An FE $$^2$$ -Scheme for Magneto-Electro-Mechanically Coupled Boundary Value Problems

Labusch, Matthias; Schröder, Jörg; Keip, Marc‐André

doi:10.1007/978-3-319-68883-1_5

Cited by 3 publications

(1 citation statement)

References 77 publications

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“…Extensions of the method to the realm of multi-physics and generalized continua have been proposed by many groups, e.g. for thermo-mechanical [4,26], electro-mechanical [14,15], magneto-mechanical [39], micromorphic [5,27] or even three-field problems [17,28] -see also the references therein.…”

Section: Introductionmentioning

confidence: 99%

An efficient monolithic solution scheme for FE$^2$ problems

Lange,

Hütter,

Kiefer

2021

Preprint

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The FE 2 method is a very flexible but computationally expensive tool for multiscale simulations. In conventional implementations, the microscopic displacements are iteratively solved for within each macroscopic iteration loop, although the macroscopic strains imposed as boundary conditions at the micro-scale only represent estimates. In order to reduce the number of expensive micro-scale iterations, the present contribution presents a monolithic FE 2 scheme, for which the displacements at the micro-scale and at the macro-scale are solved for in a common Newton-Raphson loop. In this case, the linear system of equations within each iteration is solved by static condensation, so that only very limited modifications to the conventional, staggered scheme are necessary. The proposed monolithic FE 2 algorithm is implemented into the commercial FE code Abaqus. Benchmark examples demonstrate that the monolithic scheme saves up to ≈ 70% of computational costs.

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Section: Introductionmentioning

confidence: 99%

An efficient monolithic solution scheme for FE$^2$ problems

Lange,

Hütter,

Kiefer

2021

Preprint

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Residual stresses in hot bulk formed parts: microscopic stress analysis for austenite-to-martensite phase transformation

et al. 2021

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In this contribution, the two-scale analysis of residual stress states in a hot bulk formed part with subsequent cooling in the framework of the $$\hbox {FE}^2$$ FE 2 -method is presented. The induction of specific residual stress states in order to improve a component’s properties is an area of current research. In general, residual stresses can be induced inside a component in different ways, e.g., quenching, phase transformation in hot forming processes or dislocation movements. It is widely known that different types of residual stresses can be characterized based on the scale the type acts on. In addition to the macroscopic residual stress analysis, in which residual stresses of first type are considered, this contribution specifically analyzes the microscopic residual stress evolution as a consequence of the cooling of the component.

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Solutions for maximum coupling in multiferroic magnetoelectric composites by material design

Jayachandran

Guedes

Rodrigues

2018

Sci Rep

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Electrical control of magnetization offers an extra degree of freedom in materials possessing both electric and magnetic dipole moments. A stochastic optimization combined with homogenization is applied for the solution for maximum magnetoelectric (ME) coupling coefficient α of a laminar ME composite with the thickness and orientation of ferroelectric phase as design variables. Simulated annealing with a generalized Monte Carlo scheme is used for optimization problem. Optimal microstructure with single and poly-crystalline configurations that enhances the overall α is identified. It is found that juxtaposing a preferentially oriented ferroelectric material with a ferromagnetic ferrite into a composite would result in manifold increase in magnetoelectric coupling. The interface shear strains are found to be richly contributing to the ME coupling. The preferential orientation of the ferroelectric phase in the optimal ME composite laminate is demonstrated using the optimal pole figure analyses.

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An FE $$^2$$ -Scheme for Magneto-Electro-Mechanically Coupled Boundary Value Problems

Cited by 3 publications

References 77 publications

An efficient monolithic solution scheme for FE$^2$ problems

An efficient monolithic solution scheme for FE$^2$ problems

Residual stresses in hot bulk formed parts: microscopic stress analysis for austenite-to-martensite phase transformation

Solutions for maximum coupling in multiferroic magnetoelectric composites by material design

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