The properties and geometry of bone in the mandible play a key role in mandible behaviour during a person's lifetime, and attention needs to be paid to the influence of bone properties. We analysed the effect of bone geometry, size and bone properties in mandible behaviour, experimenting on cadaveric mandibles and FE models. The study was developed using the geometry of a cadaveric mandible without teeth. Three models of cadaveric condyles were experimentally tested with instrumented with four rosettes, and a condyle reaction of 300 N. Four finite element models were considered to validate the experiments and analyse mandible behaviour. One numeric model was simulated with 10 muscles in a quasi-static condition. The experimental results present different condyle stiffness's, of 448, 215 and 254 N/mm. The values presented in the rosettes are influenced by bone geometry and bone thickness; maximum value was -600 με in rosette #4, and the maximum strain difference between mandibles was 111%. The numerical results show that bone density decreases and strain distribution increases in the thinner mandible regions. Nevertheless, the global behaviour of the structure remains similar, but presents different strain magnitudes. The study shows the need to take into account bone characteristics and their evolutions in order to improve implant design and fixation throughout the patient life. The change in bone stiffness promotes a change in maximum strain distribution with same global behaviour.

The centre of resistance and centre of rotation of a tooth are key concepts in orthodontics. Determining the coordinates of these points is essential for planning orthodontic tooth movement. The paper proposes a procedure for experimental determination of the two centres, verifies a previously developed mathematical theory through computer simulations and evaluates the effect of nonlinearity of the periodontal ligament on the parameters related to the centres. The paper relies on the mathematical theory of a rigid body embedded in an elastic medium, physical experiment, finite element method and a simple nonlinear theory of the tooth. The concept of the centre of resistance requires a revision if nonlinearity is taken into account.

The general theory of linearized elasticity with eigenstrain is considered with applications to continuous, discrete and discretized structures. It is shown that any eigenstrain can be uniquely decomposed into impotent and nilpotent constituents. The proven theorem on decomposition is based on the concepts of functional analysis, in particular, with respect to Hilbert functional spaces. This unique decomposition allows for the individual and independent control of stress, strain and displacement (e.g. shape control). The associated algorithm avoids the cumbersome solution of boundary‐value problems with eigenstrain in connection with these control problems. Decomposition of eigenstrain opens the practically important opportunity to fully separate the control of strain and stress produced by force loading.

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