Anisotropic viscoelastic constitutive law assuming plane stress state

The viscoelastic material constitutive law based on the anisotropic generalized Maxwell model, which assumes a three-dimensional (3D) stress state, is reduced to a plane-stress state to efficiently analyze thin plate-like laminated structures. When the method used to derive the elasticity coefficient matrix for purely elastic problems is applied to viscoelastic problems under a plane-stress assumption, the rheological model breaks down. Therefore, the time-evolution equation for the out-of-plane strain is formulated so that the parallel Maxwell elements share a common strain. To enhance compatibility with existing constitutive laws, an algorithm is also proposed to convert material constants for a 3D stress state into those applicable to a plane-stress state. A virtual stress relaxation test based on homogenization theory under a 3D stress state is applied to an unidirectionally reinforced thermoplastic epoxy resin with glass fibers. From these results, both the raw material constants for the 3D stress state and the corresponding converted constants for plane-stress conditions are obtained. Furthermore, the validity of the derived constitutive law and the proposed approach for reducing the material constants is verified by comparing the out-of-plane strain predicted by the law with the results of virtual material tests. By combining the anisotropic viscoelastic constitutive law proposed in this study for plane-stress states with layer theory, laminated composites can be efficiently analyzed using shell elements.