A sub-stepping scheme for multi-scale analysis of solids

Somer, D.D.; Neto, E. A. de Souza; Dettmer, Wulf G.; Perić, D.

doi:10.1016/j.cma.2008.11.013

Cited by 46 publications

(31 citation statements)

References 14 publications

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“…The standard computational algorithms for elasto-plasticity and viscoplasticity are employed that underly the multi-scale approach, and we refer the reader to [40,[42][43][44][45][46] for detailed descriptions of the computational schemes behind the present simulations. It should be emphasized that in order to ensure the robustness and efficiency of the multi-scale simulations the recently proposed sub-stepping procedure is utilized [47].…”

Section: Numerical Examplesmentioning

confidence: 99%

On micro‐to‐macro transitions for multi‐scale analysis of non‐linear heterogeneous materials: unified variational basis and finite element implementation

Perić

Neto

Feijóo

et al. 2010

Numerical Meth Engineering

Self Cite

154

118

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SUMMARYThis work describes a homogenization-based multi-scale procedure required for the computation of the material response of non-linear microstructures undergoing small strains. Such procedures are important for computer modelling of heterogeneous materials when the length-scale of heterogeneities is small compared to the dimensions of the body. The described multi-scale procedure relies on a unified variational basis which, apart from the continuum-based variational formulation at both micro-and macroscales of the problem, also includes the variational formulation governing micro-to-macro transitions. This unified variational basis leads naturally to a generic finite element-based framework for homogenization-based multi-scale analysis of heterogenous solids. In addition, the unified variational formulation provides clear axiomatic basis and hierarchy related to the choice of boundary conditions at the microscale. Classical kinematical constraints are considered over the representative volume element: (i) Taylor, (ii) linear boundary displacements, (iii) periodic boundary displacement fluctuations and (iv) minimal constraint, also known as uniform boundary tractions. In this context the Hill-Mandel averaging requirement, which links microscopic and macroscopic stress power, plays a fundamental role in defining the microscopic forces compatible with the assumed kinematics. Numerical examples of both microscale and two-scale finite element simulations of elasto-plastic material with microcavities are presented to illustrate the main features and scope of the described computational strategy.

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Section: Numerical Examplesmentioning

confidence: 99%

On micro‐to‐macro transitions for multi‐scale analysis of non‐linear heterogeneous materials: unified variational basis and finite element implementation

Perić

Neto

Feijóo

et al. 2010

Numerical Meth Engineering

Self Cite

154

118

View full text Add to dashboard Cite

show abstract

“…Although this method is known to be computationally expensive, it is trivially parallelizable as the computations at the microscale are completely independent of each other [367][368][369][370]. Also, a number of methods have been recently developed aiming at reducing the computational cost and increasing the accuracy of multiscale analysis [371][372][373][374][375]. These methods are typically based on decomposing the macroscale problem and selective usage of computational techniques discussed in Refs.…”

Section: Analysis At the Rve Levelmentioning

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

190

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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“…In the current implementation, we are using the latter option. The sub-stepping scheme discussed in [35] could be another option worth to be considered. Needless to say, a comparison study, say by means of numerical experiments, of those techniques would be necessary to choose the most efficient one and is a topic of further study.…”

Section: Some Algorithmic Aspectsmentioning

confidence: 99%

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Nguyen

Lloberas-Valls

Stroeven

et al. 2011

Computer Methods in Applied Mechanics and Engineering

137

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The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction-separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE 2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method.

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A sub-stepping scheme for multi-scale analysis of solids

Cited by 46 publications

References 14 publications

On micro‐to‐macro transitions for multi‐scale analysis of non‐linear heterogeneous materials: unified variational basis and finite element implementation

On micro‐to‐macro transitions for multi‐scale analysis of non‐linear heterogeneous materials: unified variational basis and finite element implementation

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

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

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