# Modelling of High-Velocity Impact on Woven Carbon Fibre-Reinforced Plastic Laminate
## 1 Introduction  
Across a large number of industrial sectors, composites are the material of choice for the design of lightweight, more energy-efficient and net zero structures, due to their excellent stiffness and strength-to-density ratio. However, the design of composite structures is still limited by the lack of understanding of composite materials, especially their response to high-rate dynamic loading, such as high-velocity impacts, which is important in a number of industrial sectors. For instance, composite materials used in aerospace applications are very often exposed to impact and extreme dynamic loading, including impacts of orbiting particles on spacecraft, ballistic impact on aircraft, foreign object debris impact on jet engines, bird strikes, etc. The complexity of the material response arises primarily from the extreme level of material anisotropy and pronounced heterogeneity. Due to these uncertainties, modern simulation tools are limited in their capability to predict material degradation, its progression and failure. Challenging areas remain in the predictive modelling of the dynamic behaviour of composite structures and materials, including the modelling of damage and failure, such as damage induced by shock wave propagation outside of the impact zone as well as modelling of damage for the purpose of residual strength assessment and for structural health monitoring. A number of attempts have been made to develop predictive simulation tools. Owing to the brittle properties of composite materials, a number of failure criteria have been developed, including quadratic failure criteria (Tsai-Hill [1] and Tsai-Wu [2]), which are frequently used for analysis of long fibre laminates. Both criteria account for the interactions between different stress components and different failure modes. However, the interactions of the failure modes in the models prevent analysts from identifying the specific failure mode of the composite material. [PERSON] [3,4] proposed a failure model for transversally isotropic composite material, with different in-plane failure modes. This model is significant and widely used because it is implemented in LS-Dyna [5] and DYNA3D [6], but it is not able to represent the delamination due to the tensile loading. A comprehensive review of the other failure criteria used for modelling composites can be found in [7] and in World-Wide Failure Exercise (WWFE) [8,9]. The latter includes a critical evaluation and validation of the models against the benchmark experiments. The WWFE concluded that a universally robust and accurate model, in all test cases considered, did not exist. The failure models typically set the material constants and stress to zero when the failure criterion is reached and are not capable of modelling progressive damage. Due to the high level of heterogeneity of composites, one approach for modelling of damage evolution was based on the micromechanical criteria for material constituents (fibres and matrix) and application of a homogenisation technique to the continuum level. The examples for this approach, where the evolution of damage in the material constituents was described on the basis of Continuum Damage Mechanics (CDM) laws, are [8,9]. Other than the CDM models based on homogenisation, a number of authors use continuum evolution laws and experimentally determined the material parameters for the considered composite materials. For instance, [PERSON] and [PERSON] [10] developed a thermodynamically consistent model for elastic damage for fibre-reinforced laminate, where the evolution was controlled by modified Voce law, given in terms of internal variables. A similar approach was used by [PERSON] et al. in [11], [PERSON] and coworkers in [12], etc. Models suitable for the analysis of composite structures with progressive damage capabilities are typically based on a continuum damage mechanics approach and account for gradual material deterioration; see, for instance, [13, 14, 15, 16, 17, 18], among many others.