Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e. ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established.

纸是一种复杂的材料，由微观水平的纤维素纤维网络组成。在制造过程中，由于纸幅在纵向上的张力，网在约束条件下干燥。这产生了内部应变，该内部应变被存储在所生产的片材中。暴露于湿气循环后，这些菌株可能会释放出来。这会导致永久性收缩，从而可能导致不稳定性，例如纸张的卷曲或起伏。本文的主要目的是为这种不可逆的收缩建模，并将其大小与纤维和网络的特性联系起来。为此，随机生成不同覆盖率的光纤网络（即 纤维所占的面积与片材的面积之比）是通过周期性的代表性体积元（RVE）进行建模的。在这种RVE中，使用有限元方法结合纤维尺度上的运动硬化可塑性模型来捕获不可逆的响应。计算结果表明，不可逆应变的大小随覆盖率的增加而增加，直到一定的覆盖率，超过该覆盖率的幅度减小。通过考虑独立式纤维段相对于网络中粘合纤维段的面积分数来解释这种现象。从而建立了薄层级不可逆应变对网络微观结构参数的结构性质依赖性。