JID:AESCTE AID:4081 /FLA [m5G; v1.218; Prn:4/07/2017; 13:52] P.1(1-8) Aerospace Science and Technology ••• (••••) •••–••• Contents lists available at ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte 1 67 2 68 3 69 4 70 5 71 6 72 7 73 8 74 9 75 10 76 11 77 12 78 13 79 14 80 15 81 16 82 17 83 18 84 19 85 20 86 21 87 22 88 23 89 24 90 25 91 26 92 27 93 28 94 29 95 30 96 31 97 32 98 33 99 34 100 35 101 36 102 37 103 38 104 39 105 40 106 41 107 42 108 43 109 44 110 45 111 46 112 47 113 48 114 49 115 50 116 51 117 52 118 53 119 54 120 55 121 56 122 57 123 58 124 59 125 60 126 61 127 62 128 63 129 64 130 65 131 66 132 Constitutive modeling of solid propellants for three dimensional nonlinear finite element analysis Birkan Tunç, ¸ Sebnem Özüpek ∗ Bo˘ gaziçi University, Mechanical Engineering Department, 34342 Bebek, Istanbul, Turkey a r t i c l e i n f o a b s t r a c t Article history: Received 6 March 2017 Received in revised form 12 June 2017 Accepted 18 June 2017 Available online xxxx Keywords: Solid propellant Constitutive model Damage Viscoelasticity Finite element analysis A three dimensional constitutive model for solid propellants is proposed and implemented in a finite element software. The effects of viscoelasticity, large deformation, temperature, pressure, softening in monotonic and cyclic loadings are represented. Damage is assumed to initiate by failure of the particle- binder bond or failure in the binder itself. Opening of the micro-cracks resulting from either failure is associated with the evolution of damage. Stress softening during unloading and reloading is captured via a cyclic function modifying the viscoelastic stress. The implementation algorithm is stable and robust, therefore analysis of general geometries and loadings are possible. The model may be calibrated with a small number of test data, therefore is suitable for practical use in the industry.  2017 Elsevier Masson SAS. All rights reserved. 1. Introduction Composite solid propellants exhibit highly nonlinear mechani- cal behavior due to large deformation, temperature, loading rate, superimposed pressure, cyclic loading and damage. A constitutive model that accounts for the effect of these factors may be quite complex and need a large number of test data to calibrate model parameters. On the other hand, prediction of structural integrity of a rocket motor grain and reliable determination of its service life typically require accurate, three-dimensional stress analysis. A constitutive model developed as part of a computational proce- dure, such as finite element analysis, needs not only to realistically predict the behavior of the propellant under various loading condi- tions, but also be well suited for numerical implementation. To be of practical use in the industry, the amount of test data required should be minimized. Furthermore, a robust and numerically stable implementation algorithm should be developed in order to mini- mize convergence difficulties that may result from mathematical nonlinearities. In the following, recent literature on propellant constitutive modeling is reviewed in terms of model development, computa- tional implementation, verification–validation and application to stress analysis. Several of the following constitutive models aim to represent the nonlinearity due to damage within the linear viscoelastic * Corresponding author. E-mail addresses: tuncbirkan@gmail.com (B. Tunç), ozupek@boun.edu.tr (¸ S. Özüpek). framework. Park and Schapery’s [1] viscoelastic constitutive model with growing damage is based on thermodynamics framework and internal state variables [2]. The model was initially proposed as one-dimensional and later extended to three dimensions by Ha and Schapery [3]. Simulation results for uniaxial and biaxial load- ing cases were presented. A variation of the model was proposed by Jinseng et al. [4] where damage was assumed to evolve as a function of temperature. The validation was based on uniaxial test data and homogeneous deformation. Also based on Park and Schapery’s framework, Wang et al. [5] investigated the behavior of propellants at low temperature and high strain rate and accurately predicted uniaxial homogeneous deformations. Xu et al.’s [6] model accounted for propellant porosity. Uniaxial monotonic loading was well represented, however the nonlinear effects during unloading were not captured. The predictive capa- bility for three dimensional analysis was not provided. Chyuan [7] conducted linear viscoelastic stress analysis of a rocket motor grain to study the effect of thermal loading. Propellant non-linearity was included [8] by varying the bulk modulus as a function of com- pressive stresses. The study showed that for compressive thermal stress states, non-linear bulk modulus modeling significantly af- fects the response as compared to linear analysis with constant bulk modulus. Hur et al.’s [9] constitutive model is based on the calculation of effective shear and bulk modulus of the propellant including the effect of voids, in addition to the binder and the particles. The moduli of the binder were assumed to depend on temperature and strain rate. Damage evolution was modeled as strain-controlled nucleation of voids. The model was implemented in a finite element code. Uniaxial and biaxial loading simulations http://dx.doi.org/10.1016/j.ast.2017.06.025 1270-9638/ 2017 Elsevier Masson SAS. All rights reserved.