Development and validation of modified composite material constitutive model considering shear bimodular effects

Establishing a reasonable constitutive model is fundamental for accurately guiding the design of aerospace composite structures. This study investigates the mechanical behavior of carbon fiber reinforced polymer (CFRP) composites through quasi-static tensile and compression tests, and the results show that the bimodularity of composite materials is manifested in not only Young's modulus but also shear modulus. However, existing bimodular composite material constitutive models show limitations in reasonably describing the shear bimodular effect. We present a complete shear bimodular model (CSBM) based on transversely isotropic unidirectional composites. This model establishes strain–stress relationships in the material principal strain coordinate system, defines compliance related to longitudinal–transverse shear modulus through shear strain signs, and derives the transverse-thickness shear modulus and its corresponding compliance under complex strain states from the physical meaning of shear modulus, thus achieving a complete description of shear bimodularity. Theoretical analysis demonstrates that the modified model satisfies the consistency criterion for bimodular materials, thereby establishing its rationality and universality. The material nonlinearity caused by bimodularity is resolved by deriving the tangent stiffness matrices of CSBM under complex strain states, and a complete numerical implementation scheme is established. Experimental and numerical results verify the effectiveness of the CSBM. The cantilever beam example shows that the CSBM has better convergence efficiency than the existent model. This study provides a more complete theoretical framework for the mechanical analysis of bimodular composites.