A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric, fully-coupled, thermoviscoplastic response of shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of large-strain, transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be viscoplasticity with strain hardening and thermal hardening, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used for the shell equations with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. The energy-balance equation is solved using a Galerkin procedure, with the temperature as the fundamental unknown.

Spatial discretization is performed in one dimension (meridional direction) for the momentum and constitutive equations of the shell, and in two dimensions (meridional and thickness directions) for the energy-balance equation. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) for the momentum equation; a predictor-corrector version of the trapezoidal rule is used for the energy-balance equation; and an explicit scheme consistent with the central difference method is used to integrate the constitutive equations. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to the thickness, mass density, Young's modulus, two of the material parameters characterizing the viscoplastic response and the three parameters characterizing the thermal response. Time histories of the response and sensitivity coefficients are presented, along with spatial distributions of some of these quantities at selected times.

Mechanical properties of materials in microscales are different from those of bulk materials. In this paper, a new procedure is proposed to identify the material properties of elastoplastic thin gold films by including the tip geometry of the indenter as a design variable, approximating the experimental data using polynomial responses, and performing sensitivity analysis with respect to regression coefficients. A comparison between experiment and analysis is made for the responses throughout the whole indentation process, not the data at the end of the process. This is important because the material shows loading history dependent responses. The uncertainty related to the indenter tip geometry was taken care of by including the radius of the tip as a variable of the optimization. Two fifthorder response surfaces were constructed to fit the experimental data and a test statistic is used to identify unessential coefficients. It turns out that the constant term of the load step is unessential and, thus, removed. The response surfaces have smaller values of coefficients at the higher-order terms, which is common for the regular response surfaces. However, the test statistics showed different trends for loading and unloading steps. In the case of the loading step, the test statistic is higher for the higher-order terms. In the case of unloading step, however, it is higher for the lowerorder terms. Sensitivity with respect to the regression coefficients showed consistent trends: higher-order terms have higher sensitivities. This trend foresees difficulties in material property identification, as smaller coefficients have higher sensitivity. It turns out that the hardening exponent is the most sensitive variable due to the error in the experiment measurement.

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