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On the derivation of linear elasticity from atomistic models
1. | Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching, Germany |
[1] |
Marco Cicalese, Antonio DeSimone, Caterina Ida Zeppieri. Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers. Networks and Heterogeneous Media, 2009, 4 (4) : 667-708. doi: 10.3934/nhm.2009.4.667 |
[2] |
Manuel Friedrich, Bernd Schmidt. On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. Networks and Heterogeneous Media, 2015, 10 (2) : 321-342. doi: 10.3934/nhm.2015.10.321 |
[3] |
Julian Braun, Bernd Schmidt. On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Networks and Heterogeneous Media, 2013, 8 (4) : 879-912. doi: 10.3934/nhm.2013.8.879 |
[4] |
Andrea Braides, Margherita Solci, Enrico Vitali. A derivation of linear elastic energies from pair-interaction atomistic systems. Networks and Heterogeneous Media, 2007, 2 (3) : 551-567. doi: 10.3934/nhm.2007.2.551 |
[5] |
Lucia Scardia, Anja Schlömerkemper, Chiara Zanini. Towards uniformly $\Gamma$-equivalent theories for nonconvex discrete systems. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 661-686. doi: 10.3934/dcdsb.2012.17.661 |
[6] |
Gianni Dal Maso, Flaviana Iurlano. Fracture models as $\Gamma$-limits of damage models. Communications on Pure and Applied Analysis, 2013, 12 (4) : 1657-1686. doi: 10.3934/cpaa.2013.12.1657 |
[7] |
Uri M. Ascher. Discrete processes and their continuous limits. Journal of Dynamics and Games, 2020, 7 (2) : 123-140. doi: 10.3934/jdg.2020008 |
[8] |
Zhuchun Li, Yi Liu, Xiaoping Xue. Convergence and stability of generalized gradient systems by Łojasiewicz inequality with application in continuum Kuramoto model. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 345-367. doi: 10.3934/dcds.2019014 |
[9] |
Claudio Canuto, Anna Cattani. The derivation of continuum limits of neuronal networks with gap-junction couplings. Networks and Heterogeneous Media, 2014, 9 (1) : 111-133. doi: 10.3934/nhm.2014.9.111 |
[10] |
Julián Fernández Bonder, Analía Silva, Juan F. Spedaletti. Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2125-2140. doi: 10.3934/dcds.2020355 |
[11] |
Gianni Dal Maso. Ennio De Giorgi and $\mathbf\Gamma$-convergence. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1017-1021. doi: 10.3934/dcds.2011.31.1017 |
[12] |
Alexander Mielke. Deriving amplitude equations via evolutionary $\Gamma$-convergence. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2679-2700. doi: 10.3934/dcds.2015.35.2679 |
[13] |
Daniele Boffi, Franco Brezzi, Michel Fortin. Reduced symmetry elements in linear elasticity. Communications on Pure and Applied Analysis, 2009, 8 (1) : 95-121. doi: 10.3934/cpaa.2009.8.95 |
[14] |
Tobias Wichtrey. Harmonic limits of dynamical systems. Conference Publications, 2011, 2011 (Special) : 1432-1439. doi: 10.3934/proc.2011.2011.1432 |
[15] |
Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks and Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661 |
[16] |
Yanxing Cui, Chuanlong Wang, Ruiping Wen. On the convergence of generalized parallel multisplitting iterative methods for semidefinite linear systems. Numerical Algebra, Control and Optimization, 2012, 2 (4) : 863-873. doi: 10.3934/naco.2012.2.863 |
[17] |
Yachun Li, Xucai Ren. Non-relativistic global limits of the entropy solutions to the relativistic Euler equations with $\gamma$-law. Communications on Pure and Applied Analysis, 2006, 5 (4) : 963-979. doi: 10.3934/cpaa.2006.5.963 |
[18] |
Cornel Marius Murea, Dan Tiba. Topological optimization and minimal compliance in linear elasticity. Evolution Equations and Control Theory, 2020, 9 (4) : 1115-1131. doi: 10.3934/eect.2020043 |
[19] |
Sylvia Serfaty. Gamma-convergence of gradient flows on Hilbert and metric spaces and applications. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1427-1451. doi: 10.3934/dcds.2011.31.1427 |
[20] |
Antonio De Rosa, Domenico Angelo La Manna. A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties. Communications on Pure and Applied Analysis, 2021, 20 (5) : 2101-2116. doi: 10.3934/cpaa.2021059 |
2020 Impact Factor: 1.213
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