Asymptotic numerical method for finite plasticity

Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

“…The key point is the regularization based on the consistency equation introduced in [126] and assessed for boundary value problems in [121][122][123]. FE computations for large strain modellings were discussed in [75,121,124].…”

“…There are many theories for finite strain elastoplasticity. We consider here, for instance, a classical elastoplastic model based on the Kirchhoff stress tensor, see for instance [115,124]. A Lagrangian approach is used, the main unknowns being the position of the current point x or the displacement u=x−X, the gradient of the position vector bold∇bold-italicx and the gradient of the velocity ∇v=false(d/dtfalse)∇x that are considered to be functions of the Lagrangian variable X∈Ω0.…”

“…The same relation between bold∇bold-italicxm and the first Piola–Kirchhoff stress tensor boldTm is easily deduced and it is in the same form (2.7) as in the hyperelastic case. The continuation method for elastoplastic bodies is slightly modified as compared with elasticity, we refer to the papers [122,124] for the complete procedure and various applications.…”

“…So this calibration can be done from a boundary value problem or directly from the material law. The present numerical results were done with the choice η1=10−3, η2=10−4, η3=10−4, η4=10−4 according to the discussion in [75,124]. Indeed, the computed stress–strain curve in figure 12 differs very little from the theoretical one.…”