Modeling of deformation and fracture of fibrillar structures

In the present paper the simplest 2D model of the material on the basis of fibrils is proposed. The single fibril is represented as two-layer stripe consisting of particles which interact via Lennard-Jones potential. In order to create the material fibrils are randomly added on the plane and connected in the places of the intersections. Molecular dynamics simulation of the uniaxial tension of this material is carried out. Stress-strain diagram is obtained. It is shown that fracture of the material takes place for 3% deformation. At the same time fracture of the single fibril takes place for 10% deformation. The dependences of the Young modulus of the material on the initial distribution of fibrils and density of the sample are investigated. It is shown that in some particular cases Young modulus of the sample can be two times larger than averaged value. Mean square deviation is approximately 20%. It decreases with the density of the sample. Young modulus grows linearly with the increase of density. The parameter which characterizes the ordering of fibrils is introduced. It is shown that ordering can essentially increase Young modulus in ordering direction (till 2,5 times).