A novel algorithm for rate independent small strain crystal plasticity based on the infeasible primal-dual interior point method

Scheunemann, Lisa; Nigro, Paulo S. B.; Schröder, Jörg; Pimenta, Paulo de Mattos

doi:10.1016/j.ijplas.2019.07.020

Cited by 25 publications

(20 citation statements)

References 49 publications

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“…In line with the classical framework [4], the evolution of plastic strains is related to the slip rate on the individual slip systems by εp = 12 α=1 P α γα where P α = sym(m α ⊗ n α ). The explicit orientation definition of the slip systems for fcc crystals can be found in [5]. For the onset of yielding on the individual slip systems, a set of yield conditions ϕ α = τ α − g α ≤ 0, where g α (t = 0) = τ 0 with the Schmid stress τ α = σ : P α , the slip resistance g α and its inital value τ 0 , is considered.…”

Section: Single Crystal Plasticitymentioning

confidence: 99%

“…where S = diag(s), s = s 1 ...s 12 T , Λ = diag(λ), λ = λ 1 ...λ 12 T and Γ = diag(γ), γ = γ 1 ...γ 12 T . Numerical examples demonstrating the performance of the method in comparison to well-established approaches from the literature can be found in [5].…”

Section: Single Crystal Plasticitymentioning

confidence: 99%

“…An effect of considering the Lagrange parameters ρ α γ explicitely, meaning considering the KKT conditions related to γα , can be illustrated with a material point simulation, where a single crystal is considered in under simple shear condition with the orientation given by (0, 0, 0), see [5] for details. A single time step in which plasticity initiates is simulated using the algorithms, A1 with and A2 without considering the KKT condition of γα .…”

Section: Remarks On Kkt Conditionsmentioning

confidence: 99%

“…They can be grouped into rate independent and rate dependent approaches, where both classes are governed by inherent shortcomings, as discussed in, e.g., [3]. This contribution outlines an algorithmic formulation for single crystal plasticity at small strains for the rate independent case relying on an infeasible primal-dual interior point method, which has been presented in [5]. It is able to bypass several issues known in rate independent algorithms.…”

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confidence: 99%

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Remarks on a primal‐dual interior point algorithm for single crystal plasticity

Scheunemann

Nigro

Schröder

2021

Proc Appl Math & Mech

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In the field of single crystal plasticity, different algorithms exist for the solution of the constitutive equations. They can be grouped into rate independent and rate dependent approaches, where both classes are governed by inherent shortcomings, as discussed in, e.g., [3]. This contribution outlines an algorithmic formulation for single crystal plasticity at small strains for the rate independent case relying on an infeasible primal‐dual interior point method, which has been presented in [5]. It is able to bypass several issues known in rate independent algorithms. Besides a brief overview of the continuum mechanical and algorithmic framework, aspects on different formulations related to the Karush‐Kuhn‐Tucker (KKT) conditions are discussed.

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Section: Single Crystal Plasticitymentioning

confidence: 99%

Section: Single Crystal Plasticitymentioning

confidence: 99%

Section: Remarks On Kkt Conditionsmentioning

confidence: 99%

mentioning

confidence: 99%

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Remarks on a primal‐dual interior point algorithm for single crystal plasticity

Scheunemann

Nigro

Schröder

2021

Proc Appl Math & Mech

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“…Sakineh [15] presented novel interior-point algorithms for solving nonlinear convex optimization problems. Scheunemann et al [16] presented an algorithm for rat-independent small-strain crystal plasticity based on the infeasible primal-dual interior-point method…”

Section: Introductionmentioning

confidence: 99%

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

et al. 2021

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In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

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Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

Carvalho

Bortoli

Pires

2022

Numerical Meth Engineering

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A computational framework is proposed to model anisotropic metallic polycrystals subjected to mechanically induced loadings. It enables the simulation of crystal‐plasticity‐like phenomena at finite strains. The unified framework of thermodynamically consistent constitutive equations is formulated such that it couples the crystallographic slip and martensitic transformation theories. The constitutive description for the slip plasticity evolution incorporates an anisotropic hyperelastic law with self and latent‐hardening. The mechanically induced martensite formation kinematics is based on the crystallographic theory of martensitic transformations. The complete set of highly coupled equations is expressed in a single system of equations and solved by a monolithic solution procedure. It is based on the Newton–Raphson methodology and incorporates the complete linearisation leading to asymptotic quadratic rates of convergence. The quasi‐static discretized evolution equations are integrated with a fully implicit scheme, except for the critical resolved slip stresses, which employ the generalized midpoint rule. The plastic flow is integrated with an implicit exponential integrator to exactly preserve the plastic incompressibility. Viscous regularizations for both deformation mechanisms are pursued to overcome numerical difficulties and model the behavior over a wide range of strain‐rate sensitivities. Numerical examples are presented to demonstrate the efficiency and predictive capability of the methodology.

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A novel algorithm for rate independent small strain crystal plasticity based on the infeasible primal-dual interior point method

Cited by 25 publications

References 49 publications

Remarks on a primal‐dual interior point algorithm for single crystal plasticity

Remarks on a primal‐dual interior point algorithm for single crystal plasticity

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

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