ALBERT

Description: For nonlinear transient problems as well as rather slow quasi-static processes explicit time integration has proven to be a suitable and robust time integration algorithm. As a consequence of the Courant-Friedrichs-Lewy (CFL) criterion small time step sizes are necessary and the overall computation time is dominated by the operations on element level. Privileged use of low order finite elements is common in explicit time integration due to their efficiency and robustness. In order to suppress artificial locking effects the work of Bischoff and Romero [1] is followed where a generalization of the method of incompatible modes (IM) is derived being equivalent to the class of enhanced assumed strain (EAS) elements originally proposed by Simo and Rifai [2]. These concepts are bound to a static elimination procedure of internal parameters which may result in a considerable expansion of the computational costs in the case of an explicit time integration scheme. In order to avoid the static elimination procedure inertia is considered for the incompatible parameters as suggested by Mattern et al. [3, 4]. This step allows integrating the incompatible parameters directly in time, but since rather large stiffnesses are related to the incompatible parameters – particularly for the volumetric mode enhancements – the highest eigenfrequency may be increased which would lead to a decrease of the time step size. This motivates scaling the masses associated to these incompatible parameters to control their effect on the time step size. It is possible to derive analytically based estimates for the scaling of the IM-masses in order to achieve results agreeing very good with the classical EAS approach including large deflections and nonlinear material behaviour with elasto-plasticity. The numerical implementation is performed using AceGen [5]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Explicit time integration has proven to be highly suitable for the simulation of very fast processes and highly nonlinear applications. As is well known the time integration algorithm is only stable if the Courant-Friedrichs-Lewy criterion is fulfilled leading usually to very small time step sizes. As a result the efficiency of the time integration algorithm is dictated by the computational time of element operations. In structural mechanics low order finite elements are attractive due to their efficiency but introduce artificial stiffness effects. To resolve the so-called locking effects a transient description – suitable for the solution in the context of explicit time integration – of the method of enhanced assumed strains (EAS) is formulated utilizing a generalization of the method of incompatible modes (IM). The element routines are computationally realised applying symbolic programming. The functionality and achieved efficiency are demonstrated on a numeric example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)