mgis.fenics Part II: Cosserat media in small deformation with mgis.fenics

When exposed to high strain rates of deformation, metal alloys with low thermal conductivity are typically liable to large quantities of plastic strain. This phenomenon of localization of high temperatures in a narrow band, known as an adiabatic shear band, occurs in many manufacturing processes such as machining or metal forming. We aim to simulate it based on the research of Forest et al [1] and Russo et al [2] that propose a thermodynamically consistent framework for both elastoplasticity and elastoviscoplasticity. Their approach builds upon a bulk of work stemming from that of the Cosserat brothers in 1909 [3] on generalized continua by introducing independent translational and rotational degrees of freedom.

Our contribution is the implementation of the elastoplasticity framework using FEniCS, the MFront library [4], and the corresponding interface between them, the mgis.fenics module. These tools automate the implementation of material behaviours and allow for complex models. We present the results for the glide and bending/torsion test, and their validation against another finite element solver (Zset) and the analytical solution. Moreover, we run the performance analysis on the Atlas-EDR cluster, at the Donostia International Physics Center (DIPC). We break down the execution time, identify the most computationally intensive components, and analyze the results from the point of view of parallel scaling.

References

• [1] Samuel Forest and Rainer Sievert. Elastoviscoplastic constitutive frameworks for generalized continua, Acta Mechanica 160, 71–111, 2003. [DOI: 10.1007/s00707-002-0975-0]
• [2] Raffaele Russo, Samuel Forest, and Franck Andrés Girot Mata. Thermomechanics of cosserat medium: modeling adiabatic shear bands in metals, Continuum Mechanics and Thermodynamics, 1–20, 2020. [DOI: 10.1007/s00161-020-00930-z]
• [3] Eugene Cosserat and François Cosserat. Theorie des corps dédormables, 1909. [DOI: 10.1038/081067a0]
• [4] Thomas Helfer, Bruno Michel, Jean-Michel Proix, Maxime Salvo, Jérôme Sercombe, and Michel Casella. Introducing the open-source mfront code generator: Application to mechanical behaviours and material knowledge management within the pleiades fuel element modelling platform, Computers & Mathematics with Applications 70, 994–1023, 2015. [DOI: 10.1016/j.camwa.2015.06.027]