) properties of cortical bone by integrating the test results with a finite element model simulation of the nanoindentation testing. Model results using different numbers of spring-dashpot units in the generalized Maxwell model showed that four spring-dashpot units are sufficient to capture the LVE behavior, while solely LVE constitutive relation is limited to fully characterize the rat femur. The LVE constitutive properties were then used along with the rate-dependent NVCZ fracture within the representative volume element (RVE), which was two-way coupled to the global scale bone. A parametric study was conducted by varying the fracture properties of the NVCZ model. The model demonstrated the capability and features to represent inelastic deformation and nonlinear fracture that are linked between length scales. This further implies that the inelastic fracture model and the two-way coupled modeling can elucidate the complex multiscale deformation and fracture of bone, while model validation and further advancements with test results remain a follow-up study and are currently in progress.

中文翻译：

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大鼠骨粘弹性变形和速率依赖性骨折损伤的建模

骨骼是一种复杂的分层结构材料，其器官级响应很大程度上受到其微观结构水平本构行为的影响，这可以决定器官内的非弹性非线性变形和断裂。在当前的研究中，寻求一种组合的实验-计算方法来首先获得局部本构属性。随后，利用新型速率相关非线性粘弹性粘聚区（NVCZ）模型的多尺度建模框架被用来探索骨骼微观结构的断裂行为及其对全局尺度（器官水平）响应的影响。为此，在大鼠股骨样本的横截面内进行了纳米压痕测试。通过将测试结果与纳米压痕测试的有限元模型模拟相结合，使用逆优化过程来识别皮质骨的各向同性线性粘弹性（LVE）特性。在广义麦克斯韦模型中使用不同数量的弹簧缓冲器单元的模型结果表明，四个弹簧缓冲器单元足以捕获LVE行为，而仅LVE本构关系仅限于充分表征大鼠股骨。然后将 LVE 本构特性与代表性体积元素 (RVE) 内的速率依赖性 NVCZ 骨折一起使用，该骨折与全局尺度骨骼双向耦合。通过改变 NVCZ 模型的断裂特性进行了参数研究。该模型展示了表示长度尺度之间相关的非弹性变形和非线性断裂的能力和特征。这进一步意味着非弹性断裂模型和双向耦合建模可以阐明复杂的多尺度骨骼变形和断裂，而模型验证和测试结果的进一步进展仍然是后续研究，目前正在进行中。