1 |
Arsigny, V., Fillard, P., Pennec, X. and Ayache, N. (2006), "Geometric means in a novel vector space structure on symmetric positive-definite matrices", SIAM J. Matr. Analy. Appl.
|
2 |
Asokan, B. and Zabaras, N. (2006), "A stochastic variational multiscale method for diffusion in heterogeneous random media", J. Comput. Phys., 654-676.
|
3 |
Bobrowski, A. (2005), Functional Analysis for Probability and Stochastic Processes, Cambridge, Cambridge University Press.
|
4 |
Brady, L., Arwade, S., Corr, D., Gutierrez, M., Breysse, D., Grigoriu, M. and Zabaras, N. (2006), "Probability and materials: From nano-to macro-scale: A summary", Probab. Eng. Mech., 193-199.
|
5 |
Clement, A., Soize, C. and Yvonnet, J. (2013), "Uncertainity quantification in computational stochastic multiscale analysis of nonlinear elastic materials", Comput. Meth. Appl. Mech. Eng., 61-82.
|
6 |
Del Maso, G., De Simone, A. and Mora, M. (2006), "Quasistatic evolution problems for linearly elastic perfectly plastic materials", Arch. Rat. Mech. Analy., 237-291.
|
7 |
Evensen, G. (2009), Data Assimilation-The Ensemble Kalman Filter, Berlin, Springer.
|
8 |
Demmie, P. and Ostaja-Starzewski, M. (2015), "Local and non-local material models,spatial randomness and impact loading", Arch. Appl. Mech.
|
9 |
Do, X.N., Ibrahimbegovic, A. and Brancherie, D. "Localized failure in damage dynamics", Coupled Syst. Mech., 4, 211-235.
|
10 |
Do, X.N., Ibrahimbegovic, A. and Brancherie, D. (2015), "Combined hardening and localized failure with softening plasticity in dynamics", Coupled Syst. Mech., 4, 115-136.
DOI
|
11 |
Gelman, A., Carlin, J., Stern, H. and Rubin, D. (2014), Bayesian Data Analysis, Boca Raton, Taylor and Francis.
|
12 |
Ghanem, R. and Das, S. (2011), Stochastic Upscaling for Inelastic Material Behavior from Limited Experimental Data, Computational Methods for Microstructure-Property Relationships, Springer, Berlin.
|
13 |
Han, W. and Daya Reddy, B. (2013), Plasticity, Mathematical Theory and Numerical Analysis, Springer Verlag, New York, U.S.A.
|
14 |
Gorguluarslan, R. and Choi, S.K. (2014), "A simulation based upscaling technique for multiscale modeling of engineering systems under uncertainity", J. Multisc. Comput. Eng., 549-566.
|
15 |
Halpen, B. and Nguyen, Q. (1974), "Plastic and visco-plastic materials with generalized potential", Mech. Res. Commun., 43-47.
|
16 |
Halpen, B. and Nguyen, Q. (1975), "Sur les materiaux standard generalises", J. de Mecan., 39-63.
|
17 |
Hawkins-Daarud, A., Prudhomme, S., Van der Zee, K. and Oden, J. (2013), "Bayesian calibration, validation and uncertainity quantification of diffuse interface models of tumor growth", J. Math. Biol., 1457-1485.
|
18 |
Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics, Springer, Berlin.
|
19 |
Ibrahimbegovic, A., Gharzeddine, F. and Chorfi, L. (1998), "Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation", J. Numer. Meth. Eng., 1499-1535.
|
20 |
Ibrahimbegovic, A. and Matthies, H.G. (2012), "Probabilistic multiscale analysis of inelastic localized failure in solid mechanics", Comput. Assist. Meth. Eng. Sci., 277-304.
|
21 |
Ibrahimbegovic, A., Markovic, D. and Gatuingt, F. (2003). "Constitutuve model of coupled damageplasticity and its finte element implementation", Rev. Europeenn. Des Elem., 381-405.
|
22 |
Kaipio, J. and Somersalo, E. (2004), Statistical and Computational Inverse Problems, Springer, Berlin.
|
23 |
Luenberger, D. (1969), Optimization by Vector Space Methods, John Wiley and Sons, Chichester.
|
24 |
Kennedy, M. and O'Hagan, A. (2001), "Bayesian calibration of computer models", J. Roy. Stat. Ser. B, 425-464.
|
25 |
Koutsourelakis, P. (2007), "Stochastic upscaling in solid mechanics: An exercise in machine learning", J. Comput. Physi., 301-325.
|
26 |
Liu, Y., Steven Greene, M., Chen, W., Dikin, D. and Liu, W. (2013), "Computational microstructure characterization and reconstruction for stochastc multiscale material design", Comput. Aid. Des., 65-76.
|
27 |
Markovic, D. and Ibrahimbegovic, A. (2006), "Complementary energy based FE modeling of coupled elasto-plastic and damage behavior for continuum microstructure compurtations", Comput. Meth. Appl. Mech. Eng., 5077-5093.
|
28 |
Matthies, H.G. (1991), "Computation of constitutive response", In P. Wriggers, and W. Wagner, Nonlinear Computational Mechanics: State of the Art, Springer Verlag Berlin, Heidelberg.
|
29 |
Matthies, H.G. (2007), "Uncertainity quantification with stochastic finite elements", Encyclop. Comput. Mech.
|
30 |
Matthies, H.G. and Ibrahimbegovic, A. (2014), "Stochastic multiscale coupling of inelastic processes in solid mechanics. In M. Papadrakakis, and G. Stefanou", Multiscale Modelling and Uncertainity Quantification of Materials and Structures, Springer, Berlin.
|
31 |
Matthies, H.G., Zander, E., Rosic, B., Litvinenko, A. and Pajonk, O. (2016), "Inverse problems in a Bayesian setting", In A. Ibrahimbegovic, Computational Methods for Solids and Fluids-Multiscale Analysis, Probability Aspects, and Model Reduction, Springer, Berlin.
|
32 |
Ngo, V.M., Ibrahimbegovic, A. and Brancherie, D. (2014), "Stress-resultant model and finite element analysis of reinforced concrete frames under combined mechanical and thermal loads", Coupled Syst. Mech., 3, 111-144.
DOI
|
33 |
Papoulis, A. (1991), Probability Random Variables, and Stochastic Processes, McGraw-Hill, New York, U.S.A.
|
34 |
Ngo, V.M., Ibrahimbegovic, A. and Hajdo, E. (2014), "Nonlinear instability problems including localized plastic failure and large deformations for extreme thermomechanical load", Coupled Syst. Mech., 3, 89-110.
DOI
|
35 |
Nguyen, Q. (1977), "On the elastic plastic initial-boundary value problem and its numerical implementation", J. Numer. Meth. Eng., 817-832.
|
36 |
Pajonk, O., Rosic, B., Litvinenko, A. and Matthies, H.M. (2012), "A deterministic filter for non- Gaussian Bayesian estimation-applications to dynamical system estimation with noisy measurements", Phys. D, 775-788.
|
37 |
Pian, T. and Sumihara, K. (1984), "Rational approach for assumed stress finite elements", J. Numer. Meth. Eng., 1685-1695.
|
38 |
Rosic, B. and Matthies, H.G. (2014), "Variational theory and computations in stochastic plasticity", Arch. Comput. Meth. Eng., 457-509.
|
39 |
Rosic, B., Litvinenko, A., Pajonk, O. and Matthies, H.G. (2012), "Sampling-free linear Bayesian update of polynomial chaos representation", J. Comput. Phys., 5761-5787.
|
40 |
Rosic, B., Sykora, J., Pajonk, O., Kucerova, A. and Matthies, H.G. (2016), "Comparison of numerical approaches to Bayesian updating", In A. Ibrahimbegovic, Comutational Methods for Solids and Fluids-Multiscale Analysis, Probability Aspects and Model Reduction, Springer, Berlin.
|
41 |
Starzewski, M. (2008), Microstructural Randomness and Scaling in Mechanics of Materials, Boca Raton, Chapman and Hall.
|
42 |
Tarantola, A. (2005), Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, U.S.A.
|
43 |
Stefanou, G., Savvas, D. and Papadrakakis, M. (2015), "Stochastic finite element analysis of composite structure based on material microstructure", Compos. Struct., 384-392.
|
44 |
Steven Greene, M., Liu, Y., Chen, W. and Liu, W. (2011), "Computational uncertainity analysis in multiresolution material via stochastic constitutive theory", Comput. Meth. Appl. Mech. Eng., 309-325.
|
45 |
Suquet, P. and Lahellec, N. (2014), Elasto-Plasticity of Heterogeneous Materials at Different Scales, Procedia IUTAM.
|
46 |
Yvonnet, J. and Bonnet, G. (2014), "A consistent nonlocal scheme based on filter for the homogenenization of heterogeneous linear materials with non-separated scales", J. Sol. Struct., 196-209.
|