Mixed stress-displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity

Fahrendorf, Frederik; Morganti, Simone; Reali, Alessandro; Hughes, Thomas J.R.; Lorenzis, Laura De

doi:10.1016/j.cma.2020.113112

Cited by 24 publications

(8 citation statements)

References 54 publications

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“…Here, we do not intend to arrive at formulations with strain or stress fields as independent fields. Because such formulations increase the number of unknowns significantly, also they require solution spaces with higher regularity such as Hilbert space H (div, Ω ) [59][60][61][62]; this regularity is needed to fulfill the continuity condition of normal traction between elements while tangential traction can be discontinuous. The term L HYB1 mass is exactly the same as L DD mass defined in Eq.…”

Section: Optionmentioning

confidence: 99%

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Bahmani

Sun

2021

Computer Methods in Applied Mechanics and Engineering

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We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid modelbased/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distance-minimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives. c

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Section: Optionmentioning

confidence: 99%

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Bahmani

Sun

2021

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…Here, we do not intend to arrive at formulations with strain or stress fields as independent fields. Because such formulations increase the number of unknowns significantly, also they require solution spaces with higher regularity such as Hilbert space H(div, Ω) (Arnold and Falk, 1988;Korsawe et al, 2006;Teichtmeister et al, 2019;Fahrendorf et al, 2020); this regularity is needed to fulfill the continuity condition of normal traction between elements while tangential traction can be discontinuous. The term L HYB1 mass is exactly the same as L DD mass defined in Eq.…”

Section: Option 2: Hybrid Data-driven Poroelasticity 1 (Model-based S...mentioning

confidence: 99%

An accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Bahmani,

Sun

2020

Preprint

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We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid model-based/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distanceminimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives.

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“…This can be avoided using mixed methods, which can be computationally even more efficient using isogeometric collocation (IGA-C) as the same basis functions can be used for the discretization of primary and secondary fields, and at the same time also alleviate locking effects [39,41,47,48]. Recently, already the successful application of mixed IGA-C to linear elasto-plasticity has been demonstrated [49], which requires the evaluation and evolution of the internal variables only at collocation points (compared to quadrature points in FEM), but avoids their differentiation (compared to primal collocation methods).…”

Section: Introductionmentioning

confidence: 99%

Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects

Weeger

Schillinger

Müller

2022

Computer Methods in Applied Mechanics and Engineering

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Mixed stress-displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity

Cited by 24 publications

References 54 publications

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

An accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects

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