Yin, Huiming; Liu, Chao Anisotropy and asymmetry of the elastic tensor of lattice materials. (English) Zbl 07786979 J. Elasticity 154, No. 5, 659-691 (2023). MSC: 74B10 74B20 74Q15 PDFBibTeX XMLCite \textit{H. Yin} and \textit{C. Liu}, J. Elasticity 154, No. 5, 659--691 (2023; Zbl 07786979) Full Text: DOI
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
Sfyris, D.; Sfyris, G. I. Linear theory of 2 and 3-monoatomic multilattices: solutions of the shift vector equation. (English) Zbl 1523.74016 Contin. Mech. Thermodyn. 35, No. 5, 1927-1942 (2023). MSC: 74E15 74B05 PDFBibTeX XMLCite \textit{D. Sfyris} and \textit{G. I. Sfyris}, Contin. Mech. Thermodyn. 35, No. 5, 1927--1942 (2023; Zbl 1523.74016) Full Text: DOI
Bishara, Dana; Li, Shaofan A machine-learning aided multiscale homogenization model for crystal plasticity: application for face-centered cubic single crystals. (English) Zbl 1522.74110 Comput. Mech. 72, No. 1, 77-93 (2023). MSC: 74S99 74S05 74E15 74C20 74Q15 74A25 68T05 PDFBibTeX XMLCite \textit{D. Bishara} and \textit{S. Li}, Comput. Mech. 72, No. 1, 77--93 (2023; Zbl 1522.74110) Full Text: DOI
Baggio, R.; Salman, O. U.; Truskinovsky, L. Homogeneous nucleation of dislocations as a pattern formation phenomenon. (English) Zbl 1517.74016 Eur. J. Mech., A, Solids 99, Article ID 104897, 17 p. (2023). MSC: 74E15 74C99 74A60 PDFBibTeX XMLCite \textit{R. Baggio} et al., Eur. J. Mech., A, Solids 99, Article ID 104897, 17 p. (2023; Zbl 1517.74016) Full Text: DOI arXiv
DiCarlo, Antonio; Bonella, Sara; Ferrario, Mauro; Ciccotti, Giovanni Continuum mechanics from molecular dynamics via adiabatic time and length scale separation. (English) Zbl 1515.82108 Lett. Math. Phys. 113, No. 1, Paper No. 24, 48 p. (2023). MSC: 82C21 82M37 PDFBibTeX XMLCite \textit{A. DiCarlo} et al., Lett. Math. Phys. 113, No. 1, Paper No. 24, 48 p. (2023; Zbl 1515.82108) Full Text: DOI
Hudson, Thomas; Rindler, Filip Elasto-plastic evolution of single crystals driven by dislocation flow. (English) Zbl 1524.74087 Math. Models Methods Appl. Sci. 32, No. 5, 851-910 (2022). MSC: 74E15 74C15 74A60 PDFBibTeX XMLCite \textit{T. Hudson} and \textit{F. Rindler}, Math. Models Methods Appl. Sci. 32, No. 5, 851--910 (2022; Zbl 1524.74087) Full Text: DOI arXiv
Buze, Maciej; Woolley, Thoms E.; Mihai, Angela A stochastic framework for atomistic fracture. (English) Zbl 1486.74007 SIAM J. Appl. Math. 82, No. 2, 526-548 (2022). MSC: 74A45 74A25 74S60 PDFBibTeX XMLCite \textit{M. Buze} et al., SIAM J. Appl. Math. 82, No. 2, 526--548 (2022; Zbl 1486.74007) Full Text: DOI arXiv
Luo, Tao; Xiang, Yang; Yang, Jerry Zhijian Finite temperatue Cauchy-Born rule and stability of crystalline solids with point defects. (English) Zbl 1483.74021 Multiscale Model. Simul. 19, No. 4, 1710-1735 (2021). MSC: 74E15 74A25 74F05 74B20 PDFBibTeX XMLCite \textit{T. Luo} et al., Multiscale Model. Simul. 19, No. 4, 1710--1735 (2021; Zbl 1483.74021) Full Text: DOI
Andrews, Bartholomew; Conduit, Gareth Absence of diagonal force constants in cubic Coulomb crystals. (English) Zbl 1472.82022 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2244, Article ID 20200518, 16 p. (2020). MSC: 82C22 82C20 PDFBibTeX XMLCite \textit{B. Andrews} and \textit{G. Conduit}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2244, Article ID 20200518, 16 p. (2020; Zbl 1472.82022) Full Text: DOI arXiv
Amendola, Ada On the optimal prediction of the stress field associated with discrete element models. (English) Zbl 1477.74002 J. Optim. Theory Appl. 187, No. 3, 613-629 (2020). MSC: 74A10 65N30 82B21 PDFBibTeX XMLCite \textit{A. Amendola}, J. Optim. Theory Appl. 187, No. 3, 613--629 (2020; Zbl 1477.74002) Full Text: DOI
Uchimali, Mahendaran; Rao, Balkrishna C.; Vedantam, Srikanth Constitutively informed multi-body interactions for lattice particle models. (English) Zbl 1442.74012 Comput. Methods Appl. Mech. Eng. 366, Article ID 113052, 18 p. (2020). MSC: 74A25 65M75 65N75 76M28 PDFBibTeX XMLCite \textit{M. Uchimali} et al., Comput. Methods Appl. Mech. Eng. 366, Article ID 113052, 18 p. (2020; Zbl 1442.74012) Full Text: DOI
Yan, Jiale; Li, Shaofan; Zhang, A-Man; Kan, Xingyu; Sun, Peng-Nan Updated Lagrangian particle hydrodynamics (ULPH) modeling and simulation of multiphase flows. (English) Zbl 1452.76186 J. Comput. Phys. 393, 406-437 (2019). MSC: 76M28 65M75 76N06 76D45 76T10 PDFBibTeX XMLCite \textit{J. Yan} et al., J. Comput. Phys. 393, 406--437 (2019; Zbl 1452.76186) Full Text: DOI
Friedrich, Manuel; Mainini, Edoardo; Piovano, Paolo; Stefanelli, Ulisse Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule. (English) Zbl 1419.74056 Arch. Ration. Mech. Anal. 231, No. 1, 465-517 (2019). MSC: 74A60 82D80 PDFBibTeX XMLCite \textit{M. Friedrich} et al., Arch. Ration. Mech. Anal. 231, No. 1, 465--517 (2019; Zbl 1419.74056) Full Text: DOI arXiv
James, Richard D. Materials from mathematics. (English) Zbl 1409.74035 Bull. Am. Math. Soc., New Ser. 56, No. 1, 1-28 (2019). Reviewer: Alexandre Danescu (Lyon) MSC: 74N30 74N05 74N20 74G65 82B26 74-02 PDFBibTeX XMLCite \textit{R. D. James}, Bull. Am. Math. Soc., New Ser. 56, No. 1, 1--28 (2019; Zbl 1409.74035) Full Text: DOI
Olson, Derek; Li, Xingjie; Ortner, Christoph; Van Koten, Brian Force-based atomistic/continuum blending for multilattices. (English) Zbl 1402.65136 Numer. Math. 140, No. 3, 703-754 (2018). MSC: 65N12 74S30 65N15 82D80 74M25 82D25 74E15 81V45 PDFBibTeX XMLCite \textit{D. Olson} et al., Numer. Math. 140, No. 3, 703--754 (2018; Zbl 1402.65136) Full Text: DOI arXiv Link
Delfani, M. R. Nonlinear elasticity of monolayer hexagonal crystals: theory and application to circular bulge test. (English) Zbl 1406.74101 Eur. J. Mech., A, Solids 68, 117-132 (2018). MSC: 74B20 74E15 PDFBibTeX XMLCite \textit{M. R. Delfani}, Eur. J. Mech., A, Solids 68, 117--132 (2018; Zbl 1406.74101) Full Text: DOI
Sfyris, D.; Sfyris, G. I. Influence of partial blistering on the global and the local stress and couple stress field for a monolayer graphene resting on substrate. (English) Zbl 1395.74058 Math. Mech. Solids 23, No. 4, 617-635 (2018). MSC: 74K35 74R99 PDFBibTeX XMLCite \textit{D. Sfyris} and \textit{G. I. Sfyris}, Math. Mech. Solids 23, No. 4, 617--635 (2018; Zbl 1395.74058) Full Text: DOI
Braides, Andrea; Kreutz, Leonard An integral-representation result for continuum limits of discrete energies with multibody interactions. (English) Zbl 1386.49017 SIAM J. Math. Anal. 50, No. 2, 1485-1520 (2018). MSC: 49J45 74Q99 49J27 PDFBibTeX XMLCite \textit{A. Braides} and \textit{L. Kreutz}, SIAM J. Math. Anal. 50, No. 2, 1485--1520 (2018; Zbl 1386.49017) Full Text: DOI arXiv
Desmoulins, A.; Kochmann, D. M. Local and nonlocal continuum modeling of inelastic periodic networks applied to stretching-dominated trusses. (English) Zbl 1439.74330 Comput. Methods Appl. Mech. Eng. 313, 85-105 (2017). MSC: 74Q10 74S05 74E30 PDFBibTeX XMLCite \textit{A. Desmoulins} and \textit{D. M. Kochmann}, Comput. Methods Appl. Mech. Eng. 313, 85--105 (2017; Zbl 1439.74330) Full Text: DOI
Sfyris, Dimitris Twinning mechanism and habit lines in monolayer-thick free-standing graphene: theoretical predictions. (English) Zbl 1423.74718 Int. J. Eng. Sci. 113, 1-19 (2017). MSC: 74N05 74M25 82D25 PDFBibTeX XMLCite \textit{D. Sfyris}, Int. J. Eng. Sci. 113, 1--19 (2017; Zbl 1423.74718) Full Text: DOI
Braun, Julian Connecting atomistic and continuous models of elastodynamics. (English) Zbl 1372.35298 Arch. Ration. Mech. Anal. 224, No. 3, 907-953 (2017). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q74 74B20 74A25 35L20 PDFBibTeX XMLCite \textit{J. Braun}, Arch. Ration. Mech. Anal. 224, No. 3, 907--953 (2017; Zbl 1372.35298) Full Text: DOI arXiv
Sfyris, Dimitris Phonon, Cauchy-Born and homogenized stability criteria for a free-standing monolayer graphene at the continuum level. (English) Zbl 1406.74160 Eur. J. Mech., A, Solids 55, 134-148 (2016). MSC: 74E15 74B20 PDFBibTeX XMLCite \textit{D. Sfyris}, Eur. J. Mech., A, Solids 55, 134--148 (2016; Zbl 1406.74160) Full Text: DOI
Sfyris, Dimitris On configurational weak phase transitions in graphene. (English) Zbl 1355.82032 Contin. Mech. Thermodyn. 28, No. 4, 1093-1110 (2016). MSC: 82C26 PDFBibTeX XMLCite \textit{D. Sfyris}, Contin. Mech. Thermodyn. 28, No. 4, 1093--1110 (2016; Zbl 1355.82032) Full Text: DOI
Braun, Julian; Schmidt, Bernd Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory. (English) Zbl 1356.35239 Calc. Var. Partial Differ. Equ. 55, No. 5, Paper No. 125, 36 p. (2016). Reviewer: Adina Chirila (Brasov) MSC: 35Q74 74B20 35J57 35J62 PDFBibTeX XMLCite \textit{J. Braun} and \textit{B. Schmidt}, Calc. Var. Partial Differ. Equ. 55, No. 5, Paper No. 125, 36 p. (2016; Zbl 1356.35239) Full Text: DOI arXiv
Bergel, Guy L.; Li, Shaofan The total and updated Lagrangian formulations of state-based peridynamics. (English) Zbl 1398.74303 Comput. Mech. 58, No. 2, 351-370 (2016). MSC: 74S05 45A05 45K05 74A05 70S05 PDFBibTeX XMLCite \textit{G. L. Bergel} and \textit{S. Li}, Comput. Mech. 58, No. 2, 351--370 (2016; Zbl 1398.74303) Full Text: DOI
Kim, Hyun-Gyu A comparative study of hyperelastic and hypoelastic material models with constant elastic moduli for large deformation problems. (English) Zbl 1341.74151 Acta Mech. 227, No. 5, 1351-1362 (2016). MSC: 74S05 74B20 PDFBibTeX XMLCite \textit{H.-G. Kim}, Acta Mech. 227, No. 5, 1351--1362 (2016; Zbl 1341.74151) Full Text: DOI
Kumar, Ajeet; Kumar, Siddhant; Gupta, Prakhar A helical Cauchy-Born rule for special Cosserat rod modeling of nano and continuum rods. (English) Zbl 1338.74012 J. Elasticity 124, No. 1, 81-106 (2016). MSC: 74B20 74A25 74Q15 PDFBibTeX XMLCite \textit{A. Kumar} et al., J. Elasticity 124, No. 1, 81--106 (2016; Zbl 1338.74012) Full Text: DOI
Podolskaya, E. A.; Panchenko, A. Yu.; Freidin, A. B.; Krivtsov, A. M. Loss of ellipticity and structural transformations in planar simple crystal lattices. (English) Zbl 1382.74012 Acta Mech. 227, No. 1, 185-201 (2016). MSC: 74A50 74N05 74N15 74B20 PDFBibTeX XMLCite \textit{E. A. Podolskaya} et al., Acta Mech. 227, No. 1, 185--201 (2016; Zbl 1382.74012) Full Text: DOI
Ulz, Manfred H. A multiscale molecular dynamics method for isothermal dynamic problems using the seamless heterogeneous multiscale method. (English) Zbl 1423.74037 Comput. Methods Appl. Mech. Eng. 295, 510-524 (2015). MSC: 74A25 74Q05 PDFBibTeX XMLCite \textit{M. H. Ulz}, Comput. Methods Appl. Mech. Eng. 295, 510--524 (2015; Zbl 1423.74037) Full Text: DOI
Kim, Wonbae; Chung, Hayoung; Cho, Maenghyo Anisotropic hyperelastic modeling for face-centered cubic and diamond cubic structures. (English) Zbl 1423.74197 Comput. Methods Appl. Mech. Eng. 291, 216-239 (2015). MSC: 74E15 74S05 PDFBibTeX XMLCite \textit{W. Kim} et al., Comput. Methods Appl. Mech. Eng. 291, 216--239 (2015; Zbl 1423.74197) Full Text: DOI
De Tommasi, D.; Puglisi, G.; Saccomandi, G. Multiscale mechanics of macromolecular materials with unfolding domains. (English) Zbl 1349.74285 J. Mech. Phys. Solids 78, 154-172 (2015). MSC: 74M25 74L15 92D20 PDFBibTeX XMLCite \textit{D. De Tommasi} et al., J. Mech. Phys. Solids 78, 154--172 (2015; Zbl 1349.74285) Full Text: DOI arXiv
Acharya, Amit; Fressengeas, Claude Continuum mechanics of the interaction of phase boundaries and dislocations in solids. (English) Zbl 1325.74116 Chen, Gui-Qiang G. (ed.) et al., Differential geometry and continuum mechanics. Proceedings of the ICMS workshop, Edinburgh, UK, June 17–21, 2013. Cham: Springer (ISBN 978-3-319-18572-9/hbk; 978-3-319-18573-6/ebook). Springer Proceedings in Mathematics & Statistics 137, 123-165 (2015). MSC: 74N20 PDFBibTeX XMLCite \textit{A. Acharya} and \textit{C. Fressengeas}, Springer Proc. Math. Stat. 137, 123--165 (2015; Zbl 1325.74116) Full Text: DOI arXiv
Endres, F.; Steinmann, P. An extended molecular statics algorithm simulating the electromechanical continuum response of ferroelectric materials. (English) Zbl 1309.74027 Comput. Mech. 54, No. 6, 1515-1527 (2014). MSC: 74F15 74A25 74N30 PDFBibTeX XMLCite \textit{F. Endres} and \textit{P. Steinmann}, Comput. Mech. 54, No. 6, 1515--1527 (2014; Zbl 1309.74027) Full Text: DOI
Kim, W. K.; Luskin, M.; Perez, D.; Voter, A. F.; Tadmor, E. B. Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics. (English) Zbl 1303.74007 J. Mech. Phys. Solids 63, 94-112 (2014). MSC: 74A45 74S05 74S60 PDFBibTeX XMLCite \textit{W. K. Kim} et al., J. Mech. Phys. Solids 63, 94--112 (2014; Zbl 1303.74007) Full Text: DOI
El Kass, D.; Monneau, R. Atomic to continuum passage for nanotubes: a discrete Saint-Venant principle and error estimates. (English) Zbl 1292.82052 Arch. Ration. Mech. Anal. 213, No. 1, 25-128 (2014). MSC: 82D80 81V45 74G50 PDFBibTeX XMLCite \textit{D. El Kass} and \textit{R. Monneau}, Arch. Ration. Mech. Anal. 213, No. 1, 25--128 (2014; Zbl 1292.82052) Full Text: DOI
Chen, Xian; Srivastava, Vijay; Dabade, Vivekanand; James, Richard D. Study of the cofactor conditions: conditions of supercompatibility between phases. (English) Zbl 1294.74050 J. Mech. Phys. Solids 61, No. 12, 2566-2587 (2013). MSC: 74N05 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Mech. Phys. Solids 61, No. 12, 2566--2587 (2013; Zbl 1294.74050) Full Text: DOI arXiv
Lu, Jianfeng; Ming, Pingbing Convergence of a force-based hybrid method in three dimensions. (English) Zbl 1393.74166 Commun. Pure Appl. Math. 66, No. 1, 83-108 (2013). MSC: 74Q15 74A25 PDFBibTeX XMLCite \textit{J. Lu} and \textit{P. Ming}, Commun. Pure Appl. Math. 66, No. 1, 83--108 (2013; Zbl 1393.74166) Full Text: DOI Link
Schmidt, Bernd; Fraternali, Fernando Universal formulae for the limiting elastic energy of membrane networks. (English) Zbl 1244.74080 J. Mech. Phys. Solids 60, No. 1, 172-180 (2012). MSC: 74K15 PDFBibTeX XMLCite \textit{B. Schmidt} and \textit{F. Fraternali}, J. Mech. Phys. Solids 60, No. 1, 172--180 (2012; Zbl 1244.74080) Full Text: DOI arXiv
Fraternali, F.; Lorenz, C. D.; Marcelli, G. On the estimation of the curvatures and bending rigidity of membrane networks via a local maximum-entropy approach. (English) Zbl 1238.92008 J. Comput. Phys. 231, No. 2, 528-540 (2012). MSC: 92C40 92C05 94A17 65C20 PDFBibTeX XMLCite \textit{F. Fraternali} et al., J. Comput. Phys. 231, No. 2, 528--540 (2012; Zbl 1238.92008) Full Text: DOI arXiv
Pacheco, A. A.; Batra, R. C. Instabilities in shear and simple shear deformations of gold crystals. (English) Zbl 1172.74020 J. Mech. Phys. Solids 56, No. 11, 3116-3143 (2008). MSC: 74G60 74E15 74A25 PDFBibTeX XMLCite \textit{A. A. Pacheco} and \textit{R. C. Batra}, J. Mech. Phys. Solids 56, No. 11, 3116--3143 (2008; Zbl 1172.74020) Full Text: DOI
Braides, Andrea; Truskinovsky, Lev Asymptotic expansions by \(\Gamma \)-convergence. (English) Zbl 1160.74363 Contin. Mech. Thermodyn. 20, No. 1, 21-62 (2008). MSC: 74G65 74Q05 PDFBibTeX XMLCite \textit{A. Braides} and \textit{L. Truskinovsky}, Contin. Mech. Thermodyn. 20, No. 1, 21--62 (2008; Zbl 1160.74363) Full Text: DOI