Partial List of Reprents and Preprints

  1. Quasistatic fracture evolution. ArXive for Mathematics (2022) arXiv:2212.08753. (With Debdeep Bhattacharya and Patrick Diehl.) (page)

  2. Angles between subspaces and nearly optimal approximation in GFEM. Computer Methods in Applied Mechanics and Engineering. 402 (2022): 115628. (With Paul Sinz and Michael Stuebner.) (page)

  3. A fracture multiscale model for peridynamic enrichment within the partition of unity method. Advances in Engineering Software. 176 2023. (With Matthias Birner, Patrick Diehl, and Mark Alexander Schwitzer.) (page)

  4. Controlling the dispersion of meta-materials in three dimensions. Proceedings of the Royal Society A. 478, no. 2263 (2022).. (With Abiti Adili, Yue Chen, and Shawn Walker.) (page)

  5. Bloch spectra for high contrast elastic media. Journal of Differential Equations. 332 (2022): 1–49. (With Ruchira Perrra.) (page) (PDF)

  6. Bloch waves in high contrast electro-magnetic materials. European Society of Applied and Industrial Mathematics: Mathemtical Modeling and Numerical Analysis. 56.5 (2022): 1483-1519. (With Robert Viator, Silvia Jimenez Bolanos, and Abiti Adili.) (page) (PDF)

  7. Quasistatic fracture using nonlinear-nonlocal elastostatics with explicit tangent stiffness. Int. J. Numerical Methods in Engineering. (2022) 23:18 4183--4208. (With Patrick Diehl.) (page)

  8. Simulating grain shape effects and damage in grannular media using PeriDEM, SIAM Journal on Computing. 45(1):B1-B26 (2023). (With Debdeep Bhattacharya.) (page)

  9. Quasistatic evolution with unstable forces, Multiscale Modeling and Simulation, Accepted for Publication (2023). (With Debdeep Bhattacharya.) (PDF)

  10. Peridynamics- based discrete element method (PeriDEM) model of granular systems involving breakage of arbitrairly shaped particles, Journal of the Mechanics and Physics of Solids. (2021) 151 no. 104376. (With Prashant K. Jha, Prathemesh S. Desai, and Debdeep Bhattacharya.) (page)

  11. A comparative review of peridynamics and phase-field models for engineering fracture mechanics, Computational Mechanics, (2022) 69: 1259--1293. (With Patrick Diehl, Thomas Wick, and Mayank Tyagi .) (page)

  12. Lorentz resonance in the homogenization of plasmonic crystals, Proceedings of the Royal Society of London A 477 (2021). (With Wei Li and Matthias Meyer.) (PDF)

  13. Nonlocal elastodynamics and fracture, Nonlinear Differential Equations and Applications NoDEA 28, Article number: 23 (2021). (With Prashant Jha.), https://doi.org/10.1007/s00030-021-00683-x (PDF) (page)

  14. Kinetic relations and local energy balance for LEFM from a nonlocal peridynamic model, International Journal of Fracture, (2020) 226: 81-95, DOI: 10.1007/s10704-020-00480-0. (With Prashant Jha.) (PDF) (page)

  15. Numerical convergence of finite difference approximations for state based peridynamic fracture models. Computer Methods in Applied Mechanics and Engineering, 351 (2019), pp. 184-225. (With Prashant Jha.) (PDF) (page)

  16. Finite Element Convergence for State‐Based Peridynamic Fracture Models. Communications on Applied Mathematics and Computation. 31 May 2019 (With Prashant Jha.) (PDF) (page)

  17. Complex Fracture Nucleation and Evolution with Nonlocal Elastodynamics Journal of Peridynamics and Nonlocal Modeling. 5 April 2019. (With Richard Lehoucq and Prashant Jha.) (PDF)

  18. Controlling refraction using sub-wavelength resonators. Appl. Sci. 2018, 8(10), 1942; doi:10.3390/app8101942 (With Yue Chen.) (PDF)

  19. Free damage propagation with memory. Journal of Elasticity. Published March 14, 2018. (With Eyad Said and Prashant Jha.) (PDF)

  20. Numerical analysis of nonlocal fracture models in Holder space. SIAM J. Numer. Anal. 56 (2018), pp. 906-941. (With Prashant Jah.) (PDF)

  21. Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics. International Journal of Numerical Methods in Engineering. Published March 12, 2018. (With Prashant Jha.) (PDF)

  22. Effective Maxwell's equations for perfectly conducting split ring resonators. Archive for Rational Mechanics and Analysis. Published March 22, 2018 (With Ben Schweizer.) (PDF)

  23. Novel metamaterial surfaces from perfectly conducting subwavelength corrugation. SIAM Journal on Applied Mathematics, 77, Issue 4, 2017, pp. 1269-1291. (With Anthony Polizzi and Lokendra Thakur.) (PDF)

  24. Creating Band Gaps in Periodic Media. SIAM Multiscale Modeling and Simulation, 15, 2017, pp. 1612-1650. (With Robert Viator.) (PDF)

  25. Cohesive Dynamics and Brittle Fracture. Journal of Elasticity, 124, Issue 2, 2016, pp. 143-191. (PDF)

  26. Erratum: Cohesive Dynamics and Brittle Fracture. Journal of Elasticity, 125, Issue 1, 2016, pp. 137. (PDF)

  27. Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures. Journal of Computational Physics, 325, (2016), pp. 38-52. (With Paul Sinz and Michael Stuebner.) (PDF)

  28. Multiscale Analysis of an Abstract Evolution Equation with Applications to Nonlocal Models for Heterogeneous Media. ESAIM: M2AN, 50 Number 5, 2016, pp. 1425-1455. (With Qiang Du and Tadele Mengesha.) (PDF)

  29. Complex Fracture Nucleation and Evolution with Nonlocal Elastodynamics. February 2, 2015 (With Stewart Silling and Richard Lehoucq.) arXiv:1602.00247(Link to arXiv)

  30. Bloch Waves in Crystals and Periodic High Contrast Media. ESAIM M2AN. June 16, 2016. (With Robert Viator.) (PDF)

  31. Peridynamics, Fracture, and Nonlocal Continuum Models. SIAM News, Volume 47, Number 3, April 2014. (With Qiang Du.) (Link to SIAM News)

  32. Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics. Journal of Elasticity, 117, Issue 1, 2014 pp 21-50. (PDF)

  33. Tuning gain and bandwidth of traveling wave tubes using metamaterial beam-wave interaction structures. Journal of Applied Physics 116, 144504 (2014); doi: 10.1063/1.4897235 (PDF)

  34. Multiscale Methods for Engineering Double Negative Metamaterials. Photonics and Nanostructures - Fundamentals and Applications, 11 (2013) 442-452. (With Yue Chen.) (PDF)

  35. Resonance and Double Negative Behavior in Metamaterials. Archchive for Rational Mechanics and Analysis, 2013, Volume 209, Issue 3, pp 835-868. (With Yue Chen.) (Link)

  36. Double Negative Dispersion Relations from Coated Plasmonic Rods. (With Yue Chen). Multiscale Modeling and Simulation, SIAM 11 (2013) 191-212 (Link)

  37. Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method. (With Ivo Babuska and Xu Huang). Mathematical Modeling and Numerical Analysis (M2AN), 48 Number 2 (2014) 493-515. (PDF)

  38. Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems. (With Ivo Babuska). Multiscale Modeling and Simulation, SIAM 9 (2011) 373-406. (PDF)

  39. Tunable Double Negative Band Structure from Non-Magnetic Coated Rods. (With Yue Chen). New Journal of Physics Volume 12 August 2010. (Link)

  40. Correctors and field fluctuations for the pε(x)-Laplacian with rough exponents. J. Math. Anal. Appl. 372 (2010) 448-469. (With Silvia Jimenez). (PDF)

  41. Optimal lower bounds on the local stress inside random thermoelastic composites. Acta Mechanica. 2010, Volume 213, Issue 1-2, pp 97-109. (With Yue Chen). (PDF)

  42. Sub-wavelength plasmonic crystals: dispersion relations and effective properties. Proc. Roy. Soc. London A. Published online Feb 10,2010 doi: 10.1098/rspa.2009.0542. (With Santiago Fortes and Stephen Shipman). (PDF)

  43. Convergent Power Series for Fields in Positive or Negative High-Contrast Periodic Media. (With Santiago Fortes and Stephen Shipman). Communications in Partial Differential Equations 36 (2011) 1016--1043. (PDF)

  44. Representation formulas for L-infinity norms of weakly convergent sequencies of gradient fields in homogenization. arXiv:1009.4429v2 [math.AP] 23 Sep 2010 (With Tadele Mengesha). Mathematical Modeling and Numerical Analysis (M2AN) 46 (2012) 1121--1146. (Link)

  45. Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation. Journal of Elasticity. 2012, Volume 106, Issue 1, pp 71-103. (With Bacim Alali). (PDF)

  46. Optimal lower bounds on local stress inside random media. SIAM Journal On Applied Mathematics 70, 2009, pp. 1260--1282. (With Bacim Alali). (PDF)

  47. New bounds on local strain fields inside random heterogeneous materials. Mechanics of Materials 53 , 2012, pp. 111-122. (With Bacim Alali.) (PDF)

  48. The penetration function and its application to microscale problems. BIT Numerical Mathematics 48, 2008, pp. 167--187. (With Ivo Babuska and Michael Stuebner). (PDF).

  49. Local field assessment inside multiscale composite architectures. Multiscale Modeling and Simulation, SIAM 6, 2007, pp. 937--962. (With Timothy Breitzman and Endel Iarve). (PDF)

  50. Bounds for the torsional rigidity of shafts with arbitrary cross sections containing cylindrically orthotropic fibers. Proc. Roy. Soc. London A436, 2007, pp. 3291--3309. (With Tungyang Chen.) (PDF)

  51. Homogenization and field concentrations in heterogeneous media. arXiv.math AP / 0603172v1 7Mar 2006. SIAM Journal on Mathematical Analysis, 38, 2006, pp. 1048--1059. (PDF)

  52. Inverse homogenization and design of microstructure for pointwise stress control. The Quarterly Journal of Mechanics and Applied Mathematics, 59, 2006, pp. 139--161. (With Michael Stuebner.) (PDF)

  53. Optimal lower bounds on the hydrostatic stress amplification inside random two-phase elastic composites." Journal of the Mechanics and Physics of Solids, 53, 2005, pp. 2471--2481. (PDF)

  54. Optimal design of composite structures for strength and stiffness: an inverse homogenization approach. Structural and Multidisciplinary Optimization, 33, 2007, pp. 351--362. (With Michael Stuebner.) (PDF)

  55. Optimal lower bounds on the dilatational strain inside random two-phase elastic composites subjected to hydrostatic loading. Mechanics of Materials, 38, 2006, pp. 833--839. (PDF)

  56. Exact scaling laws for electrical conductivity properties of nematic polymer nano-composite monodomains. Advanced Functional Materials, 15, 2005, pp. 627--638. (With Zheng Z., Forest M. G., Zhou R., and Wang A) (PDF)

  57. Configurations of nonlinear materials with electric fields that minimize L^p norms. Physica B, 338, 2003, pp. 48--53. (PDF)

  58. Bounds and extremal confgurations for the torsional rigidity of coated fiber reinforced shafts. SIAM J. Applied Mathematics, 65, 2004, pp. 299--315. (With Tungyang Chen.) (PDF)

  59. Homogenization theory and the assessment of extreme field values in composites with random microstructure. SIAM J. Applied Mathematics, 65, 2004, pp. 475--493. (PDF)

  60. Optimal lower bounds on the electric-field concentration in composite media. Journal of Applied Physics, vol. 96, 2004, pp. 2821--2827. (PDF)

  61. Bounds on the distribution of extreme values for the stress in composite materials. Journal of the Mechanics and Physics of Solids, vol. 52, 2004, pp. 1053--1069. (PDF)

  62. Assessment of the local stress state through macroscopic variables. Philosophical Transactions Mathematical, Physical & Engineering Sciences, vol. 361, 2003, pp. 921--946. (PDF)

  63. Relaxation through homogenization for optimal design problems with gradient constraints. Journal of Optimization Theory and Applications, vol. 114, 2002, pp. 27--54. (PDF)

  64. Stress constrained G closure and relaxation of structural design problems. Quarterly of Applied Mathematics. vol. LXII, 2004, pp. 295--321. (PDF)

  65. Design of functionally graded composite structures in the presence of stress constraints. International Journal of Solids and Structures, vol. 39, 2002, pp. 2575--2586. (PDF)

  66. Optimal inequalities for gradients of solutions of elliptic equations occurring in two-phase heat conductors. SIAM Journal on Mathematical Analysis, vol. 32 (2001), no. 5, 1081--1093. (PDF)

  67. Optimal design of gradient fields with applications to electrostatics. Nonlinear Partial Differential Equations and Their Applications: College de France Seminare Volume XIV, D. Cioranescu and J.-L. Lions Editors. Studies in Applied Mathematics and its Applications, vol. 31, Elsevier, Amsterdam, 2002, pp. 509--532. (With Ani Velo). (PDF)

  68. Reinforcement of Elastic Structures in the presence of imperfect bonding. Quarterly of Applied Mathematics Vol. 59, No. 2 (June 2001), pp. 353-364 (PDF)

  69. Bounds for the effective conductivity of a composite with imperfect interface. Proceedings of the Royal Society of London, vol. 457 (2001), 1501--1517. (With D.R.S. Talbot). (PDF)

  70. Optimal bounds on electric field fluctuations for random composites. Journal of Applied Physics, vol. 88, 2000, pp. 4287--4293. (PDF)

  71. The effect of the interface on the dc transport properties of nonlinear composite materials. Journal of Applied Physics vol. 86 no. 3, 1999, pp. 1480-1487. (With David R.S. Talbot.) (PDF)

  72. Optimal fiber configurations for maximum torsional rigidity. Archive for Rational Mechanics and Analysis, vol. 144, 1998, pp. 79--106. (PDF)

  73. An isoperimetric inequality for the torsional rigidity of imperfectly bonded fiber reinforced cylinders. Journal of Elasticity. 55 (1999), no. 1, 1--10. (PDF)

  74. The Second Stekloff eigenvalue and energy dissipation inequalities for functionals with surface energy. SIAM Journal on Mathematical Analysis, vol. 29 (1998), no. 3, 673--680. (PDF)

  75. On existence of energy minimizing configurations for mixtures of two imperfectly bonded conductors. Recent advances in structural modelling and optimization. Control Cybernet. 27 (1998), no. 2, 217--234. (PDF)

  76. Variational methods, bounds, and size effects for two phase composites with coupled heat and mass transport processes at the two phase interface. Journal of the Mechanics and Physics of Solids, vol. 47, 1999, pp. 1699--1736. (PDF)

  77. Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites. Proceedings Royal Society of London, Mathematical, Physical and Engineering Sciences, vol. 454, 1998, 1371-1382. (PDF)

  78. Variational methods, size effects and extremal microgeometries for elastic composites with imperfect interface. Mathematical Models and Methods in Applied Sciences. 5 (1995), 1139--1173. (With Bogdan Vernescu.) (PDF)

  79. Critical radius size effects and inverse problems for composites with imperfect interface. Journal of Applied Physics. 79 (1996), 8964--8966. (With Bogdan Vernescu.) (PDF)

  80. Design of particle reinforced heat conducting composites with interfacial thermal barriers. Journal of Composite Materials. 32 (1998), 1322--1331. (PDF)

  81. Reciprocal relations, bounds and size effects for composites with highly conducting interface. SIAM Journal on Applied Math. 57 (1997), 347--363. (PDF)

  82. Reinforced Mindlin Plates with Extremal Stiffness. Int. J. Solids and Structures. 28 (1997), 3691--3704. (With Alejandro Diaz.) (PDF)

  83. Composites with imperfect interface. Proceedings of the Royal Society of London A 452 (1996), 329--358. (With B. Vernescu.) (PDF)

  84. Extremal eigenvalue problems for two phase conductors. Archive for Rational Mechanics and Analysis. (1996) 136:010--117. (page)

  85. A saddle-point theorem with application to structural optimization. Journal of Optimization Theory and Applications. 81 (1994), 549--567. (PDF)

  86. Homogenization of two-phase emulsions. Proceedings of the Royal Society of Edinburgh 124A (1994), 1119--1134. (With Bogdan Vernescu.) (PDF)

  87. Inequalities for electric and elastic polarization tensors with applications to random composites. Journal of the Mechanics and Physics of Solids. 41 (1993), 809--833. (PDF)

  88. Optimal bounds on effective elastic tensors for orthotropic composites. Proceedings of the Royal Society of London. 444 (1994), 399--410. (PDF)

  89. Optimal design and relaxation for reinforced plates subject to random transverse loads. Probabilistic Engineering Mechanics. 9 (1994), 167--177. (PDF)

  90. Laminar elastic composites with crystallographic symmetry SIAM Journal on Applied Mathematics. 50 (1990), 683--702. (With Richard James and Adam Lutoborsky) (PDF)

  91. Saturation of the even order bounds on effective moduli by finite-rank laminates. Journal of Applied Physics. 67 (1990), 7300--7306. (PDF)

  92. Darcy's law for slow viscous flow past a stationary array of bubbles. Proceedings of the Royal Society of Edinburgh. 114A (1990), 71--79 (With Marco Avellaneda.) (PDF)

  93. Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials. Archive for Rational Mechanics and Analysis. 102 (1988), 331--350. (With Robert V. Kohn). (PDF)

  94. On the effective elasticity of a two-dimensional homogenized incompressible elastic composite. Proceedings of the Royal Society of Edinburgh. 110A (1988), 45--61. (PDF)