Design of 3D statistically similar Representative Volume Elements based on Minkowski functionals

Scheunemann, Lisa; Balzani, Daniel; Brands, Dominik; Schröder, Jörg

doi:10.1016/j.mechmat.2015.03.005

Cited by 38 publications

(35 citation statements)

References 38 publications

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“…The size of the RVE has been also examined in the context of the granular media by Meier et al [281] where the discrete element method is used to evaluate the size of the RVE. Balzani et al [282] and Scheunemann et al [283] proposed the construction of a statistically similar representative volume element (SSRVE) to reduce the size and accordingly the computational effort associated with a large complex RVE. They compared the stress-strain curves obtained with their proposed SSRVE including three inclusions with the one obtained from a very large RVE and showed a good agreement of the results along with a significant reduction of computation time of the problem.…”

Section: 22mentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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Section: 22mentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

View full text Add to dashboard Cite

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“…Further studies and information regarding the construction of SSRVE can be also found for the two-dimensional case in, e.g., [4,7,8]. On the construction of three-dimensional SSRVEs using Minkowski Functionals as statistical descriptors we refer to [73].…”

Section: Construction Of Ssvesmentioning

confidence: 99%

“…The reliability of this method especially for DP steel microstructures was shown in, e.g., [4,7,8,78]. For an extension of this method to 3D see [9] and for the construction using Minkowski Functionals as statistical descriptors we refer to [73].…”

Section: Introductionmentioning

confidence: 98%

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

et al. 2015

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The microstructure of dual-phase steels consisting of a ferrite matrix with embedded martensite inclusions is the main contributor to the mechanical properties such as high ultimate tensile strength, high work hardening rate, and good ductility. Due to the composite structure and the wide field of applications of this steel type, a wide interest exists in corresponding virtual computational experiments. For a reliable modeling, the microstructure should be included. For that reason, in this paper we follow a computational strategy based on the definition of a representative volume element (RVE). These RVEs will be constructed by a set of tomographic measurements and mechanical tests. In order to arrive at more efficient numerical schemes, we also construct statistically similar RVEs, which are characterized by a lower complexity compared with the real microstructure but which represent the overall material behavior accurately. In addition to the morphology of the microstructure, the austenite-martensite transformation during the steel production has a relevant influence on the mechanical properties and is considered in this contribution. This transformation induces a volume expansion of the martensite phase. A further effect is determined in nanoindentation test, where it turns out that the hardness in the ferrite phase increases exponentially when approaching the martensitic inclusion. To capture these gradient properties in the computational model, the volumetric expansion is applied to the martensite phase, and the arising equivalent plastic strain distribution in the ferrite phase serves as basis for a locally graded modification of the ferritic yield curve. Good accordance of the model considering the gradient yield behavior in the ferrite phase is observed in the numerical simulations with experimental data.Keywords Reconstruction of microstructure · Dual-phase steel · RVE · Microheterogeneous materials · EBSD-FIB · SSRVE · Volume expansion of martensite · Multiscale simulations

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“…SSRVEs are constructed based on the solution of an optimization problem, as proposed in [4] and modified in [5]. Using a staggered optimization scheme, the similarity of statistical measures as well as mechanical behavior is ensured considering various influences, such as parameterization type i of the microstructure of the SSRVE, different sets of statistical descriptors G and respective weighting factors ω.…”

Section: Statistically Similar Rvesmentioning

confidence: 99%

Study on statistically similar RVEs for real microstructures based on different statistical descriptors

Scheunemann

Balzani

Brands

et al. 2015

Proc Appl Math and Mech

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A method for constructing statistically similar representative volume elements (SSRVEs) for a real dual-phase (DP) steel microstructure is presented in this contribution. The advantageous material properties of such kind of steels originate from the interaction of the microstructure constituents of the material on the microscale. In order to capture these effects directly in the material modeling, the FE 2 method is a suitable tool, where an RVE representing the microstructure of a material is used in the microscopic boundary value problem, which is solved at each Gauss-point of the macroscopic boundary value problem. However, RVEs based on real microstructures typically implicate high computational expenses due to the complexity of the underlying microstructure and its discretization. SSRVEs, which have a lower complexity than conventional RVEs but are still able to represent the material, can be used instead. Here, different statistical measures for the construction of SSRVEs and their comparison are the main focus.

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Design of 3D statistically similar Representative Volume Elements based on Minkowski functionals

Cited by 38 publications

References 38 publications

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

Study on statistically similar RVEs for real microstructures based on different statistical descriptors

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