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A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics

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Abstract

In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.

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Acknowledgements

The research was supported by the Research Executive Agency through the T-MAPPP project (FP7 PEOPLE 2013 ITN-G.A.n607453). The Spanish Ministry of Economy and Competitiveness (Ministerio de Economía y Competitividad, MINECO) through the projects HIRMA (RTC-2016-4967-5), PRECISE (BIA2017-83805-R) is also greatly acknowledged. Finally Dr. Larese gratefully acknowledges the support of the Spanish ministry through her Juan de la Cierva Incorporacion (IJCI-2015-26484).

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  1. International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Barcelona, Spain

    I. Iaconeta, A. Larese, R. Rossi & E. Oñate

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Iaconeta, I., Larese, A., Rossi, R. et al. A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics. Comput Mech 63, 1243–1260 (2019). https://doi.org/10.1007/s00466-018-1647-9

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