A robust three-node shell element for laminated composites with matrix damage

A constitutive model for laminated composite shells with transverse matrix damage and its associated shell constitutive equations in three-dimensional space are developed. A single, physically relevant state variable is used in each lamina to track the state of transverse damage. The state variable also defines a physically relevant, solution dependent, characteristic length for the problem. Therefore, the constitutive model does not introduce constitutive mesh dependency on the solution. The model predicts crack initiation and evolution in good agreement with published experimental results for several materials and many different laminate stacking sequences. Input material parameters are limited to elastic properties and fracture toughness in modes I and II. Unlike continuum damage mechanics models, no adjustable parameters are needed to describe the initiation and evolution of damage. That is, the material parameters needed for the analysis are limited to invariant material properties that can be measured with standard test methods. The excellent predictive capabilities of the model and its versatility of application to a variety of materials and laminate configurations hinges upon computation of energy release rate for the entire laminate as a results of cracks propagating in any one lamina. Such computation requires knowledge about the state variables in all laminae when computing damage evolution in any one lamina, which in turn requires implementation of the constitutive equations directly into the element formulation. Therefore, the constitutive model is integrated into a shell element based on 1,2-order shell theory, and further implemented as a user element into commercial finite element analysis software.