Development of a three-dimensional nonlinear viscoelastic constitutive model of solid propellant

A three dimensional nonlinear viscoelastic constitutive model for the solid propellant is developed. In their earlier work, the authors have developed an isotropic constitutive model and verified it for one dimensional case. In the present work, the validity of the model is extended to three-dimensional cases. Large deformation, dewetting and cyclic loading effects are treated as the main sources of nonlinear behavior of the solid propellant. Viscoelastic dewetting criteria is used and the softening of the solid propellant due to dewetting is treated by the modulus decrease. The nonlinearities during cyclic loading are accounted for by the functions of the octahedral shear strain measure. The constitutive equation is implemented into a finite element code for the analysis of propellant grains. A commercial finite element package ‘ABAQUS’ is used for the analysis and the model is introduced into the code through a user subroutine. The model is evaluated with different loading conditions and the predicted values are in good agreement with the measured ones. The resulting model applied to analyze a solid propellant grain for the thermal cycling load.

Three-dimensional conformal breast irradiation in the prone position

The prone position can be used for the planning of adjuvant radiotherapy after conservative breast surgery in order to deliver less irradiation to lung and cardiac tissue. In the present study, we compared the results of three-dimensional conformal radiotherapy planning for five patients irradiated in the supine and prone position. Tumor stage was T1N0M0 in four patients and T1N1M0 in one. All patients had been previously submitted to conservative breast surgery. Breast size was large in three patients and moderate in the other two. Irradiation in the prone position was performed using an immobilization foam pad with a hole cut into it to accommodate the breast so that it would hang down away from the chest wall. Dose-volume histograms showed that mean irradiation doses reaching the ipsilateral lung were 8.3 ± 3.6 Gy with the patient in the supine position and 1.4 ± 1.0 Gy with the patient in the prone position (P = 0.043). The values for the contralateral lung were 1.3 ± 0.7 and 0.3 ± 0.1 Gy (P = 0.043) and the values for cardiac tissue were 4.6 ± 1.6 and 3.0 ± 1.7 Gy (P = 0.079), respectively. Thus, the dose-volume histograms demonstrated that lung tissue irradiation was significantly lower with the patient in the prone position than in the supine position. Large-breasted women appeared to benefit most from irradiation in the prone position. Prone position breast irradiation appears to be a simple and effective alternative to the conventional supine position for patients with large breasts, since they are subjected to lower pulmonary doses which may cause less pulmonary side effects in the future.