Material spatial randomness: From statistical to representative volume element☆

By Martin Ostoja-Starzewski. 2006

629 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3a30987490f0cda1e15952a5f72dbd1257a6b4b4

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

On the Size of RVE in Finite Elasticity of Random Composites (2006, background): “In the small deformation theory the effective strain energy function <eff 1⁄4 (1)2 ɛ: Ceff : ɛ is equal to the complementary energy function <* eff 1⁄4 (1)2σ: Seff : σ and hierarchies (8) and (9) can be combined to give [17]:”
Tensor-based methods for numerical homogenization from high-resolution images (2013, methodology): “The reader can refer to [23, 24, 39, 48] for methodologies to estimate the size of the representative volume.”
Architectured materials in engineering and biology: fabrication, structure, mechanics and performance (2015, background): “grains in metals) is significantly smaller than the size of the component.(6) However, current knowledge in multi-scale modelling and design(7) suggests that this traditional divide might disappear in modern materials.”
Statistical volume element method for predicting microstructure–constitutive property relations (2008, background): “SVE is a newly introduced concept to capture the microstructure randomness in a material by conducting a cell model simulation of a domain which is smaller than a conventional RVE but larger than the microstructure characteristic length scale [29].”
A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials (2013, methodology): “Given a polycrystalline realization, consisting of Ng grains and subjected to a given set of consistent boundary conditions, since the material is supposed to not develop microcracks, stress and strain volume averages can be used to extract the apparent elastic modula, see for example [3, 76, 100].”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, background): “However, it must remain sufficiently small to be considered as a volume element of the structure, fulfill space separation condition and also due to computational efficiency [91, 119].”
A critical reliability evaluation of fibre reinforced composite materials based on probabilistic micro and macro-mechanical analysis (2010, methodology): “[7], typically obtained through an image processing technique and linked to a suitable micromechanical model (Class A2).”
Particulate random composites homogenized as micropolar materials (2014, background): “proved to be among the most effective for identifying the RVE size and the overall constitutive moduli for linear elastic and thermoelastic, as well as non-linear and non-elastic, material systems [7, 14, 16].”
Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions (2010, background): “…in the linear case, one could isolate a representative volume element at position X , (cid:4) rve ( X ) (this representative volume element is supposed to be defined using for example meth-ods which are proposed in [22, 23, 35]) and assume that the microstructure is perfectly define at such scale.”