A 10-node composite tetrahedral finite element for solid mechanics

Ostien, Jakob T.; Foulk, James W.; Mota, Alejandro; Veilleux, Michael

doi:10.1002/nme.5218

Cited by 28 publications

(28 citation statements)

References 15 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the third instance of the notched cylinder example, the subdomain Ω 1 is discretized using composite tetrahedral elements [45], whereas the subdomain Ω 2 is discretized using hexahedral elements. The discretizations of these domains are shown in Figure 16 (a) and (b), respectively.…”

Section: Nonconformal Hex-to-tet Couplingmentioning

confidence: 99%

“…16 10 − 14 10 − 12 10 − 10 10 − 8 10 − 6 10 − 4 10 − 2 10 0 Convergence behavior of the four algorithms of Section 2.4 for the singular bar problem. The plotted error measure for the Schwarz iterations (n) is defined in(45) in the notation of Algorithms 2-5. Occasionally, the Modified Schwarz method (green) displays non-monotonic convergence, as shown in the right plot.…”

mentioning

confidence: 99%

“…The displacement component u 3 at the final load step for the notched cylinder problem. Coupled solutions computed on composite tetrahedral[45] and hexahedral meshes of Ω 1 and Ω 2 respectively. (a) Ω 1 (b) Ω Absolute errors in the displacement component u 3 at the final load step for the notched cylinder problem.…”

mentioning

confidence: 99%

“…(a) Ω 1 (b) Ω Absolute errors in the displacement component u 3 at the final load step for the notched cylinder problem. Error computed on coupled composite tetrahedral[45] and hexahedral meshes of Ω 1 and Ω 2 with respect to the reference solution on Ω ref .…”

mentioning

confidence: 99%

“…The displacement component u 3 at the final load step for the notched cylinder problem stretched to a prescribed displacement of ∆ = 25.6 × 10 −3 . Coupled solutions computed on composite tetrahedral[45] and hexahedral meshes for Ω 1 and Ω 2 , respectively.…”

mentioning

confidence: 99%

See 4 more Smart Citations

The Schwarz alternating method in solid mechanics

Mota

Tezaur

Alleman

2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

We advance the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics. We prove that the Schwarz alternating method converges to the solution of the problem on the entire domain and that the convergence rate is geometric provided that each of the subdomain problems is well-posed, i.e. their corresponding energy density functions are quasi-convex. It is shown that the use of a Newton-type method for the solution of the resultant nonlinear system leads to two kinds of block linearized systems, depending on the treatment of the Dirichlet boundary conditions. The first kind is a symmetric block-diagonal linear system in which each diagonal block is the tangent stiffness of each subdomain, i.e. the off-diagonal blocks are all zero and the coupling terms appear only on the right-hand side. The second kind is a nonsymmetric block system with off-diagonal coupling terms. Several variants of the Schwarz alternating method are proposed for the first kind of linear system, including one in which the Schwarz alternating iterations and the Newton iterations are combined into a single scheme. This version of the method is particularly attractive, as it lends itself to a minimally intrusive implementation into existing finite element codes. Finally, we demonstrate the performance of the proposed variants of the Schwarz alternating method on several one-dimensional and three-dimensional examples.

show abstract

Section: Nonconformal Hex-to-tet Couplingmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

The Schwarz alternating method in solid mechanics

Mota

Tezaur

Alleman

2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Foulk

Ostien

Talamini

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016).We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five-field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

show abstract

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

Seidl

Granzow

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

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.

show abstract

A 10-node composite tetrahedral finite element for solid mechanics

Cited by 28 publications

References 15 publications

The Schwarz alternating method in solid mechanics

The Schwarz alternating method in solid mechanics

Extending a 10‐node composite tetrahedral finite element for solid mechanics

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

Contact Info

Product

Resources

About