Mathematical modelling of head impact with craniocerebral injury

In the present paper, we review known mathematical models of a human head, which are applied in the contact problems of biomechanics. The finite element model was constructed from voxel data. This model involves of three main materials: soft tissue, skull and brain, defined on the basis of computed tomography with using the algorithm developed by the authors. In the paper, the iterative method of Schwarz domain decomposition was used for two contacting 3D bodies which allowed us to consider the solving of the stress-strain state problem in the usual formulation for the each contacting body. According to the offered iteration algorithm, two steps are performed in each iteration, where the conjugation conditions for the displacements and stresses are fulfilled in turn for the nodes on the contact surface. The validation of the developed finite element model has been conducted for the case of a short duration impact. A number of computational experiments have been carried out for establishing critical values of a contact force leading to severe injuries. At the impact force values in the range of 4000-6000 N, moderate and serious injuries can occur; the impact force values above 7000 N are considered as resulting in severe injuries with loss of consciousness for a long period; the force of 10000 N most probably can cause the death of an injured.