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A direct approach to numerical homogenization in finite elasticity
1. | CERMICS, Ecole Nationale des Ponts et Chaussées & INRIA Rocquencourt, 6 & 8 Av. B. Pascal, 77455 Champs-sur-Marne, France |
[1] |
Shalela Mohd Mahali, Song Wang, Xia Lou. Determination of effective diffusion coefficients of drug delivery devices by a state observer approach. Discrete and Continuous Dynamical Systems - B, 2011, 16 (4) : 1119-1136. doi: 10.3934/dcdsb.2011.16.1119 |
[2] |
Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. Specified homogenization of a discrete traffic model leading to an effective junction condition. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2173-2206. doi: 10.3934/cpaa.2018104 |
[3] |
Guillaume Bal. Homogenization in random media and effective medium theory for high frequency waves. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 473-492. doi: 10.3934/dcdsb.2007.8.473 |
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Sista Sivaji Ganesh, Vivek Tewary. Bloch wave approach to almost periodic homogenization and approximations of effective coefficients. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1989-2024. doi: 10.3934/dcdsb.2021119 |
[5] |
Yang Yang, Jian Zhai. Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticity. Inverse Problems and Imaging, 2019, 13 (6) : 1309-1325. doi: 10.3934/ipi.2019057 |
[6] |
Y. Efendiev, B. Popov. On homogenization of nonlinear hyperbolic equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 295-309. doi: 10.3934/cpaa.2005.4.295 |
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Agnes Lamacz, Ben Schweizer. Effective acoustic properties of a meta-material consisting of small Helmholtz resonators. Discrete and Continuous Dynamical Systems - S, 2017, 10 (4) : 815-835. doi: 10.3934/dcdss.2017041 |
[8] |
Annie Raoult. Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics. Communications on Pure and Applied Analysis, 2009, 8 (1) : 435-456. doi: 10.3934/cpaa.2009.8.435 |
[9] |
Irena Lasiecka, W. Heyman. Asymptotic behavior of solutions in nonlinear dynamic elasticity. Discrete and Continuous Dynamical Systems, 1995, 1 (2) : 237-252. doi: 10.3934/dcds.1995.1.237 |
[10] |
Michael Eden, Michael Böhm. Homogenization of a poro-elasticity model coupled with diffusive transport and a first order reaction for concrete. Networks and Heterogeneous Media, 2014, 9 (4) : 599-615. doi: 10.3934/nhm.2014.9.599 |
[11] |
Lorena Bociu, Jean-Paul Zolésio. Existence for the linearization of a steady state fluid/nonlinear elasticity interaction. Conference Publications, 2011, 2011 (Special) : 184-197. doi: 10.3934/proc.2011.2011.184 |
[12] |
Jean Louis Woukeng. $\sum $-convergence and reiterated homogenization of nonlinear parabolic operators. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1753-1789. doi: 10.3934/cpaa.2010.9.1753 |
[13] |
Mogtaba Mohammed, Mamadou Sango. Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing. Networks and Heterogeneous Media, 2019, 14 (2) : 341-369. doi: 10.3934/nhm.2019014 |
[14] |
Irena PawŃow, Wojciech M. Zajączkowski. Global regular solutions to three-dimensional thermo-visco-elasticity with nonlinear temperature-dependent specific heat. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1331-1372. doi: 10.3934/cpaa.2017065 |
[15] |
Rita Ferreira, Elvira Zappale. Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1747-1793. doi: 10.3934/cpaa.2020072 |
[16] |
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 |
[17] |
Anna Marciniak-Czochra, Andro Mikelić. A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium. Discrete and Continuous Dynamical Systems - S, 2014, 7 (5) : 1065-1077. doi: 10.3934/dcdss.2014.7.1065 |
[18] |
Markus Gahn, Maria Neuss-Radu, Peter Knabner. Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface. Networks and Heterogeneous Media, 2018, 13 (4) : 609-640. doi: 10.3934/nhm.2018028 |
[19] |
Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks and Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61 |
[20] |
Frédéric Legoll, William Minvielle. Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 1-27. doi: 10.3934/dcdss.2015.8.1 |
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