Algorithmic Information Theory for the Precise Engineering of Flexible Material Mechanics

Abstract

The structure of fibrous assemblies is highly complex, being both random and regular at the same time, which leads to the complexity of its mechanical behaviour. Using algorithms such as machine learning to process complex mechanical property data requires consideration and understanding of its information principles. There are many different methods and instruments for measuring flexible material mechanics, and many different mechanics models exist. There is a need for an evaluation method to determine how close the results they obtain are to the real material mechanical behaviours. This paper considers and investigates measurements, data, models and simulations of fabric’s low-stress mechanics from an information perspective. The simplification of measurements and models will lead to a loss of information and, ultimately, a loss of authenticity in the results. Kolmogorov complexity is used as a tool to analyse and evaluate the algorithmic information content of multivariate nonlinear relationships of fabric stress and strain. The loss of algorithmic information content resulting from simplified approaches to various material measurements, models and simulations is also evaluated. For example, ignoring the friction hysteresis component in the material mechanical data can cause the model and simulation to lose more than 50% of the algorithm information, whilst the average loss of information using uniaxial measurement data can be as high as 75%. The results of this evaluation can be used to determine the authenticity of measurements and models and to identify the direction for new measurement instrument development and material mechanics modelling. It has been shown that a vast number of models, which use unary relationships to describe fabric behaviour and ignore the presence of frictional hysteresis, are inaccurate because they hold less than 12% of real fabric mechanics data. The paper also explores the possibility of compressing the measurement data of fabric mechanical properties.