Modeling delamination in composite structures by incorporating the Fermi-Dirac distribution function and hybrid damage indicators

Conventional finite element approaches for modeling delaminations; in laminated composite structures use the Heaviside unit step function at the interfacial nodes in the delaminated zone of the structure to model the possible jumps in the displacement field during "breathing" of the delaminated layers. In quantum mechanics, the Fermi-Dirac distribution applies to Fermion particles whose characteristics are half-integer spins. The present paper uses the Fermi-Dirac distribution function to model a smoother transition in the displacement and the strain fields of the delaminated interfaces during the opening and closing of the delaminated layers under vibratory loads. This paper successfully shows that the Fermi-Dirac distribution function can be used to more accurately model the dynamic effects of delaminations in laminated composite structures. Optimizing the parameters in the Fermi-Dirac distribution function can lead to more accurate modeling of the dynamic and transient behavior of the delaminated zones in laminated composite structures. Further applications of the Fermi-Dirac distribution function in other physics based dynamic models are suggested. This paper also effectively demonstrates how hybrid sensors comprising of out of plane displacement sensors and in plane strain sensors can effectively map a composite structure to detect and locate the delaminated zones. It also shows how simple mode shapes can be used to determine the locations of single and multiple delaminations in laminated composite structures.