ABSTRACT
To overcome this problem the fractional creep functions have been approximated by a certain number of DIRICHLET-series in (Aschenbrenner, 2006). If DIRICHLET-series are used instead of fractional creep functions the influence of the strain history on the new strain increment can be lumped in one factor per series. However, for long load duration, the DIRICHLET-series and the fractional creep functions deviate from each other, as the DIRICHLET-series exhibit a strain limit while the fractional creep functions predict infinite strain for infinite loading time. There are a number of papers that have been published more or less recently, which contain attempts and strategies to reduce the computational effort associated with the aforementioned time-history effects of the fractional differential equation, e.g. (Padovan, 1987), (Podlubny, 1999), (Ford, 2001), (Schmidt et al., 2002) and (Aschenbrenner, 2006). The majority of these papers focus on the fading impact of previous strain states on the new strain increment with progressing time. In some of the papers mentioned above it is speculated that stress states with a certain distance in time can be neglected. This might or might not lead to accurate computational results. In any case, the strategies proposed in these papers require the definition of a “time horizon” that separates between a range in time where strain history does have impact on the new strain development and a range in time with no impact. To be sure about the appropriateness of the defined ‘time horizon’ the computation should be repeated using different ‘time-horizon’ positions.
