3-D Constitutive Model for Asphalt on the Basis of Fractional Creep Functions
3-D Constitutive Model for Asphalt on the Basis of Fractional Creep Functions
复制标题
基于分数蠕变函数的沥青 3-D 本构模型
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Werkmeister
中科院分区：
文献类型：
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作者：
M. Oeser;S. Freitag;B. Moller;F. Wellner;S. Werkmeister
本文提出了一种改进的利用应变分数时间导数模拟沥青随时间变化的方法。推导了Kelvin体和Maxwell体相应的分数蠕变函数。利用这些蠕变函数，可以比用整数阶时间导数更真实地描述沥青随时间变化的变形行为(特别是加载开始时的递减蠕变行为和长期加载时的渐变行为)。为了考虑任意加载过程，分数阶蠕变函数用Dirichlet级数近似，并转化为所谓的遗传积分。为了求解遗传积分，有必要将加载过程细分为增量。如果蠕变函数与应力无关，则遗传积分可以在增量内解析求解。如果存在应力相关性，则用数值方法求解积分。为此，提出了一种高效的数值求解算法。负荷历史通过带有内部变量的级数公式进入该算法。材料模型以一维形式发展，并针对三维应力-应变空间进行了修正。这涉及到对正交异性材料行为、塑性压缩和膨胀的描述的考虑。
In this paper an improved method for modelling the time-dependent behaviour of asphalt using fractional time derivatives of strains is presented. The corresponding fractional creep functions for the KELVIN and MAXWELL body are derived. By means of these creep functions it is shown that the time-dependent deformation behaviour of asphalt (especially the degressive creep behaviour at the beginning of loading and the progressive behaviour for long load duration) may be described more realistically than by time derivatives of integer order. In order to account for arbitrary loading processes, the fractional creep functions are approximated using DIRICHLET series and converted into so-called hereditary integrals. In order to solve the hereditary integrals it is necessary to subdivide the loading process into increments. If the creep functions are independent of stress, the hereditary integrals may be solved analytically within an increment. If stress dependencies exist, the integrals are solved numerically. An efficient numerical solution algorithm is developed for this purpose. The load history enters this algorithm via series formulations with internal variables. The material model is developed in a onedimensional form and modified for the three-dimensional stress-strain space. This involves a consideration of the description of orthotropic material behaviour, plastic compression and dilation.