Notches, as currently widely implemented shear connector in timber-concrete composite structures, ensure the internal state of equilibrium shear forces between compressive forces in concrete and tension forces in timber. The shear force propagation in the contact surface depends on geometrical shape of notches and their dimension. The geometric irregularities of notches induce high stress concentration in the vicinity of the joints that leads to failure of the structure. Thereafter, it reflects singularities and interfacial cracks. As a result of the difference elastic properties of both composite materials, slip in the contact surface occurs. The critical state of composite structures features the developing fractures caused by cracks at the interfaces. The conventional assumption based on the fully open-crack model induces to physically unacceptable behavior: Oscillatory singularities in stress and displacement fields that lead to interpenetration of both faces. These singularities can be neglected by defining the frictionless contact zones of certain length at the tips of interface cracks and can be described analytical for fully open-crack and contact-zone models.