A new constitutive model for human trabecular bone is presented in the present study. As the model is based on indentation tests performed on single trabeculae it is formulated in a microscale. The constitutive law takes into account non-linear viscoelasticity of the tissue. The elastic response is described by the hyperelastic Mooney-Rivlin model while the viscoelastic effects are considered by means of the hereditary integral in which stress depends on both time and strain. The material constants in the constitutive equation are identified on the basis of the stress relaxation tests and the indentation tests using curve-fitting procedure. The constitutive model is implemented into finite element package Abaqus^® by means of UMAT subroutine. The curve-fitting error is low and the viscoelastic behaviour of the tissue predicted by the proposed constitutive model corresponds well to the realistic response of the trabecular bone.

本研究提出了一种新的人类小梁骨本构模型。由于该模型基于对单个小梁进行的压痕测试，因此将其微尺度化。本构定律考虑了组织的非线性粘弹性。弹性响应由超弹性的Mooney-Rivlin模型描述，而粘弹性效应则通过遗传积分来考虑，其中应力取决于时间和应变。本构方程中的材料常数是根据应力松弛测试和压痕测试使用曲线拟合程序确定的。本构模型被实现成有限元件封装的Abaqus ^®通过UMAT子例程。曲线拟合误差低，并且由所提出的本构模型预测的组织的粘弹性行为与小梁骨的实际响应非常吻合。