Braides, Andrea; Causin, Andrea; Solci, Margherita; Truskinovsky, Lev Beyond the classical Cauchy-Born rule. (English) Zbl 07771235 Arch. Ration. Mech. Anal. 247, No. 6, Paper No. 107, 113 p. (2023). MSC: 74A25 74E15 49Sxx PDFBibTeX XMLCite \textit{A. Braides} et al., Arch. Ration. Mech. Anal. 247, No. 6, Paper No. 107, 113 p. (2023; Zbl 07771235) Full Text: DOI arXiv
Lauerbach, Laura; Neukamm, Stefan; Schäffner, Mathias; Schlömerkemper, Anja Onset of fracture in random heterogeneous particle chains. (English) Zbl 07763421 Hujdurović, Ademir (ed.) et al., European congress of mathematics. Proceedings of the 8th congress, 8ECM, Portorož, Slovenia, June 20–26, 2021. Berlin: European Mathematical Society (EMS). 927-946 (2023). MSC: 74Q05 74R10 74A45 41A60 74G65 PDFBibTeX XMLCite \textit{L. Lauerbach} et al., in: European congress of mathematics. Proceedings of the 8th congress, 8ECM, Portorož, Slovenia, June 20--26, 2021. Berlin: European Mathematical Society (EMS). 927--946 (2023; Zbl 07763421) Full Text: DOI arXiv
Carioni, Marcello; Fischer, Julian; Schlömerkemper, Anja External forces in the continuum limit of discrete systems with non-convex interaction potentials: compactness for a \(\Gamma \)-development. (English) Zbl 1521.74007 J. Convex Anal. 30, No. 1, 217-247 (2023). MSC: 74A25 74A20 82B21 PDFBibTeX XMLCite \textit{M. Carioni} et al., J. Convex Anal. 30, No. 1, 217--247 (2023; Zbl 1521.74007) Full Text: arXiv Link
Gladbach, Peter; Olbermann, Heiner Approximation of the Willmore energy by a discrete geometry model. (English) Zbl 1522.53011 Adv. Calc. Var. 16, No. 2, 403-424 (2023). Reviewer: Benedikt Kolbe (Bonn) MSC: 53A70 53A05 57R05 PDFBibTeX XMLCite \textit{P. Gladbach} and \textit{H. Olbermann}, Adv. Calc. Var. 16, No. 2, 403--424 (2023; Zbl 1522.53011) Full Text: DOI arXiv
Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, Florian Distribution of cracks in a chain of atoms at low temperature. (English) Zbl 1482.82018 Ann. Henri Poincaré 22, No. 12, 4131-4172 (2021). MSC: 82B21 74B20 74G65 60F10 PDFBibTeX XMLCite \textit{S. Jansen} et al., Ann. Henri Poincaré 22, No. 12, 4131--4172 (2021; Zbl 1482.82018) Full Text: DOI arXiv
Picandet, Vincent; Challamel, Noël Nonlocality of one-dimensional bilinear hardening-softening elastoplastic axial lattices. (English) Zbl 1446.74094 Math. Mech. Solids 25, No. 2, 475-497 (2020). MSC: 74C05 74A25 82B21 PDFBibTeX XMLCite \textit{V. Picandet} and \textit{N. Challamel}, Math. Mech. Solids 25, No. 2, 475--497 (2020; Zbl 1446.74094) Full Text: DOI
Braides, Andrea; Cermelli, Paolo; Dovetta, Simone \(\Gamma\)-limit of the cut functional on dense graph sequences. (English) Zbl 1439.05068 ESAIM, Control Optim. Calc. Var. 26, Paper No. 26, 25 p. (2020). MSC: 05C12 05C42 05C63 PDFBibTeX XMLCite \textit{A. Braides} et al., ESAIM, Control Optim. Calc. Var. 26, Paper No. 26, 25 p. (2020; Zbl 1439.05068) Full Text: DOI arXiv Link
Cicalese, Marco; Gloria, Antoine; Ruf, Matthias From statistical polymer physics to nonlinear elasticity. (English) Zbl 1459.82347 Arch. Ration. Mech. Anal. 236, No. 2, 1127-1215 (2020). MSC: 82D60 74B20 49J45 60F15 60F10 PDFBibTeX XMLCite \textit{M. Cicalese} et al., Arch. Ration. Mech. Anal. 236, No. 2, 1127--1215 (2020; Zbl 1459.82347) Full Text: DOI arXiv
Truskinovsky, Lev; Vainchtein, Anna Strictly supersonic solitary waves in lattices with second-neighbor interactions. (English) Zbl 1448.82027 Physica D 389, 24-50 (2019). MSC: 82C20 34C15 34C60 PDFBibTeX XMLCite \textit{L. Truskinovsky} and \textit{A. Vainchtein}, Physica D 389, 24--50 (2019; Zbl 1448.82027) Full Text: DOI
Lauerbach, Laura; Schäffner, Mathias; Schlömerkemper, Anja On continuum limits of heterogeneous discrete systems modelling cracks in composite materials. (English) Zbl 1525.74171 GAMM-Mitt. 40, No. 3, 184-206 (2018). MSC: 74Q05 74R10 49J45 74A45 74G65 PDFBibTeX XMLCite \textit{L. Lauerbach} et al., GAMM-Mitt. 40, No. 3, 184--206 (2018; Zbl 1525.74171) Full Text: DOI
Schäffner, Mathias; Schlömerkemper, Anja On Lennard-Jones systems with finite range interactions and their asymptotic analysis. (English) Zbl 1407.49015 Netw. Heterog. Media 13, No. 1, 95-118 (2018). MSC: 49J45 74R10 74G10 74G65 74A25 PDFBibTeX XMLCite \textit{M. Schäffner} and \textit{A. Schlömerkemper}, Netw. Heterog. Media 13, No. 1, 95--118 (2018; Zbl 1407.49015) Full Text: DOI arXiv
Eugster, Simon R.; dell’Isola, Francesco Exegesis of the introduction and sect. I from “Fundamentals of the mechanics of continua” by E. Hellinger. (English) Zbl 07775186 ZAMM, Z. Angew. Math. Mech. 97, No. 4, 477-506 (2017). MSC: 74Axx 74Kxx 01Axx PDFBibTeX XMLCite \textit{S. R. Eugster} and \textit{F. dell'Isola}, ZAMM, Z. Angew. Math. Mech. 97, No. 4, 477--506 (2017; Zbl 07775186) Full Text: DOI
Sharma, Basant Lal Continuum limit of discrete Sommerfeld problems on square lattice. (English) Zbl 1381.35169 Sādhanā 42, No. 5, 713-728 (2017). MSC: 35Q60 35J05 35P25 78A45 PDFBibTeX XMLCite \textit{B. L. Sharma}, Sādhanā 42, No. 5, 713--728 (2017; Zbl 1381.35169) Full Text: DOI arXiv Link
Benešová, Barbora; Kružík, Martin Weak lower semicontinuity of integral functionals and applications. (English) Zbl 1378.49011 SIAM Rev. 59, No. 4, 703-766 (2017). MSC: 49J45 49-02 49S05 49J20 74A05 PDFBibTeX XMLCite \textit{B. Benešová} and \textit{M. Kružík}, SIAM Rev. 59, No. 4, 703--766 (2017; Zbl 1378.49011) Full Text: DOI arXiv
Le Dret, Hervé; Raoult, Annie Hexagonal lattices with three-point interactions. (English. French summary) Zbl 1372.74074 J. Math. Pures Appl. (9) 108, No. 5, 613-632 (2017). MSC: 74Q05 74Q15 74K35 49J45 PDFBibTeX XMLCite \textit{H. Le Dret} and \textit{A. Raoult}, J. Math. Pures Appl. (9) 108, No. 5, 613--632 (2017; Zbl 1372.74074) Full Text: DOI HAL
Sharma, Basant Lal Diffraction of waves on square lattice by semi-infinite rigid constraint. (English) Zbl 1467.35111 Wave Motion 59, 52-68 (2015). MSC: 35J05 35A35 76Q05 78A40 PDFBibTeX XMLCite \textit{B. L. Sharma}, Wave Motion 59, 52--68 (2015; Zbl 1467.35111) Full Text: DOI
Friedrich, Manuel; Schmidt, Bernd On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. (English) Zbl 1332.74044 Netw. Heterog. Media 10, No. 2, 321-342 (2015). MSC: 74R10 49J45 70G75 PDFBibTeX XMLCite \textit{M. Friedrich} and \textit{B. Schmidt}, Netw. Heterog. Media 10, No. 2, 321--342 (2015; Zbl 1332.74044) Full Text: DOI arXiv
Sharma, Basant Lal Near-tip field for diffraction on square lattice by rigid constraint. (English) Zbl 1327.78013 Z. Angew. Math. Phys. 66, No. 5, 2719-2740 (2015). MSC: 78A45 39A14 47B35 PDFBibTeX XMLCite \textit{B. L. Sharma}, Z. Angew. Math. Phys. 66, No. 5, 2719--2740 (2015; Zbl 1327.78013) Full Text: DOI
Sharma, Basant Lal Near-tip field for diffraction on square lattice by crack. (English) Zbl 1333.74049 SIAM J. Appl. Math. 75, No. 4, 1915-1940 (2015). Reviewer: Vladimir Čadež (Beograd) MSC: 74J20 74S30 74G25 74G30 PDFBibTeX XMLCite \textit{B. L. Sharma}, SIAM J. Appl. Math. 75, No. 4, 1915--1940 (2015; Zbl 1333.74049) Full Text: DOI
Sharma, Basant Lal Diffraction of waves on square lattice by semi-infinite crack. (English) Zbl 1322.78010 SIAM J. Appl. Math. 75, No. 3, 1171-1192 (2015). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78A45 39A14 47A40 74S20 74H10 74J20 47A68 78M20 PDFBibTeX XMLCite \textit{B. L. Sharma}, SIAM J. Appl. Math. 75, No. 3, 1171--1192 (2015; Zbl 1322.78010) Full Text: DOI Link
Friedrich, Manuel; Schmidt, Bernd An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem. (English) Zbl 1302.74144 J. Nonlinear Sci. 24, No. 1, 145-183 (2014). MSC: 74R10 49J45 74G75 PDFBibTeX XMLCite \textit{M. Friedrich} and \textit{B. Schmidt}, J. Nonlinear Sci. 24, No. 1, 145--183 (2014; Zbl 1302.74144) Full Text: DOI arXiv
Geers, M. G. D.; Peerlings, R. H. J.; Peletier, M. A.; Scardia, L. Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. (English) Zbl 1282.74067 Arch. Ration. Mech. Anal. 209, No. 2, 495-539 (2013). MSC: 74N05 49J45 74G65 82D25 74E15 PDFBibTeX XMLCite \textit{M. G. D. Geers} et al., Arch. Ration. Mech. Anal. 209, No. 2, 495--539 (2013; Zbl 1282.74067) Full Text: DOI arXiv Link
Meunier, Nicolas; Pantz, Olivier; Raoult, Annie Elastic limit of square lattices with three-point interactions. (English) Zbl 1253.82016 Math. Models Methods Appl. Sci. 22, No. 11, 1250032, 21 p. (2012). MSC: 82B20 81V45 74A50 82D20 PDFBibTeX XMLCite \textit{N. Meunier} et al., Math. Models Methods Appl. Sci. 22, No. 11, Article ID 1250032, 21 p. (2012; Zbl 1253.82016) Full Text: DOI
Zeman, Jan; Peerlings, Ron H. J.; Geers, Marc G. D. Non-local energetics of random heterogeneous lattices. (English) Zbl 1270.74056 J. Mech. Phys. Solids 59, No. 6, 1214-1230 (2011). MSC: 74E35 74Q20 PDFBibTeX XMLCite \textit{J. Zeman} et al., J. Mech. Phys. Solids 59, No. 6, 1214--1230 (2011; Zbl 1270.74056) Full Text: DOI arXiv Link
Alicandro, Roberto; Cicalese, Marco; Gloria, Antoine Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity. (English) Zbl 1294.74056 Arch. Ration. Mech. Anal. 200, No. 3, 881-943 (2011). MSC: 74Q10 37L60 60D05 60G35 74B20 PDFBibTeX XMLCite \textit{R. Alicandro} et al., Arch. Ration. Mech. Anal. 200, No. 3, 881--943 (2011; Zbl 1294.74056) Full Text: DOI Link
Schmidt, Bernd On the passage from atomic to continuum theory for thin films. (English) Zbl 1156.74028 Arch. Ration. Mech. Anal. 190, No. 1, 1-55 (2008). MSC: 74K35 74A25 PDFBibTeX XMLCite \textit{B. Schmidt}, Arch. Ration. Mech. Anal. 190, No. 1, 1--55 (2008; Zbl 1156.74028) Full Text: DOI
Giannoulis, Johannes; Herrmann, Michael; Mielke, Alexander Lagrangian and Hamiltonian two-scale reduction. (English) Zbl 1152.81449 J. Math. Phys. 49, No. 10, 103505, 42 p. (2008). MSC: 37K60 37N20 70H03 82B03 82C03 PDFBibTeX XMLCite \textit{J. Giannoulis} et al., J. Math. Phys. 49, No. 10, 103505, 42 p. (2008; Zbl 1152.81449) Full Text: DOI arXiv
Alicandro, Roberto; Braides, Andrea; Cicalese, Marco Continuum limits of discrete thin films with superlinear growth densities. (English) Zbl 1148.49010 Calc. Var. Partial Differ. Equ. 33, No. 3, 267-297 (2008). MSC: 49J45 74K35 74B20 82B20 PDFBibTeX XMLCite \textit{R. Alicandro} et al., Calc. Var. Partial Differ. Equ. 33, No. 3, 267--297 (2008; Zbl 1148.49010) Full Text: DOI
Schmidt, Bernd Qualitative properties of a continuum theory for thin films. (English) Zbl 1142.74026 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 1, 43-75 (2008). MSC: 74K35 74A25 PDFBibTeX XMLCite \textit{B. Schmidt}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 1, 43--75 (2008; Zbl 1142.74026) Full Text: DOI EuDML
Ortner, Christoph; Süli, Endre Analysis of a quasicontinuum method in one dimension. (English) Zbl 1139.74004 ESAIM, Math. Model. Numer. Anal. 42, No. 1, 57-91 (2008). MSC: 74A25 74S99 PDFBibTeX XMLCite \textit{C. Ortner} and \textit{E. Süli}, ESAIM, Math. Model. Numer. Anal. 42, No. 1, 57--91 (2008; Zbl 1139.74004) Full Text: DOI EuDML
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis Atomistic to continuum limits for computational materials science. (English) Zbl 1144.82018 ESAIM, Math. Model. Numer. Anal. 41, No. 2, 391-426 (2007). Reviewer: Agneta Balint (Timişoara) MSC: 82B21 81V45 PDFBibTeX XMLCite \textit{X. Blanc} et al., ESAIM, Math. Model. Numer. Anal. 41, No. 2, 391--426 (2007; Zbl 1144.82018) Full Text: DOI Numdam EuDML
Martinsson, Per-Gunnar; Babuška, Ivo Mechanics of materials with periodic truss or frame micro-structures. (English) Zbl 1140.74532 Arch. Ration. Mech. Anal. 185, No. 2, 201-234 (2007). MSC: 74Q20 74A40 74E30 80A20 PDFBibTeX XMLCite \textit{P.-G. Martinsson} and \textit{I. Babuška}, Arch. Ration. Mech. Anal. 185, No. 2, 201--234 (2007; Zbl 1140.74532) Full Text: DOI
Braides, Andrea; Lew, Adrian J.; Ortiz, Michael Effective cohesive behavior of layers of interatomic planes. (English) Zbl 1093.74013 Arch. Ration. Mech. Anal. 180, No. 2, 151-182 (2006). MSC: 74E15 74G65 82D25 PDFBibTeX XMLCite \textit{A. Braides} et al., Arch. Ration. Mech. Anal. 180, No. 2, 151--182 (2006; Zbl 1093.74013) Full Text: DOI Link
Le Bris, Claude; Lions, Pierre-Louis From atoms to crystals: a mathematical journey. (English) Zbl 1136.81371 Bull. Am. Math. Soc., New Ser. 42, No. 3, 291-363 (2005). MSC: 81Q10 35B35 35J10 35J60 35Q40 81Q05 81V55 82D25 PDFBibTeX XMLCite \textit{C. Le Bris} and \textit{P.-L. Lions}, Bull. Am. Math. Soc., New Ser. 42, No. 3, 291--363 (2005; Zbl 1136.81371) Full Text: DOI
Le Dret, H.; Lewandowski, R.; Priour, D.; Chagneau, F. Numerical simulation of a cod end net. I: Equilibrium in a uniform flow. (English) Zbl 1060.74026 J. Elasticity 76, No. 2, 139-162 (2004). MSC: 74G65 74B20 PDFBibTeX XMLCite \textit{H. Le Dret} et al., J. Elasticity 76, No. 2, 139--162 (2004; Zbl 1060.74026) Full Text: DOI
Alicandro, Roberto; Focardi, Matteo; Gelli, Maria Stella Finite-difference approximation of energies in fracture mechanics. (English) Zbl 1072.49020 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 3, 671-709 (2000). Reviewer: Fabián Flores-Bazan (Concepción) MSC: 49M25 49J45 74R10 65N06 74S20 PDFBibTeX XMLCite \textit{R. Alicandro} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 3, 671--709 (2000; Zbl 1072.49020) Full Text: Numdam EuDML