Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids
Topic of this paper are constitutive equations for elastic-viscoplastic bodies and their numerical integration. In this field, much research is done all over the world, and a lot of controversy is still going on. The first part of the paper gives a summary and review of the assumptions used previously by the second author as a basis for his constitutive model [e.g.: the authors and \textit{A. M. Lush}, Int. J. Plast. 5, No.5, 521-549 (1989; Zbl 0695.73009); the second author, Mech., Res. Commen. 11, 345-352 (1984; Zbl 0567.73006); J. Mech. Phys. Solids 31, 105-122 (1983; Zbl 0507.73026)]. An essential feature not occurring in other approaches is the hyperelastic relation connecting stress and logarithmic elastic strain, a generalization of Hooke's law suitable for moderately large deformation. The authors point out and discuss differences between their and other researchers' work. In the main part of the paper, a new procedure for the time integration of the constitutive equations is reported. Finally, the excellent agreement of numerical and analytical solutions to several problems verifies the accuracy of the integration procedure. The paper constitutes an essential contribution to the prediction of the behavior of elastic-viscoplastic bodies under load.
multiplicative decomposition of deformation gradient
consistent, closed-from elasto-viscoplastic tangent operator
implicit two-point, deformation driven finite element algorithms
hyperelastic relation connecting stress and logarithmic elastic strain
time integration of the constitutive equations
scientific article; zbMATH DE number 4209697
scientific article