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Soil stresses after installation of driven piles
Published in Frans B.J. Barends, Application of Stress-Wave Theory to Piles, 2022
in which Dijkl is a fourth order tensor de-pending on material parameters. The term with ρ (mass density) results from the natural reference theory (Besseling, 1985). In finite deformation analyses an objective stress rate, σ˙ijo, is needed in the definition of the constitutive model. Here the Jaumann stress rate is used, which is defined as follows: () σ˙ijo=σ˙ij+σikωkj−ωikσkj
A particle finite element method applied to modeling and simulation of machining processes
Published in Angelos P. Markopoulos, J. Paulo Davim, Advanced Machining Processes, 2017
Juan Manuel Rodríguez, Pär Jonsén, Ales Svoboda
where: Lυ(•) denotes the Lie objective stress rateτ denotes the Kirchhoff stress tensor
Continuum theory of granular materials
Published in M. Oda, K. Iwashita, Mechanics of Granular Materials, 2020
The above relationship suggests the following symmetric definition of the objective stress rate: σ∇ij=〈N2lf21i∇kj〉+Qij
Prediction of residual stresses of second kind in deep drawing using an incremental two-scale material model
Published in Philosophical Magazine, 2020
J. Hofinger, H. Erdle, T. Böhlke
In finite element analysis, objective stress rates are often used for the internal formulation of the equilibrium equations. In order to correctly implement a material law, understanding these different stress rates is key for a correct solution. ABAQUS for example uses the Jaumann rate of Cauchy stress (ABAQUS theory manual, [25]), which is defined asThe steps to formulate the material law (14) with respect to the Jaumann rate of Cauchy stress are given in Appendix 2 of Meissonnier et al. [26], and stated explicitly using the notation of this paper in Appendix 2. These steps lead to the following relation of the tangent moduliand allow to formulate the material law (14) formulated in