Geodesic
Numerical schemes of higher approximation orders for dynamic problems of elastoviscoplastic media
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 8-17.

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For a stable numerical solution of the constitutive system of an elastoviscoplastic model of a continuous medium with the von Mises yield condition and hardening, an explicit-implicit second-order scheme was proposed. It includes explicit approximation of the equations of motion and implicit approximation of the constitutive relations containing a small relaxation time parameter in the denominator of the non-linear free term. To match the approximation orders of the explicit elastic and implicit corrective steps, an implicit second-order approximation was constructed for isotropic elastoviscoplastic medium with hardening model. The obtained solutions with the second-order implicit approximation of the stress deviators of the elastoviscoplastic system of equations allow limiting case when relaxation time tends to zero. Correction formulas were obtained in this case, and they can be interpreted as regularizers of numerical solutions for elastoplastic systems with hardening.
Keywords: numerical simulation, elastoviscoplastic media, semi-linear hyperbolic systems, explicit-implicit schemes of higher orders. 
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Vasily I. Golubev; Ilia S. Nikitin; Xi Mi. Numerical schemes of higher approximation orders for dynamic problems of elastoviscoplastic media. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 8-17. http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a1/

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