Model order reduction in hyperelasticity: a proper generalized decomposition approach

This paper deals with the extension of proper generalized decomposition methods to non-linear problems, in particular, to hyperelasticity. Among the different approaches that can be considered for the linearization of the doubly weak form of the problem, we have implemented a new one that uses asymptotic numerical methods in conjunction with proper generalized decomposition to avoid complex consistent linearization schemes necessary in Newton strategies. This approach results in an approximation of the problem solution in the form of a series expansion. Each term of the series is expressed as a finite sum of separated functions. The advantage of this approach is the presence of only one tangent operator, identical for every term in the series. The resulting approach has proved to render very accurate results that can be stored in the form of a meta-model in a very compact format. This opens the possibility to use these results in real-time, reaching kHz feedback rates, or to be used in deployed, handheld devices such as smartphones and tablets. Copyright (c) 2013 John Wiley & Sons, Ltd.