Adjoint-based error estimation and mesh adaptation for stabilized finite deformation elasticity

Granzow, Brian; Oberai, Assad A.; Shephard, Mark S.

doi:10.1016/j.cma.2018.03.035

Cited by 8 publications

(2 citation statements)

References 37 publications

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“…We refer to U as the global state variables. Performing integration by parts on (1) and using the relations in (2), it can be shown [92][93][94][95] that this strategy leads to the stabilized finite element formulation: find…”

Section: Stabilized Finite Element Formulationmentioning

confidence: 99%

Calibration of elastoplastic constitutive model parameters from full‐field data with automatic differentiation‐based sensitivities

Seidl

Granzow

2021

Numerical Meth Engineering

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We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

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Section: Stabilized Finite Element Formulationmentioning

confidence: 99%

Calibration of elastoplastic constitutive model parameters from full‐field data with automatic differentiation‐based sensitivities

Seidl

Granzow

2021

Numerical Meth Engineering

Self Cite

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“…However, especially for problems undergoing large strains, this mixed three field approach shows limited performance and robustness [ 22 ]. Further, variational multiscale (VMS) formulations have been used for nonlinear solid mechanics [ 39 , 50 , 51 ]. VMS is frequently used in computational fluid mechanics with the key advantage that these formulations offer both stabilization as well as benefits in turbulence modeling.…”

Section: Introductionmentioning

confidence: 99%

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

Karabelas

Gsell

Haase

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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An automated approach for parallel adjoint-based error estimation and mesh adaptation

Granzow

Oberai

Shephard

2019

Engineering with Computers

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Adjoint-based error estimation and mesh adaptation for stabilized finite deformation elasticity

Cited by 8 publications

References 37 publications

Calibration of elastoplastic constitutive model parameters from full‐field data with automatic differentiation‐based sensitivities

Calibration of elastoplastic constitutive model parameters from full‐field data with automatic differentiation‐based sensitivities

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

An automated approach for parallel adjoint-based error estimation and mesh adaptation

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