Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split

Kaygorodtseva

2019

Z Angew Math Mech

A special aspect of parameter identification in finite‐strain elasto‐plasticity is considered. Namely, we analyze the impact of the measurement errors on the resulting set of material parameters. In order to define the sensitivity of parameters with respect to the measurement errors, a mechanics‐based distance between two sets of parameters is introduced. Using this distance function, we assess the reliability of certain parameter identification procedures. The assessment involves introduction of artificial noise to the experimental data; the noise can be both correlated and uncorrelated. An analytical procedure to speed up Monte Carlo simulations is presented. As a result, a simple tool for estimating the robustness of parameter identification is obtained. The efficiency of the approach is illustrated using a model of finite‐strain viscoplasticity, which accounts for combined isotropic and kinematic hardening. It is shown that dealing with correlated measurement errors, most stable identification results are obtained for non‐diagonal weighting matrix. At the same time, there is a conflict between the stability and accuracy.

“…Robust and efficient numerical procedures for the case where

ψ_{kin 1}

and

ψ_{kin 2}

are of neo‐Hookean type are presented in []. The case where

ψ_{kin 1}

and

ψ_{kin 2}

are of Mooney‐Rivlin type can be dealt with using an explicit update formula from [].…”

Section: Illustration Problem: Model With Combined Isotropic‐kinematimentioning

confidence: 99%

Parameter identification in elasto‐plasticity: distance between parameters and impact of measurement errors

Kaygorodtseva

2019

Z Angew Math Mech

“…In the special case of the flow rule (53) which corresponds to α = 0, the evolution equation governing C cr has the same structure as that for the model of multiplicative viscoplasticity proposed in [51]. An explicit update formula is described in [57] for this evolution equation; this explicit solution can be used for the presented creep model as well. As a result, the overall time stepping can be reduced to the solution of a single scalar equation (cf.…”

Section: Remarkmentioning

confidence: 99%

“…This decomposition allows one to incorporate evolving backstresses in a thermodynamically consistent way in different applications (see [23] for shape memory alloys, [7,11,28,49,51,61,67] for conventional plasticity and viscoplasticity, [22] for unconventional plasticity). Accurate and efficient numerical implementation of various models based on the nested multiplicative split was discussed, among others, in [20,46,51,57,67]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Modelling of cyclic creep in the finite strain range using a nested split of the deformation gradient

Larichkin

2017

Z. Angew. Math. Mech.

A new phenomenological model of cyclic creep, which is suitable for applications involving finite creep deformations of the material, is proposed. The model accounts for the effect of the transient increase of the creep strain rate upon the load reversal. In order to extend the applicability range of the model, the creep process is fully coupled to the classical Kachanov-Rabotnov damage evolution. As a result, the proposed model describes all the three stages of creep. Large strain kinematics is described in a geometrically exact manner using the assumption of a nested multiplicative split, originally proposed by Lion for finite strain plasticity. The model is thermodynamically admissible, objective, and w-invariant. The implicit time integration of the proposed evolution equations is discussed. The corresponding numerical algorithm is implemented into the commercial FEM code MSC.Marc. The model is validated using this code; the validation is based on real experimental data on cyclic torsion of a thick-walled tubular specimen made of the D16T aluminium alloy. The numerically computed stress distribution exhibits a "skeletal point" within the specimen, which simplifies the analysis of test data.

“…Schüler et al 46 used the algorithm to model the viscoelastic behaviour of a bituminous binding agent. The closed-form solution reported by Shutov et al 42 is implemented as a part of efficient implicit procedures for finite-strain viscoplasticity 47 and finite strain creep. 24 In the current study, a new explicit update formula is suggested for a more general case of the Mooney-Rivlin hyperelasticity.…”

Section: Introductionmentioning

confidence: 99%

Efficient time stepping for the multiplicative Maxwell fluid including the Mooney‐Rivlin hyperelasticity

Numerical Meth Engineering

2017

A popular version of the finite-strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of the Mooney-Rivlin type; it is a special case of the viscoplasticity model proposed by Simo and Miehe in 1992. A simple, efficient, and robust implicit time-stepping procedure is suggested. Lagrangian and Eulerian versions of the algorithm are available, with equivalent properties. The numerical scheme is iteration free, unconditionally stable, and first order accurate. It exactly preserves the inelastic incompressibility, symmetry, and positive definiteness of the internal variables and w-invariance. The accuracy of the stress computations is tested using a series of numerical simulations involving a nonproportional loading and large strain increments. In terms of accuracy, the proposed algorithm is equivalent to the modified Euler backward method with exact inelastic incompressibility; the proposed method is also equivalent to the classical integration method based on exponential mapping. Since the new method is iteration free, it is more robust and computationally efficient. The algorithm is implemented into MSC.MARC, and a series of initial boundary value problems is solved to demonstrate the usability of the numerical procedures.