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C. T. J. Dodson. A survey of paper mechanics in fundamental terms. In The Fundamental Properties of Paper Related to its Uses, Trans. of the Vth Fund. Res. Symp. Cambridge, 1973, (F. Bolam, ed.), pp 202–226, FRC, Manchester, 2018.


The object of this survey is to review recent work on the mechanical properties of paper with particular reference to the role of fundamental parameters and to attempt an assessment of the current position. Precisely which parameters are to be distinguished as fundamental is of course still a major field for research, so it is hoped that a spirit of reasonableness will be perceived in the interpretations that are offered below.

As a preliminary to the survey, some physical and chemical properties of cellulose are collected together with associated properties of fibres and certain structural features of paper. In its end usage, the mechanical attributes of paper are influenced markedly by environmental factors such as temperature and the presence of moisture, but it still remains a problem to separate these effects in basic terms. Rheologically, paper has a long memory of its past history, but, its structural heterogeneity makes this memory appear erratic to the experimenter and it often yields counterexamples to embarrass theoretical developments. Nevertheless, there has accumulated a large body of data on the mechanical behaviour of paper and there has been considerable success in fitting this into a working patchwork of respectable theory that has served well in stimulating experimental discoveries, thereby providing for a continued regenerative development, which is the subject of this article.

The early work borrowed and developed rheological models from the textile industry and the subsequent avalanche of data needed to evaluate empirical parameters exposed an intricate interdependency of effects. This stimulated a retraction into the apparently safer realm of molecular theory by employing classical physical chemistry to exploit the accumulating data on hydrogen bonds. The reaction to the enthusiastic development of molecular models must have been dismay in many scientific papermakers, for valuable as they clearly were (and still are) these models said nothing about fibres, which manifestly distinguish paper from other materials. Accordingly, general attention was turned to models that appeared more faithful in a structural sense and might support a theory of fracture, which phenomenon of course was well known to be an eager accompaniment of any mechanical treatment. There emerged two principal developments, statistical geometry and linear network theories. Firstly, the former provided a clinically statistical treatment of fracture in open networks. Various refinements of the linear network theories were successful for well-behaved synthetic fibrous networks. Inevitably, they were not able to overcome the obstacle that physical properties of natural fibres depend on the structure and treatment of the sheet. So fitting factors of dubious heritage had to be used to fix the initial slope of predicted stress/strain curves and to represent fracture by a subsequent decay of that slope. Meanwhile, statistical geometry gave rise to a kind of statistical elasticity that acknowledged the fibrous structure and successfully derived from it a covariance with deformation of the network during straining. The same obstacle prevented absolute predictions (as had faced the linear theories) and fracture was not considered. On the other hand, two independent approaches to fracture that seemed to represent the mechanism in a phenomenological way depended on energy rather than geometrical considerations, but experiments show that-at least for thin sheets-the fracture process is governed by geometrical properties of the network.

As for the future of research on mechanical properties of paper, it is the view of the author that treatment of paper as a heterogeneous continuum will prevail while linear network theories will be recognised as being with little value for predicting the behaviour of real paper. There is clearly a rich field of research for organic and physical chemists both at the level of fibre-to-fibre bonds and in the treatment of bulk properties to answer the many questions that remain, about the role of hemicellulose and migration of water, about the interdependence of rheological- and thermal effects and about the extent to which the molecular structure and disposition of fibrils can influence bonding and hygroexpansivity, to name but a few.

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