Automatic differentiation for stress and consistent tangent computation

Rothe, Steffen; Hartmann, Stefan

doi:10.1007/s00419-014-0939-6

Cited by 18 publications

(14 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it is also undesirable to be restricted to tangent-free solvers during this phase. Motivated by the work of Rothe and Hartmann [45], we started the development of AutoMat, which leverages automatic differentiation and GPU computing to simultaneously address issues of flexibility, accuracy and performance.…”

Section: Introductionmentioning

confidence: 99%

AutoMat: automatic differentiation for generalized standard materials on GPUs

2021

View full text Add to dashboard Cite

We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example.

show abstract

Section: Introductionmentioning

confidence: 99%

AutoMat: automatic differentiation for generalized standard materials on GPUs

2021

View full text Add to dashboard Cite

show abstract

“…Following this, the program codifies these expressions for numerical usage in the form required by the finite element solver. In automatic differentiation methods, the derivative is obtained numerically by algorithmic accumulation of elementary evaluations related to the derivative. Perhaps, due to the additional programming required, these methods are generally less common.…”

Section: Introductionmentioning

confidence: 99%

Higher‐order and higher floating‐point precision numerical approximations of finite strain elasticity moduli

Connolly

Mackenzie

Gorash

2019

Numerical Meth Engineering

View full text Add to dashboard Cite

Two real-domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency are investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher-order and higher floating-point precision numerical approximation, the latter being novel in this context. A general formula for higher-order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating-point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher-order approximations in standard double precision and increased quadruple precision. It is found that, as the order of the approximation increases, the elasticity moduli tend toward the analytical solution. Using higher floating-point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli.Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.

show abstract

“…Here, several possibilities are available for the computation of this derivative. Either analytical derivations, numerical differentiation, see [16][17][18], or automatic differentiation are possible, see, for example, [19][20][21]. More modern aspects, which are based on optimality conditions, are proposed, for example, in [22].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The reason of this is related to the case of model development, which always changes the tangent operator in the phase of development. Furthermore, the complexity of the constitutive model requires a large effort and the difference between the computational times of analytical and numerical differential differentiation has changed caused by modern computer architectures, see [21].In the literature there exist only few attempts to model the whole thermo-electro-mechanical problem of the FAST-process. In the work of [23] the SPS-process is modeled without powder to study the thermal and the electrical field together with a small strain thermoelasticity relation for the tool system.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Field Assisted Sintering Technology, Part II: Simulation

Rothe

Hartmann

2017

GAMM-Mitteilungen

Self Cite

View full text Add to dashboard Cite

Field-assisted sintering technology (FAST) implies a multifield problem between electrical, thermal and mechanical fields. Based on a constitutive model proposed in [1], the numerical treatment of the three-field problem in a monolithic finite element framework is discussed. Apart from algorithmic considerations, numerical simulations are performed treating the complex contact problem, large deformations and the multifield issues themselves. This is combined with a PID-controller, which is required when the temperature process is given at specific positions in the graphite tool system and the electrical current is uncertain. The numerical simulations are validated by real experiments.

show abstract

Automatic differentiation for stress and consistent tangent computation

Cited by 18 publications

References 36 publications

AutoMat: automatic differentiation for generalized standard materials on GPUs

AutoMat: automatic differentiation for generalized standard materials on GPUs

Higher‐order and higher floating‐point precision numerical approximations of finite strain elasticity moduli

Field Assisted Sintering Technology, Part II: Simulation

Contact Info

Product

Resources

About