An anisotropic viscoelastoplastic model for composites—sensitivity analysis and parameter estimation

Because of their potential in achieving many performance enhancements, composite material systems (e.g. fiber-reinforced composites) are presently called upon to operate under wide range of stresses, temperatures, and loading rates. This in turn requires the development of general material models to capture the significant effects of anisotropy on both elastic and inelastic responses. The starting point in the present contribution is the development of a class of such viscoplastic models. Furthermore, a number of robust, computationally efficient, algorithms are also presented for the development of an overall strategy to estimate the material parameters characterizing these complex models; i.e. rate-dependent plastic flow, non-linear kinematic hardening, thermal/static recovery, anisotropic viscoelastic and viscoplastic flow. The entire procedure is automated through an integrated software namely, COnstitutive Material PARameter Estimator, COMPARE, to enable the determination of an ‘optimum’ set of material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are (i) primal analysis, (ii) sensitivity analysis, (iii) a gradient-based optimization problem and a (iv) graphical user interface. The estimation of the material parameters is cast as a minimum-error, weighted multi-objective, non-linear optimization problem with constraints. Detailed derivations of the direct differentiation sensitivity expressions are presented. In addition, numerical comparisons of the sensitivities obtained by the more traditional finite difference approaches are given to assess accuracy. Results generated by applying the developed algorithms for anisotropic, strain-controlled tensile (with comparison to typical experimental data) and constant-stress creep tests are presented to demonstrate the ability of the present models to accurately capture time-dependent anisotropic material behavior.