Efficient adjoint sensitivity analysis of isotropic hardening elastoplasticity via load steps reduction approximation

Wang, Wenjia; Clausen, Peter M.; Bletzinger, Kai‐Uwe

doi:10.1016/j.cma.2017.07.020

Cited by 13 publications

(5 citation statements)

References 26 publications

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“…Various authors have considered topology optimization problems for small-strain plasticity, 11,[56][57][58][59][60][61][62][63][64][65] but only a few have addressed finite deformation plasticity. [66][67][68][69][70] We also note that 3D numerical examples are not present in the latter, presumably due to the computational expense and complexity of implementation of these formulations.…”

Section: Pde-constrained Optimization In Finite Deformation Plasticitymentioning

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: Pde-constrained Optimization In Finite Deformation Plasticitymentioning

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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“…These gradients also play a pivotal role in, for example, perturbation analysis, mesh adaptivity, and uncertainty quantification, to name a few [24][25][26]. Despite their extensive benefit, SA is rarely performed due to cumbersome formulations, especially for the nonlinear response that characterizes LCE structures; see [27][28][29]. Fortunately, these challenges can be circumvented via automatic differentiation (AD) tools [30,31].…”

Section: Introductionmentioning

confidence: 99%

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Barrera,

Cook,

Lee

et al. 2024

Polymers

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Liquid crystal elastomers (LCEs) are responsive materials that can undergo large reversible deformations upon exposure to external stimuli, such as electrical and thermal fields. Controlling the alignment of their liquid crystals mesogens to achieve desired shape changes unlocks a new design paradigm that is unavailable when using traditional materials. While experimental measurements can provide valuable insights into their behavior, computational analysis is essential to exploit their full potential. Accurate simulation is not, however, the end goal; rather, it is the means to achieve their optimal design. Such design optimization problems are best solved with algorithms that require gradients, i.e., sensitivities, of the cost and constraint functions with respect to the design parameters, to efficiently traverse the design space. In this work, a nonlinear LCE model and adjoint sensitivity analysis are implemented in a scalable and flexible finite element-based open source framework and integrated into a gradient-based design optimization tool. To display the versatility of the computational framework, LCE design problems that optimize both the material, i.e., liquid crystal orientation, and structural shape to reach a target actuated shapes or maximize energy absorption are solved. Multiple parameterizations, customized to address fabrication limitations, are investigated in both 2D and 3D. The case studies are followed by a discussion on the simulation and design optimization hurdles, as well as potential avenues for improving the robustness of similar computational frameworks for applications of interest.

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“…The structural responses of nonlinear systems are usually calculated using the numerical integration methods, like Newmark-β method, Wilson-θ method, etc., with an iterative process embedded in each time step to determine the time-variant system matrices [8]. The response sensitivities are computed in terms of the derivatives of the structural responses with respect to the design parameters with various techniques, including the finite difference method [9], perturbation method [10], adjoint structure method [11] and direct differentiation method [12]. These methods compute the structural responses and response sensitivities in the global structure level with numerous iterations, which is very computationally expensive when a large nonlinear structure with numerous time steps is concerned.…”

Section: Introductionmentioning

confidence: 99%

Kron's substructuring method to the calculation of structural responses and response sensitivities of nonlinear systems

Tian

Weng

Xia

2021

Journal of Sound and Vibration

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Efficient adjoint sensitivity analysis of isotropic hardening elastoplasticity via load steps reduction approximation

Cited by 13 publications

References 26 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

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Kron's substructuring method to the calculation of structural responses and response sensitivities of nonlinear systems

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