A model for the through-thickness elastic-plastic behaviour of paper

An elastic-plastic material model for the out-of-plane mechanical behaviour of paper is presented. This model enables simulation the elastic-plastic behaviour under high compressive loads in the through-thickness direction (ZD). Paper does not exhibit a sharp transition from elastic to elastic-plastic behaviour. This makes it advantageous to define critical stress states based on failure stresses rather than yield stresses. Moreover, the failure stress in out-of-plane shear is strongly affected by previous plastic through-thickness compression. To cover these two features, a model based on the idea of a bounding surface that grows in size with plastic compression is proposed. Here, both the bounding and the yield surfaces are suggested as parabolas in stress space. While the bounding surface is open for compressive loads, the yield surface is bordered by the maximum applied through-thickness compression.