The influence of ondulation in fabric reinforced composites on dynamic properties in a mesoscopic scale

Structural mechanic properties of fiber reinforced plastics depend on the single components’ properties, namely matrix and fiber. Simple Micromechanical homogenization theories reach a limit when a laminate consists of fabric reinforced layers instead of unidirectional layers. The ondulations of warp and fill yarn caused by the textile semi-finished product are the reason why the mesoscopic dimension, lying between the microscopic and the macroscopic dimension, has to be taken into account when mechanically characterizing fabric reinforced composites. A one-dimensional mathematical model is formulated in order to obtain a representative sequence of one complete ondulation. Because of the ondulation the total deformation is presumed to consist of the mechanical strain and additionally a purely geometrical deformation that contributes to the total deformation behavior. A theoretical approach for a correlation between the degree of ondulation and the material’s geometrical contribution to deformation is carried out. The aforementioned mathematical model is the basis for the following finite-element-analysis. As a first step the obtained results are compared with existing representative volume elements implemented in LS-DYNA. Their suitability for modeling the above described behavior is evaluated. Especially when considering structural dynamic properties there often is only moderate compliance between theoretically based finite-element-models and experimentally determined values for the damping behavior. The investigation focuses on the material model *MAT_234 already implemented in the LS-DYNA material library. It includes a representative volume element considering the geometry of ondulations in fabrics on mesoscopic scale. A solution for the combination of the fabric reinforcement with a matrix component based on the material model *MAT_234 and its adequacy for the prediction of the material’s damping behavior are examined. Finally the finite-element-model is validated by experimentally determined values. Therefore the structural dynamic properties of a free-vibrating cantilever specimen with selected layups are measured with a laser vibrometer.