考虑老化的混凝土粘弹性分数导数模型

混凝土是一种具有分形结构的材料。采用分数微积分模型来研究具有分形结构材料的老化规律目前尚未见到。本文的目的是采用含分数阶导数的类标准线性体来模拟考虑老化的混凝土的蠕变和松弛规律。给出了分数导数与Abel核之间的关系。讨论了类标准线性体的蠕变柔量和松弛模量及其在考虑老化的混凝土中的应用。与传统的混凝土流变模型相比较表明，类标准线性体可以更好地同时拟合混凝土在不同龄期的蠕变和松弛曲线。而且其形式简单、统一，在计算过程中需要调整的参数很少。可以预见，类标准线性体在混凝土的结构设计和计算中将有着广泛的应用前景。

Viscoelastic Fractional Derivative Model of Concrete with Aging

Concrete is a material having fractal structure. Till now, we have not yet seen researches on the aging laws of a material that having fractal structure using the model of fractional calculus. The aim of this paper is to give a simulation of creep and relaxation laws of concrete with aging by using standard-linear-like body with fractional order derivatives. The relation between the fractional derivative and the Abel kernel is given. The creep compliance and relaxation modulus for standard-linear-like body and their applications in concrete with aging are discussed. It is shown by comparison with the traditional concrete rheological models that the standard-linear-like body can simultaneously simulate the creep compliance and the relaxation modulus curves of the concrete of different age very well. It has a simple and uniform form, only a few of the parameters should be adjusted in the calculation processes. It is predictable that the standard-linear-like body will have wide applications in the design and the numerical calculation of the concrete structures.