蠕动
粘弹性
应力松弛
放松(心理学)
Volterra积分方程
压力(语言学)
变形(气象学)
机械
数学
材料科学
积分方程
数学分析
物理
热力学
复合材料
心理学
社会心理学
哲学
语言学
作者
R. S. Anderssen,Alison Davies,Frank de Hoog
出处
期刊:Inverse Problems
[IOP Publishing]
日期:2008-04-08
卷期号:24 (3): 035009-035009
被引量:26
标识
DOI:10.1088/0266-5611/24/3/035009
摘要
The evolving stress–strain response of a material to an applied deformation is causal. If the current response depends on the earlier history of the stress–strain dynamics of the material (i.e. the material has memory), then Volterra integral equations become the natural framework within which to model the response. For viscoelastic materials, when the response is linear, the dual linear Boltzmann causal integral equations are the appropriate model. The choice of one rather than the other depends on whether the applied deformation is a stress or a strain, and the associated response is, respectively, a creep or a relaxation. The duality between creep and relaxation is known explicitly and is referred to as the 'interconversion equation'. Rheologically, its importance relates to the fact that it allows the creep to be determined from knowledge of the relaxation and vice versa. Computationally, it has been known for some time that the recovery of the relaxation from the creep is more problematic than the creep from the relaxation. Recent research, using discrete models for the creep and relaxation, has confirmed that this is an essential feature of interconversion. In this paper, the corresponding result is generalized for continuous models of the creep and relaxation.
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