I'm working on a solid mechanics code. I'm looking for an accurate, explicit algorithm that computes strain increment(infinitesimal/engineering) based on Deformation Gradient in a Corotational Frame(material coordinate). My material model is rate-independent, so there is no need to find any strain rates in the algorithm. Then algorithms such as Flanagan-Taylor(1987) cause some extra computational costs. My problem is categorized as large deformation, but as time steps are too small, strain increments will become infinitesimal.
Dear Hosein Sepahvand ,
In this paper given below two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a uni ed derivation of both algorithms in spite of their inherent di erences. Then the two algorithms are adapted from convected frames to a xed Cartesian frame and implemented in a small-strain nite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis.
https://upcommons.upc.edu/bitstream/handle/2117/8448/1997-IJNME-RPH-blanc.pdf
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