A Cartesian parametrization for the numerical analysis of material instability

Mota, Alejandro; Chen, Qiushi; Foulk, James W.; Ostien, Jakob T.; Lai, Zhengshou

doi:10.1002/nme.5228

Cited by 10 publications

(22 citation statements)

References 39 publications

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“…Remark In the actual numerical simulation, due to the finite size of a loading step, condition () may not be satisfied exactly. Instead, an adaptive time step algorithm will be implemented in this work. Consider the original time increment from time t n to t n + 1 , where the minimum of the objective function

μ_{n} : = \min_{q} f (bold-italicq) > 0

and μ n + 1 < 0.…”

Section: General Framework Of Numerical Bifurcation Analysismentioning

confidence: 99%

“…If the determinant function f ( q ) is differentiable, the minimization problem can be rewritten equivalently as

\frac{\partial f}{\partial bold-italicq} (bold-italicq) = 0

Existing numerical bifurcation analysis relies on a NR‐type iterative method to solve the minimization problem defined in (). In a NR‐based approach, the numerical detection of the bifurcation condition for each time increment consists of the following two steps : Sampling step: An initial sampling or sweeping is performed over the parametric space of q for the normal vector n ∈ S 2 . At each of the sampling point, the determinant function () is evaluated.…”

Section: Newton–raphson‐based Numerical Approaches and Parameterizationsmentioning

confidence: 99%

“…Efficient and robust solution of the minimization problem () or () requires a careful choice of the parameterization for the unit vector

bold-italicn (bold-italicq) \in {scriptS}^{2}

. As shown in a recent work , this choice of parameterization has a significant effect on the complexity of the determinant function f ( q ). In this work, a total of four different parameterizations will be considered in the NR‐based numerical approaches and compared with the newly proposed method to be discussed in Section 4.…”

Section: Newton–raphson‐based Numerical Approaches and Parameterizationsmentioning

confidence: 99%

“…Figure shows the four parameterizations considered in this work, which are briefly discussed herein. For more details, the reader is referred to . It should be pointed out that, due to symmetry of the bifurcation condition, only half of the spherical parametric domain or half of the cubic parametric domain needs to be searched as given by the ranges of the parameters.…”

Section: Newton–raphson‐based Numerical Approaches and Parameterizationsmentioning

confidence: 99%

“…One major assumption of this algorithm is the major symmetry of the material tangent modulus, which is loosened by Sanborn and Pr

é

vost through the modification of the gradient function. An alternative numerical approach used the Newton–Raphson (NR) method to solve the constrained minimization problem of material bifurcation, where the initial guess for the NR iteration is obtained from a sweep through the parametric space of the unit vector . Robustness and efficiency of the NR‐based methods depend on both the complexity of the objective function and the quality of the initial guess.…”

Section: Introductionmentioning

confidence: 99%

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Particle swarm optimization for numerical bifurcation analysis in computational inelasticity

Lai

Chen

2016

Num Anal Meth Geomechanics

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Summary An efficient and robust algorithm to numerically detect material instability or bifurcation is of great importance to the understanding and simulation of material failure in computational and applied mechanics. In this work, an intelligence optimizer, termed the particle swarm optimization, is introduced to the numerical solution of material bifurcation problem consisting of finding the bifurcation time as well as the corresponding bifurcation directions. The detection of material bifurcation is approached as a constrained minimization problem where the determinant of the acoustic tensor is minimized. The performance of the particle swarm optimization method is tested through numerical bifurcation analysis on both small and finite deformation material models in computational inelasticity with increasing complexity. Compared with conventional numerical approaches to detect material bifurcation, the proposed method demonstrates superior performance in terms of both computational efficiency and robustness. Copyright © 2016 John Wiley & Sons, Ltd.

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μ_{n} : = \min_{q} f (bold-italicq) > 0

and μ n + 1 < 0.…”

Section: General Framework Of Numerical Bifurcation Analysismentioning

confidence: 99%

“…If the determinant function f ( q ) is differentiable, the minimization problem can be rewritten equivalently as

\frac{\partial f}{\partial bold-italicq} (bold-italicq) = 0

Section: Newton–raphson‐based Numerical Approaches and Parameterizationsmentioning

confidence: 99%

“…Efficient and robust solution of the minimization problem () or () requires a careful choice of the parameterization for the unit vector

bold-italicn (bold-italicq) \in {scriptS}^{2}

Section: Newton–raphson‐based Numerical Approaches and Parameterizationsmentioning

confidence: 99%

Section: Newton–raphson‐based Numerical Approaches and Parameterizationsmentioning

confidence: 99%

“…One major assumption of this algorithm is the major symmetry of the material tangent modulus, which is loosened by Sanborn and Pr

é

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Particle swarm optimization for numerical bifurcation analysis in computational inelasticity

Lai

Chen

2016

Num Anal Meth Geomechanics

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A general and efficient multistart algorithm for the detection of loss of ellipticity in elastoplastic structures

Kotob

Combescure

Mazière

et al. 2019

Numerical Meth Engineering

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Summary The present paper proposes a new efficient and robust algorithm for evaluating the loss of ellipticity criterion. While commonly used in two‐dimensional models for thin metal sheet forming processes, it is rarely evaluated in three‐dimensional structures due to the computational cost. The proposed algorithm is based on a Newton‐Raphson scheme and a multisampling optimization method based on a discretization method of the half unit sphere. First the new process is compared to the existing methods in the literature and then it is applied to a structural problem, namely tubes in torsion. The evolution of the loss of ellipticity in these structures is analyzed leading to conclusions about the failure of the structure. Meanwhile, the stability of the discretized problem is analyzed in order to better understand the loss of regularity of the finiteelement method problem. These results are then used to predict the failure of an experimentally tested torsion sample.

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The Schwarz alternating method for transient solid dynamics

Mota

Tezaur

Phlipot

2022

Numerical Meth Engineering

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In our earlier work, we formulated the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics for quasi‐static problems. Herein, we advance this method for the study of transient dynamic multiscale solid mechanics problems where information is exchanged back and forth between small and large scales. The extension to dynamics relies on the notion of a global time stepper. Within each global time step, the subdomains are coupled by the standard Schwarz iterative process. Remarkably, each subdomain can use its own time step or even its own time integrator to advance its solution in time, provided that they synchronize at each global time step. We study the performance of the Schwarz method on several examples designed for this purpose. Our numerical experiments demonstrate that the method is capable of coupling regions with different mesh resolutions, different element types, and different time integration schemes (e.g., implicit and explicit), all without introducing any artifacts that afflict other coupling methods for transient dynamics. Finally, we apply the dynamic Schwarz alternating method to the simulation of a bolted joint subjected to dynamic loading, as a demonstration of the performance of the method in a realistic scenario.

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A Cartesian parametrization for the numerical analysis of material instability

Cited by 10 publications

References 39 publications

Particle swarm optimization for numerical bifurcation analysis in computational inelasticity

Particle swarm optimization for numerical bifurcation analysis in computational inelasticity

A general and efficient multistart algorithm for the detection of loss of ellipticity in elastoplastic structures

The Schwarz alternating method for transient solid dynamics

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