A three-level hierarchical approach in modeling sheet thermoforming of knitted-fabric composites

A three-level hierarchical approach in modeling thermoforming process of curved-fabric-reinforced polymer sheet is presented in this paper. In the microscopic level, fiber bundle properties are analytically obtained from fiber filament and matrix material properties using simple rule-of-mixture approach. In the mesoscopic level, the representative volume element properties are obtained from the fiber bundle and matrix material properties using the mesoscopic mesh. Subsequent updating of mesoscopic nodal mesh coordinates and imposition of further strain gives the constitutive behavior of the composite material with due consideration to fabric reorientation, hence geometrical non-linearity. In the macroscopic level, the constitutive relationship, as a function of strain state, is applied to the macroscopic mesh whereby the material property of every macroscopic element is determined from the strain state resulting from the previous incremental plunger penetration and from the material database. Using the example of plain weft-knitted-fabric composites, both experimental and theoretical strain fields show reasonable agreement.