Computer modelling and analysis of microstructures with fibres and cracks

Purpose: The aim of the research is to formulate the boundary element approach, develop the computer codes and analyze microstructures containing fibres and cracks. The computer codes can be used to analyze influence of fibres and cracks on stress fields and effective properties of materials.Design/methodology/approach: The relation between boundary displacements and tractions is established by using appropriate boundary integral equations. The variations of boundary coordinates, displacements and tractions are interpolated by using nodal values and shape functions. Additionally, equations of motion and equilibrium equations are applied for rigid fibres.Findings: The boundary element method can be simply and effectively used for materials containing fibres and cracks. The stress fields for a single fibre computed by the present approach agree very well with analytical results. The fibre, which is perpendicular to the crack has larger influence on stress intensity factors than the fibre, which is parallel to the crack.Research limitations/implications: The proposed method is efficient for linear elastic materials. For other materials the boundary element method requires fundamental solutions, which have complicated forms. The developed computer codes can be extended to materials containing many randomly distributed fibres and cracks.Practical implications: The present method can be used to analyze and optimize strength and stiffness of materials by a proper reinforcement by fibers.Originality/value: The original value of the paper is the analysis of influence of distribution of rigid fibres on effective properties of composites and the influence of positions of a fibre and a crack on stress intensity factors.