Evolution equations for tensors that characterize elastic-viscoplastic materials are often formulated in terms of a Jaumann derivative based on the spin tensor. Typically, numerical integration algorithms for such equations split the integration operation by first calculating the response due to rate of deformation, followed by a finite rotation. Invariance under superposed rigid body motions of algorithms, incremental objectivity and strong objectivity are discussed. Specific examples of steady-state simple shear at constant rate and steady-state isochoric extension relative to a rotating coordinate system are used to analyze the robustness and accuracy of different algorithms. The results suggest that it is preferable to reformulate evolution equations in terms of the velocity gradient instead of the spin tensor, since strongly objective integration algorithms can be developed using the relative deformation gradient. Moreover, this relative deformation gradient can be calculated independently of the time dependence of the velocity gradient during a typical time step.

This paper reports on the initial stages of a project to simulate the nonlinear mechanical behavior of an aging human face. A cross-section of the facial structure is considered to consist of a multilayered composite of tissues with differing mechanical behavior. The constitutive properties of these tissues are incorporated into a finite element model of the three-dimensional facial geometry. Relatively short time (elastic-viscoplastic) behavior is governed by equations previously developed which are consistent with mechanical tests. The long time response is controlled by the aging elastic components of the tissues. An aging function is introduced which, in a simplified manner, captures the observed loss of stiffness of these aging elastic components due to the history of straining as well as other physiological and environmental influences. Calculations have been performed for 30 years of exposure to gravitational forces. Progressive gravimetric soft tissue descent is simulated, which is regarded as the main indication of facial aging. Results are presented for the deformations and stress distributions in the layers of the soft tissues.

A three-dimensional finite element program is described which attempts to simulate the nonlinear mechanical behavior of an aging human face with specific reference to progressive gravimetric soft tissue descent. A cross section of the facial structure is considered to consist of a multilayered composite of tissues with differing mechanical behavior. Relatively short time (elastic-viscoplastic) behavior is governed by equations previously developed which are consistent with mechanical tests. The long time response is controlled by the aging elastic components of the tissues. An aging function is introduced which, in a simplified manner, models the observed loss of stiffness of these aging elastic components due to the history of straining as well as other physiological and environmental influences. Calculations have been performed for 30 years of exposure to gravitational forces. The deformations and stress distributions in the layers of the soft tissues are described. Overall, the feasibility of using constitutive relations which reflect the highly nonlinear elastic-viscoplastic behavior of facial soft tissues in finite element based three-dimensional mechanical analyses of the human face is demonstrated. Further developments of the program are discussed in relation to possible clinical applications. Although the proposed aging function produces physically reasonable long-term response, experimental data are not yet available for more quantitative validation.

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