Biomechanical analysis of growth strain

Growth strains appear mainly in living systems. Growth occurs in every living organism, and for a human it is most meaningful at childhood. Unfortunately, some children are born with congenital abnormalities, for example, with a congenital cleft of the hard palate. Without treatment and influence of the growth processes, such a child may become disabled. From the points of biomechanics and continuum mechanics, growth strains can be considered as eigenstrains. It is also known that mechanical stresses affect the growth processes, hence the growth deformation. Thus, orthodontic treatment can be considered as growth control problem. The paper uses the theorem of eigenstrain decomposition in a linear elastic body, which allows us to decompose the eigenstrain into two parts: stress-free (or impotent), and deformation-free (or nilpotent). The paper shows the application of the theorem in the solution of stress-free deformation control by eigenstrain, the statement of a problem of modelling of systems with eigenstrain is given. The proposed approach is used to simulate growth deformations in the treatment of congenital cleft of the hard palate. The governing equation for the growth strain is discussed and analyzed, and it is shown that under certain boundary conditions the growth will not cause stresses in the system, which greatly simplifies the solution for the problem of growth strain accumulation over time. This result is important for planning the optimal orthopedic treatment of the pathology, which leads to the problem of independent control of system deformations by means of growth strains. The governing equation is obtained for an isotropic homogeneous body, since the bone tissue of the child has no formed structure and isotropic.