2019
DOI: 10.1002/nme.6058
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A second‐order reduced asymptotic homogenization approach for nonlinear periodic heterogeneous materials

Abstract: Summary An efficient second‐order reduced asymptotic homogenization approach is developed for nonlinear heterogeneous media with large periodic microstructure. The two salient features of the proposed approach are (i) an asymptotic higher‐order nonlinear homogenization that does not require higher‐order continuity of the coarse‐scale solution and (ii) an efficient model reduction scheme for solving higher‐order nonlinear unit cell problems at a fraction of computational cost in comparison to the direct computa… Show more

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Cited by 32 publications
(14 citation statements)
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“…Even though the equilibrium equation (21) has exactly the same form derived in Geus et al, 29 the main difference is that 0 is not a projection onto the function space V c (0). Indeed, we will point out that the Green function G = C 0 ∶ 0 is a projection operator onto the function space V c (0).…”
Section: Compatibility Projection Operator and Connection To The Exismentioning
confidence: 95%
See 2 more Smart Citations
“…Even though the equilibrium equation (21) has exactly the same form derived in Geus et al, 29 the main difference is that 0 is not a projection onto the function space V c (0). Indeed, we will point out that the Green function G = C 0 ∶ 0 is a projection operator onto the function space V c (0).…”
Section: Compatibility Projection Operator and Connection To The Exismentioning
confidence: 95%
“…As Equation (24) must hold true for arbitrary tensor-valued functions W, the equilibrium equation 21can be equivalently derived from this equation. In fact, Equations (21) and (24) are the strong form and weak form of the microscopic boundary value problem (10), respectively.…”
Section: Derivation Of Microequilibrium With Compatibility-enforcing mentioning
confidence: 99%
See 1 more Smart Citation
“…Bhattacharjee and Matouš 46 applied a manifold-based order reduction model to predict the macro performance of the hyperelastic heterogenous composites. Yuan, 47 Fish, 48 and Yang et al 49 constructed and applied the multiscale reduced models to evaluate any inelastic deformations of the heterogeneous composites, and could greatly save the computing time. Further, Yang et al, 50 expanded the multiscale reduced-order approach to compute the nonlinear axisymmetric structure with periodic configuration.…”
Section: Introductionmentioning
confidence: 99%
“…Some other recent application was to find the effect of damage amplification due to micro-crack interaction (see Markenscoff and Dascalu, 2012), to simulate thermoelectric composites (see Yang et al., 2013). It is noteworthy to mention that most of the analyses are based on O(1) expansion approaches which results in inaccuracy at regions of high gradients and for low-scale separation, higher order homogenisation has been developed for transient dynamics (see Hui and Oskay, 2014), elastic composites (see Ameen et al., 2018) and for elasto-plastic heterogeneity (see Fish et al., 2019).…”
Section: Introductionmentioning
confidence: 99%