A 1D elastic plastic damage constitutive law for bone tissue
A 1D elastic plastic damage constitutive law for bone tissue
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DOI：
10.1007/s00419-009-0382-2
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发表时间：
2010-05-01
影响因子：
2.8
通讯作者：
Curnier, A.
中科院分区：
文献类型：
--
作者：
Garcia, D.;Zysset, Philippe K.;Curnier, A.
受骨科和颌面外科应用的启发，研究了皮质骨在生理应变率下循环过载的力学行为。为此，提出了一种新的一维率无关的密质骨本构模型来模拟拉伸或压缩过载过程中发生的损伤累积。我们采用了宏观和现象学描述的力学皮质骨。该模型的数学公式是建立在广义标准材料的框架内，是基于三个内部状态变量的定义：拉伸和压缩损伤变量，代表微裂纹密度和残余应变变量，代表永久应变与这些微裂纹的滑动行为。在拉伸和压缩中使用不同的损伤阈值应力。由于牛皮质骨的宏观力学行为与人类皮质骨非常相似，并且更容易获得，我们首先利用我们自己的牛密质骨的新的单轴实验结果实现了拉伸本构关系的材料常数的验证和识别。有足够的原始硬化规则，本构模型是能够再现任意循环拉伸和压缩载荷下的皮质骨行为的主要特征。该算法首次应用三个不同的预测的基础上的三个内部变量和标准之间的关系。预测的应力-应变曲线表现出与原点共线的损伤再加载，正如许多对皮质骨的循环过载实验所示。请注意，由于我们的模型是针对生理应变率确定的，因此它几乎不能应用于高应变率情况，如撞击研究中所涉及的情况。
Motivated by applications in orthopaedic and maxillo-facial surgery, the mechanical behaviour of cortical bone in cyclic overloads at physiological strain rates is investigated. To this end, a new one-dimensional rate-independent constitutive model for compact bone is proposed to simulate the damage accumulation occurring during tensile or compressive overloading. We adopted a macroscopic and phenomenological description of the mechanics of cortical bone. The mathematical formulation of the model is established within the framework of generalized standard materials and is based on the definition of three internal state variables: a tensile and a compressive damage variable that represent the microcrack density and a residual strain variable that represents the permanent strain associated with the sliding behaviour of these microcracks. Distinct damage threshold stresses are used in tension and compression. As the macroscopic mechanical behaviour of bovine cortical bone is very similar to that of human cortical bone and of much easier access, we first achieved the validation and identification of the material constants of the constitutive laws in tension using new uniaxial experimental results of bovine compact bone of our own. With adequate original hardening rules, the constitutive model is able to reproduce the main features of cortical bone behaviour under arbitrary cyclic tensile and compressive loadings. The proposed algorithm applies for the first time three distinct projections based on the relationship between the three internal variables and criteria. The predicted stress-strain curves exhibit a damaged reloading which is collinear with the origin as many cyclic overloading experiments on cortical bone have shown. Note that as our model was identified for physiological strain rates, it hardly can be applied in high strain rate situations like the ones involved in impact studies.