Kaiser, Tobias; Remmers, Joris J. C.; Geers, Marc G. D. An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics. (English) Zbl 1509.74056 Comput. Mech. 70, No. 6, 1335-1357 (2022). MSC: 74S99 74E05 74Q99 74M25 65T60 PDFBibTeX XMLCite \textit{T. Kaiser} et al., Comput. Mech. 70, No. 6, 1335--1357 (2022; Zbl 1509.74056) Full Text: DOI
Waseem, A.; Heuzé, T.; Stainier, L.; Geers, M. G. D.; Kouznetsova, V. G. Correction to: “Model reduction in computational homogenization for transient heat conduction”. (English) Zbl 1508.80005 Comput. Mech. 68, No. 1, 231 (2021). MSC: 80M40 80A19 74A15 65M60 65M06 65N30 PDFBibTeX XMLCite \textit{A. Waseem} et al., Comput. Mech. 68, No. 1, 231 (2021; Zbl 1508.80005) Full Text: DOI
Liu, L.; Sridhar, A.; Geers, M. G. D.; Kouznetsova, V. G. Computational homogenization of locally resonant acoustic metamaterial panels towards enriched continuum beam/shell structures. (English) Zbl 1507.74355 Comput. Methods Appl. Mech. Eng. 387, Article ID 114161, 35 p. (2021). MSC: 74Q05 74K10 74K25 PDFBibTeX XMLCite \textit{L. Liu} et al., Comput. Methods Appl. Mech. Eng. 387, Article ID 114161, 35 p. (2021; Zbl 1507.74355) Full Text: DOI
Waseem, Abdullah; Heuzé, Thomas; Geers, Marc G. D.; Kouznetsova, Varvara G.; Stainier, Laurent Data-driven reduced homogenization for transient diffusion problems with emergent history effects. (English) Zbl 1506.74333 Comput. Methods Appl. Mech. Eng. 380, Article ID 113773, 27 p. (2021). MSC: 74Q10 74S05 65M60 PDFBibTeX XMLCite \textit{A. Waseem} et al., Comput. Methods Appl. Mech. Eng. 380, Article ID 113773, 27 p. (2021; Zbl 1506.74333) Full Text: DOI HAL
Waseem, A.; Heuzé, T.; Stainier, L.; Geers, M. G. D.; Kouznetsova, V. G. Two-scale analysis of transient diffusion problems through a homogenized enriched continuum. (English) Zbl 1486.74116 Eur. J. Mech., A, Solids 87, Article ID 104212, 12 p. (2021). Reviewer: Vladimir Mityushev (Kraków) MSC: 74Q15 74S05 PDFBibTeX XMLCite \textit{A. Waseem} et al., Eur. J. Mech., A, Solids 87, Article ID 104212, 12 p. (2021; Zbl 1486.74116) Full Text: DOI
Sridhar, A.; Kouznetsova, V. G.; Geers, M. G. D. Frequency domain boundary value problem analyses of acoustic metamaterials described by an emergent generalized continuum. (English) Zbl 1481.74641 Comput. Mech. 65, No. 3, 789-805 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 74Q10 74A40 74F10 74S25 76Q05 PDFBibTeX XMLCite \textit{A. Sridhar} et al., Comput. Mech. 65, No. 3, 789--805 (2020; Zbl 1481.74641) Full Text: DOI
Waseem, A.; Heuzé, T.; Stainier, L.; Geers, M. G. D.; Kouznetsova, V. G. Model reduction in computational homogenization for transient heat conduction. (English) Zbl 1491.80005 Comput. Mech. 65, No. 1, 249-266 (2020); correction ibid. 68, No. 1, 231 (2021). Reviewer: Alain Brillard (Riedisheim) MSC: 80M40 80A19 74A15 65M60 65M06 65N30 PDFBibTeX XMLCite \textit{A. Waseem} et al., Comput. Mech. 65, No. 1, 249--266 (2020; Zbl 1491.80005) Full Text: DOI
van Bree, S. E. H. M.; Rokoš, O.; Peerlings, R. H. J.; Doškář, M.; Geers, M. G. D. A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials. (English) Zbl 1506.74332 Comput. Methods Appl. Mech. Eng. 372, Article ID 113333, 25 p. (2020). MSC: 74Q10 74B20 74G60 PDFBibTeX XMLCite \textit{S. E. H. M. van Bree} et al., Comput. Methods Appl. Mech. Eng. 372, Article ID 113333, 25 p. (2020; Zbl 1506.74332) Full Text: DOI arXiv
van Tuijl, Rody A.; Remmers, Joris J. C.; Geers, Marc G. D. Multi-dimensional wavelet reduction for the homogenisation of microstructures. (English) Zbl 1441.74308 Comput. Methods Appl. Mech. Eng. 359, Article ID 112652, 26 p. (2020). MSC: 74S99 65T60 74Q05 74M25 PDFBibTeX XMLCite \textit{R. A. van Tuijl} et al., Comput. Methods Appl. Mech. Eng. 359, Article ID 112652, 26 p. (2020; Zbl 1441.74308) Full Text: DOI
Rokoš, O.; Ameen, M. M.; Peerlings, R. H. J.; Geers, M. G. D. Micromorphic computational homogenization for mechanical metamaterials with patterning fluctuation fields. (English) Zbl 1474.74087 J. Mech. Phys. Solids 123, 119-137 (2019). MSC: 74Q10 74A60 PDFBibTeX XMLCite \textit{O. Rokoš} et al., J. Mech. Phys. Solids 123, 119--137 (2019; Zbl 1474.74087) Full Text: DOI arXiv
van Nuland, Tim F. W.; Silva, Priscilla B.; Sridhar, Ashwin; Geers, Marc G. D.; Kouznetsova, Varvara G. Transient analysis of nonlinear locally resonant metamaterials via computational homogenization. (English) Zbl 07273358 Math. Mech. Solids 24, No. 10, 3136-3155 (2019). MSC: 74-XX PDFBibTeX XMLCite \textit{T. F. W. van Nuland} et al., Math. Mech. Solids 24, No. 10, 3136--3155 (2019; Zbl 07273358) Full Text: DOI
Sridhar, A.; Kouznetsova, V. G.; Geers, M. G. D. A general multiscale framework for the emergent effective elastodynamics of metamaterials. (English) Zbl 1441.74135 J. Mech. Phys. Solids 111, 414-433 (2018). MSC: 74M05 74Q15 PDFBibTeX XMLCite \textit{A. Sridhar} et al., J. Mech. Phys. Solids 111, 414--433 (2018; Zbl 1441.74135) Full Text: DOI
van Tuijl, Rody A.; Remmers, Joris J. C.; Geers, Marc G. D. Integration efficiency for model reduction in micro-mechanical analyses. (English) Zbl 1446.74060 Comput. Mech. 62, No. 2, 151-169 (2018). MSC: 74-10 74M25 74Q05 PDFBibTeX XMLCite \textit{R. A. van Tuijl} et al., Comput. Mech. 62, No. 2, 151--169 (2018; Zbl 1446.74060) Full Text: DOI
Ameen, M. M.; Peerlings, R. H. J.; Geers, M. G. D. A quantitative assessment of the scale separation limits of classical and higher-order asymptotic homogenization. (English) Zbl 1406.74553 Eur. J. Mech., A, Solids 71, 89-100 (2018). MSC: 74Q05 74E05 PDFBibTeX XMLCite \textit{M. M. Ameen} et al., Eur. J. Mech., A, Solids 71, 89--100 (2018; Zbl 1406.74553) Full Text: DOI
de Geus, T. W. J.; Vondřejc, J.; Zeman, J.; Peerlings, R. H. J.; Geers, M. G. D. Finite strain FFT-based non-linear solvers made simple. (English) Zbl 1439.74045 Comput. Methods Appl. Mech. Eng. 318, 412-430 (2017). MSC: 74B20 65T50 74C05 74M25 74S99 74Q05 PDFBibTeX XMLCite \textit{T. W. J. de Geus} et al., Comput. Methods Appl. Mech. Eng. 318, 412--430 (2017; Zbl 1439.74045) Full Text: DOI arXiv
Sridhar, A.; Kouznetsova, V. G.; Geers, M. G. D. Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum. (English) Zbl 1382.74106 Comput. Mech. 57, No. 3, 423-435 (2016). MSC: 74Q05 PDFBibTeX XMLCite \textit{A. Sridhar} et al., Comput. Mech. 57, No. 3, 423--435 (2016; Zbl 1382.74106) Full Text: DOI
Bosco, E.; Kouznetsova, V. G.; Coenen, E. W. C.; Geers, M. G. D.; Salvadori, A. A multiscale framework for localizing microstructures towards the onset of macroscopic discontinuity. (English) Zbl 1398.74308 Comput. Mech. 54, No. 2, 299-319 (2014). MSC: 74S05 74Q05 74R20 74R10 74E30 PDFBibTeX XMLCite \textit{E. Bosco} et al., Comput. Mech. 54, No. 2, 299--319 (2014; Zbl 1398.74308) Full Text: DOI
Berke, P. Z.; Peerlings, R. H. J.; Massart, T. J.; Geers, M. G. D. A homogenization-based quasi-discrete method for the fracture of heterogeneous materials. (English) Zbl 1398.74305 Comput. Mech. 53, No. 5, 909-923 (2014). MSC: 74S05 74Q05 74R10 74E05 74E30 PDFBibTeX XMLCite \textit{P. Z. Berke} et al., Comput. Mech. 53, No. 5, 909--923 (2014; Zbl 1398.74305) Full Text: DOI
Pham, K.; Kouznetsova, V. G.; Geers, M. G. D. Transient computational homogenization for heterogeneous materials under dynamic excitation. (English) Zbl 1325.74125 J. Mech. Phys. Solids 61, No. 11, 2125-2146 (2013); corrigendum ibid. 64, 483 (2014). MSC: 74Q20 74H15 74E05 74N15 74Q05 74S30 PDFBibTeX XMLCite \textit{K. Pham} et al., J. Mech. Phys. Solids 61, No. 11, 2125--2146 (2013; Zbl 1325.74125) Full Text: DOI
Coenen, E. W. C.; Kouznetsova, V. G.; Geers, M. G. D. Novel boundary conditions for strain localization analyses in microstructural volume elements. (English) Zbl 1242.74083 Int. J. Numer. Methods Eng. 90, No. 1, 1-21 (2012). MSC: 74Q05 74Q15 74S05 PDFBibTeX XMLCite \textit{E. W. C. Coenen} et al., Int. J. Numer. Methods Eng. 90, No. 1, 1--21 (2012; Zbl 1242.74083) Full Text: DOI
Geers, M. G. D.; Kouznetsova, V. G.; Brekelmans, W. A. M. Computational homogenization. (English) Zbl 1298.74199 Pippan, Reinhard (ed.) et al., Multiscale modelling of plasticity and fracture by means of dislocation mechanics. Papers based on the presentations at the CISM-Bianchi session on multiscale modelling of plasticity and fracture by means of dislocation mechanics and at the CISM course on multiscale modelling and design of new materials, Udine, Italy, July 4–8, 2005. Wien: Springer (ISBN 978-3-7091-0282-4/hbk). CISM Courses and Lectures 522, 327-394 (2010). MSC: 74Q05 74S05 74F10 74E35 PDFBibTeX XMLCite \textit{M. G. D. Geers} et al., in: Multiscale modelling of plasticity and fracture by means of dislocation mechanics. Papers based on the presentations at the CISM-Bianchi session on multiscale modelling of plasticity and fracture by means of dislocation mechanics and at the CISM course on multiscale modelling and design of new materials, Udine, Italy, July 4--8, 2005. Wien: Springer. 327--394 (2010; Zbl 1298.74199) Full Text: DOI
Kouznetsova, V. G.; Geers, M. G. D.; Brekelmans, W. A. M. Computational homogenisation for nonlinear heterogeneous solids. (English) Zbl 1296.74088 Galvanetto, Ugo (ed.) et al., Multiscale modeling in solid mechanics. Computational approaches. London: Imperial College Press (ISBN 978-1-84816-307-2/hbk; 978-1-84816-308-9/ebook). Computational and Experimental Methods in Structures 3, 1-42 (2010). MSC: 74Q05 74Q15 74S05 PDFBibTeX XMLCite \textit{V. G. Kouznetsova} et al., Comput. Exp. Methods Struct. 3, 1--42 (2010; Zbl 1296.74088)
Coenen, E. W. C.; Kouznetsova, V. G.; Geers, M. G. D. Computational homogenization for heterogeneous thin sheets. (English) Zbl 1197.74082 Int. J. Numer. Methods Eng. 83, No. 8-9, 1180-1205 (2010). MSC: 74Q05 74K25 PDFBibTeX XMLCite \textit{E. W. C. Coenen} et al., Int. J. Numer. Methods Eng. 83, No. 8--9, 1180--1205 (2010; Zbl 1197.74082) Full Text: DOI
Geers, M. G. D.; Kouznetsova, V. G.; Brekelmans, W. A. M. Multi-scale computational homogenization: trends and challenges. (English) Zbl 1402.74107 J. Comput. Appl. Math. 234, No. 7, 2175-2182 (2010). MSC: 74S30 74Q99 PDFBibTeX XMLCite \textit{M. G. D. Geers} et al., J. Comput. Appl. Math. 234, No. 7, 2175--2182 (2010; Zbl 1402.74107) Full Text: DOI
Özdemir, I.; Brekelmans, W. A. M.; Geers, M. G. D. \(FE^{2}\) computational homogenization for the thermo-mechanical analysis of heterogeneous solids. (English) Zbl 1228.74065 Comput. Methods Appl. Mech. Eng. 198, No. 3-4, 602-613 (2008). MSC: 74Q05 74F05 74E05 PDFBibTeX XMLCite \textit{I. Özdemir} et al., Comput. Methods Appl. Mech. Eng. 198, No. 3--4, 602--613 (2008; Zbl 1228.74065) Full Text: DOI
Özdemir, I.; Brekelmans, W. A. M.; Geers, M. G. D. Computational homogenization for heat conduction in heterogeneous solids. (English) Zbl 1159.74029 Int. J. Numer. Methods Eng. 73, No. 2, 185-204 (2008). MSC: 74Q05 74E05 74F05 74S05 80A20 PDFBibTeX XMLCite \textit{I. Özdemir} et al., Int. J. Numer. Methods Eng. 73, No. 2, 185--204 (2008; Zbl 1159.74029) Full Text: DOI Link
Massart, T. J.; Peerlings, R. H. J.; Geers, M. G. D. An enhanced multi-scale approach for masonry wall computations with localization of damage. (English) Zbl 1194.74283 Int. J. Numer. Methods Eng. 69, No. 5, 1022-1059 (2007). MSC: 74Q05 74R99 PDFBibTeX XMLCite \textit{T. J. Massart} et al., Int. J. Numer. Methods Eng. 69, No. 5, 1022--1059 (2007; Zbl 1194.74283) Full Text: DOI
Kouznetsova, V. G.; Geers, M. G. D.; Brekelmans, W. A. M. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. (English) Zbl 1112.74469 Comput. Methods Appl. Mech. Eng. 193, No. 48-51, 5525-5550 (2004). MSC: 74Q15 74Q05 74S05 PDFBibTeX XMLCite \textit{V. G. Kouznetsova} et al., Comput. Methods Appl. Mech. Eng. 193, No. 48--51, 5525--5550 (2004; Zbl 1112.74469) Full Text: DOI
Massart, T. J.; Peerlings, R. H. J.; Geers, M. G. D. Mesoscopic modeling of failure and damage-induced anisotropy in brick masonry. (English) Zbl 1058.74627 Eur. J. Mech., A, Solids 23, No. 5, 719-735 (2004). MSC: 74R20 PDFBibTeX XMLCite \textit{T. J. Massart} et al., Eur. J. Mech., A, Solids 23, No. 5, 719--735 (2004; Zbl 1058.74627) Full Text: DOI
Kouznetsova, V.; Geers, M. G. D.; Brekelmans, W. A. M. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. (English) Zbl 1058.74070 Int. J. Numer. Methods Eng. 54, No. 8, 1235-1260 (2002). MSC: 74Q15 74Q05 74M25 74E05 PDFBibTeX XMLCite \textit{V. Kouznetsova} et al., Int. J. Numer. Methods Eng. 54, No. 8, 1235--1260 (2002; Zbl 1058.74070) Full Text: DOI