On the Solution of Quasi-Static Micro- and Mesomechanical Problems in a Dynamic Formulation

Simulations of characteristic mesoscale processes in a solid require a computational domain with a large number of structural elements (grains, inclusions, pores, etc.) and a sufficiently detailed mesh for their approximation. Reasoning that the computer power needed for such simulation increases nonlinearly with the number of structural elements, it is desirable to minimize the computational costs without loss of information and accuracy, for example, by solving quasi-static problems in a dynamic statement. Here we analyze the applicability of dynamic methods to quasi-static micro- and mesomechanical problems with explicit account of microstructure by the example of dynamic and static finite element computations of uniaxial tension for materials insensitive to strain rates. The analysis shows that the main parameter influencing the coincidence of dynamic and static solutions is the time in which the loading rate rises to its amplitude. If this rise time is longer than two travels of an elastic wave through a material, the dynamic and static problem solutions deviate by no more than 0.1% while the random access memory and the computation time needed for the static case is about ten times those for the dynamic one. Thus, explicit dynamic methods can be applied to advantage to quasi-static problems of micro- and mesomechanics.