## Publications

### Book Chapters

- “Mechanics of random materials: Stochastics, scale effects, and computation,” in
*Mechanics of Random and Multiscale Microstructures*(Eds. D. Jeulin and M. Ostoja-Starzewski), CISM Courses and Lectures Vol. 430, Springer-Wien-NewYork, 93-161, 2001. - “Selected topics in stochastic wave propagation,” Chapter 3 in Advances in Mechanics and Mathematics-II, 145 – 206, eds. D.Y. Gao and R.W. Ogden, Kluwer, 2003.
- “From lattices and composites to micropolar continua,” with I. Jasiuk, in
*Micromechanics and Nanoscale Effects: MEMS, Multi-Scale Materials and Micro-Flows*, V. M. Harik and L.-S. Luo, eds., Kluwer Academic Publishers, Amsterdam, Chapter 7, 175-212, 2004. - “Fractal solids, product measures and continuum mechanics,” with J. Li, Chapter 33 in
*Mechanics of Generalized Continua: One Hundred Years after the Cosserats*(Eds. G.A. Maugin and A.V. Metrikine), 315-323, Springer, 2010. - “Scaling and Homogenization in Spatially Random Composites,” with S.I. Ranganathan, Mathematical Methods and Models in Composites (Ed. V. Mantic), 61-102, World Scientific, 2013.
- “Fractals and randomness in mechanics of materials,”in
*Multiscale Modeling of Complex Materials: Phenomenological, Theoretical and Computational Aspects*(Eds. T. Sadowski and P. Trovalusci), CISM Courses and Lectures Vol. 556, Springer-Wien-NewYork, 107-150, 2014. - “Lattice and Particle Modeling of Damage Phenomena,” with S. Kale, in
*Handbook of Damage Mechanics*(Ed. G.Z. Voyiadjis), 203-238, Springer, 2015. - “The spectral expansion of the elasticity random field,” with A. Malyarenko,
*AIP Conf. Proc*. 1637, 647 (2014). - “Spectral expansions of three-dimensional elasticity tensor random fields,”
*1*, Sweden, in press, Springer, 2015.^{st}Västerås-Tartu Swedish-Estonian Workshop on Algebra, Geometry and Engineering Mathematics - “Tensor-valued random fields in continuum physics,” with A. Malyarenko, in
*Materials with Internal Structure*(ed. P. Trovalusci), Springer Tracts in Mechanical Engineering, pp. 75-88, 2016. DOI 10.1007978-3-319-21494-8_6 - “Stochastic continuum damage mechanics using spring lattice models,” with S. Kale, S. Koric, in
*Applied Mechanics and Materials***784**(ed. K. Saanouni), pp. 350-357, Trans Tech Publications, 2015. doi: 10.4028/www.scientific.net/AMM.784.350 - “A statistically-based homogenization approach for particle random composites as micropolar continua,” with P. Trovalusci, M.L. De Bellis, in
*Generalized Continua as Models for Classical and Advanced Materials*(eds. H. Altenbach and S. Forest), Springer, 2016. - “Scaling to RVE in random media,” with S. Kale, A. Malyarenko, B. Raghavan, S.I. Ranganathan, J. Zhang,
*Advances in Applied Mechanics***49**(eds. S.P.A. Bordas and D.S. Balint), pp. 111-212, 2016.

### Journal Articles (also ResearchGate)

[1] Dynamics of a flexible cylinder in subsonic axial flow, with M.P. Païdoussis, *AIAA Journal ***19**(11), 1467-1475, 1981.

[2] Probabilistic approach to wave propagation in structured solids, with D.R. Axelrad, *Int. J. Eng. Sci.* **22**(8-10), 1123-1133, 1984.

[3] Rayleigh wave scattering by a wedge: A boundary method approach, *Mech. Res. Comm*. **13**(1), 53-58, 1986.

[4] Propagation of Rayleigh, Scholte and Stoneley waves along random boundaries, *Probab. Eng. Mech. ***2**(2), 64-73, 1987.

[5] Graph approach to the constitutive modelling of heterogeneous solids, *Mech. Res. Comm*. **14**(4), 225-262, 1987.

[6] A master-slave manipulator for excavation and construction tasks, with M. Skibniewski, *Int. J. Robotics and Autonomous Systems ***4**, 333-337, 1988/89.

[7] Wavefront propagation in discrete random media via stochastic Huygens’ minor principle, *J. Franklin Inst*. **326**(2), 281-293, 1989.

[8] Mechanics of damage in a random granular microstructure: percolation of inelastic phases, *Int. J. Eng. Sci. (Lett. Appl. Engng. Sci.) ***27**(3), 315-326, 1989.

[9] Linear elasticity of planar Delaunay networks: Random field characterization of effective moduli, with C. Wang, *Acta Mech*. **80**, 61-80, 1989.

[10] Damage in a random microstructure: Size effects, fractals, and entropy maximization, invited paper, *Applied Mechanics Reviews *(Special Issue: *Mechanics Pan-America 1989*, C.R. Steele, A.W. Leissa and M.R.M. Crespo da Silva, Eds.) 42(11, Part 2), S202-S212, 1989.

[11] Micromechanics model of ice fields – I: Microscale constitutive laws, with R.G. Jessup, *Pure Appl. Geophys.* **132**(4), 781-802, 1990.

[12] Micromechanics model of ice fields – II: Monte Carlo simulation, *Pure Appl. Geophys. ***133**(2), 229-249, 1990.

[13] Bounds on constitutive response for a class of random material microstructures, *Comput. and Struct.* **37**, 163-167, 1990; also in *Computational Technology for Flight Vehicles *(A.K. Noor and S.L. Vennen, Eds.), Pergamon Press, 1990.

[14] Linear elasticity of planar Delaunay networks. II: Voigt and Reuss bounds, and modification for centroids, with C. Wang, *Acta Mech. ***84**, 47-61, 1990.

[15] A generalization of thermodynamic orthogonality to random media, *J. Appl. Math. Phys. (ZAMP)*. **41**, 701-712, 1990.

[16] Wavefront propagation in a class of random microstructures – I: Bilinear elastic grains, *Intl. Journal of Non-Linear Mechanics* **26**, 655-669, 1991.

[17] Transient waves in a class of random heterogeneous media, invited paper, *Applied Mechanics Reviews* (Special Issue: *Mechanics Pan-America 1991*, P.A. Kittl and D.T. Mook, Eds.) **44**(10, Part 2), S199-S209, 1991.

[18] Plastic flow of random media: micromechanics, Markov property and slip-lines, invited paper, *Applied Mechanics Reviews* (Special Issue: *Material Instabilities*, H.M. Zbib, T.G. Shawki and R.C. Batra, Eds.) **45**(3, Part 2), S75-S82, 1992.

[19] Fabrication of two-dimensional micro-structures in Fe-3.25%Si Sheet, with M. Grah, K.J. Bowman, *Scripta Metallurgica et Materialia ***26**(1), 429-434, 1992.

[20] Stochastic Hill’s equations for the study of errant rocket burns in orbit, with J.M. Longuski, *Celest. Mech. & Dyn. Astronomy* **54,** 295-303, 1992.

[21] Random fields and processes in mechanics of granular materials, *Mech. Mater. *(Special Issue: Mechanics of Granular Materials) **16**(1-2), 55-64, 1993.

[22] Micromechanics as a basis of random elastic continuum approximations, *Probab. Eng. Mech. ***8**(2), 107-114, 1993.

[23] On the critical amplitudes of acceleration wave to shock wave transition in white-noise random media. *J. Appl. Math. Phys. (ZAMP)* **44,** 865-879, 1993.

[24] Micromechanics as a basis of stochastic finite elements and differences – an overview, invited paper, *Applied Mechanics Reviews *(Special Issue: *Mechanics Pan-America 1993*, M.R.M. Crespo da Silva and C.E.N. Mazzilli, Eds.) **46**(11, Part 2), S136-S147, 1993.

[25] Micromechanically based stochastic finite elements, with K. Alzebdeh, *Finite Elements in Analysis and Design ***15**, 35-41, 1993.

[26] Micromechanics as a basis of continuum random fields, *Applied Mechanics Reviews *(Special Issue: *Micromechanics of Random Media*) **47**(1, Part 2), S221-S230, 1994.

[27] Influence of random geometry on effective properties and damage formation in 2-D composites, with P.Y. Sheng and I. Jasiuk, *ASME Journal of Engineering Materials and Technology ***116**, 384-391, 1994.

[28] Transition of acceleration waves into shock waves in random media, *Applied Mechanics Reviews* (Special Issue: *Nonlinear Waves in Solids*, J.L. Wegner and F.R. Norwood, Eds.) **48**(1, Pt. 2), 300-308, 1995. AMR-1995.pdf

[29] Linear elasticity of planar Delaunay networks – III: Self-consistent approximations, with K. Alzebdeh and I. Jasiuk. Acta Mech. **110,** 57-72, 1995.

[30] Wavefront propagation in a class of random microstructures – II: Nonlinear elastic grains. *Intl. J. Non-Linear Mech.* **30,** 771-781, 1995.

[31] Stress invariance in planar Cosserat elasticity, with I. Jasiuk. *Proc. Roy. Soc. Lond. – A* **451,** 453-470, 1995; Errata **452**, 1503, 1995.

[32] Planar Cosserat elasticity of materials with holes and intrusions, with I. Jasiuk, invited paper, *Applied Mechanics Reviews *(Special Issue: *Mechanics Pan-America 1995*, L.A. Godoy, S.R. Idelsohn, P.A.A. Laura and D.T. Mook, Eds.) **48**(11, Pt 2), S11-S18, 1995.

[33] Damage maps of disordered composites: a spring network approach, with J. D. Lee. *Intl. J. Fracture* **75,** R51-R57, 1996.

[34] The Cauchy and characteristic boundary value problems for weakly random rigid-perfectly plastic media, with H. Ilies. *Intl. J. Solids Struct.* **33**(8), 1119-1136, 1996.

[35] Composites with functionally graded interfaces: Meso-continuum concept and effective properties, with I. Jasiuk, W. Wang and K. Alzebdeh. *Acta Mater.* **44**(5), 2057-2066, 1996.

[36] Bounding of effective thermal conductivities of multiscale materials by essential and natural boundary conditions, with J. Schulte. *Phys. Rev. B* **54,** 278-285, 1996.

[37] Micromechanically based stochastic finite elements: length scales and anisotropy, with K. Alzebdeh, *Probabilistic Engng. Mech. *(Special Issue on *Stochastic Structural Dynamics*) *11*, 205-214, 1996. PEM-1996

[38] Brittle intergranular failure in 2D microstructures: Experiments and computer simulations, with M. Grah, K. Alzebdeh, P.Y. Sheng, M.D. Vaudin, K.J. Bowman. *Acta Mater.* **44**(10), 4003-4018, 1996.

[39] Spring network models in elasticity and fracture of composites and polycrystals, P.Y. Sheng and K. Alzebdeh. *Comput. Mater. Sci.* **7**(1&2), 82-93, 1996.

[40] Damage patterns and constitutive response of random matrix-inclusion composites, with P.Y. Sheng and I. Jasiuk, *Engineering Fracture Mechanics* **58**(5&6), 581-606, 1997.

[41] Random field models of heterogeneous materials. *Intl. J. Solids Struct.* **35,** 2429-2455, 1998.

[42] Fracture of random matrix-inclusion composites: scale effects and statistics, with K. Alzebdeh, A. Al-Ostaz and I. Jasiuk. *Intl. J. Solids Struct.* **35,** 2537-2566, 1998.

[43] Random field models and scaling laws of heterogeneous media, *Arch. Mech. ***50**(3), 549-558, 1998.

[44] Paper strength: Statistics and correlation structure, with M. DiMillo.* Intl. J. Fract.* **90,** L33-L38, 1998.

[45] Stochastic finite elements as a bridge between random material microstructure and global response, with X. Wang. *Comp. Meth. Appl. Mech. Eng.* **168**(1-4), 35-49, 1999.

[46] On a spring network model and effective elastic moduli of granular materials, with K. Alzebdeh. *ASME J. Appl. Mech.* **66,** 172-180, 1999.

[47] On the growth and decay of acceleration waves in random media, with J. Trebicki. *Proc. Roy. Soc. Lond. – A* **455,** 2577-2614, 1999.

[48] Scale effects in materials with random distributions of needles or cracks. *Mech. Mater.* **31**(12), 883-893, 1999.

[49] Microstructural disorder, mesoscale finite elements, and macroscopic response. *Proc. Roy. Soc. Lond. – A* **455**, 3189-3199, 1999.

[50] Kinematics and stress transfer in quasi-planar random fiber networks, with M.B. Quadrelli and D.C. Stahl. *C.R. Acad. Sci. Paris – IIb* **327,** 1223-1229, 1999.

[51] Couple-stress moduli and characteristic length of composite materials, with S. Boccara and I. Jasiuk, *Mech. Res. Comm. ***26**(4), 387-396, 1999.

[52] A discussion of ‘Hybrid stochastic finite elements and generalized Monte Carlo simulation’ by R. Ghanem,” *ASME J. Appl. Mech. ***66**, 824-825, 1999.

[53] Particle sieving by percolation through a random fiber network, with J. Castro. *Appl. Math. Modelling* **24,** 523-534, 2000.

[54] Universal material property in conductivity of planar random microstructures. *Phys. Rev. B* **62**(5), 2980-2982, 2000.

[55] Random fiber networks and special elastic orthotropy of paper, with D.C. Stahl. *J. Elasticity* **60,** 131-149, 2000.

[56] A micromechanically based couple-stress model of an elastic two-phase composite, with F. Bouyge and I. Jasiuk. *Intl. J. Solids. Struct.* **38,** 1721-1735, 2001.

[57] Scale and boundary conditions effects in elastic properties of random composites, with M. Jiang, K. Alzebdeh and I. Jasiuk. *Acta Mech.* **148,** 63-78, 2001.

[58] Scale-dependent bounds on effective elastoplastic response of random composites, with M. Jiang and I. Jasiuk. *J. Mech. Phys. Solids* **49**(3), 655-673, 2001.

[59] Michell trusses in the presence of microscale material randomness: limitation of optimality, Proc. Roy. Soc. Lond. – A **457,** 1787-1797, 2001.

[60] Crack patterns in plates with randomly placed holes: A maximum entropy approach. *Mech. Res. Comm.* **28**(2), 193-198, 2001.

[61] On geometric acoustics in random, locally anisotropic media. *Continuum Mech. Thermodyn.* **13,** 131-134, 2001.

[62] Lattice models in micromechanics. *Appl. Mech. Rev.* **55**(1), 35-60, 2002.

[63] Microstructural randomness versus representative volume element in thermomechanics. *ASME J. Appl. Mech.* **69**, 25-35, 2002.

[64] Apparent elastic and elastoplastic behavior of periodic composites, with M. Jiang and I. Jasiuk.* Intl. J. Solids Struct.* **39**(1), 199-212, 2002.

[65] A micromechanically based couple-stress model of an elastic orthotropic two-phase composite, with F. Bouyge, I. Jasiuk and S. Boccara. *Europ. J. Mech./A: Solids* **21**(3), 465-481, 2002.

[66] Apparent thermal conductivity of periodic two-dimensional composites, with M. Jiang and I. Jasiuk. *Comput. Mater. Sci.* **25**(3), 329-338, 2002.

[67] Bounds on mechanical response of multiphase composite materials with random structure, with J. Castro, *ASME Southeastern Region XI Technical Journal*, Special Inaugural Issue **1**(1), 5.1-5.8, 2002.

[68] Towards stochastic continuum thermodynamics, *J. Non-Equilib. Thermodyn.* **27**(4), 335-348, 2002.

[69] On the distance to blow-up of acceleration waves in random media, with J. Trebicki. *Cont. Mech. Thermodyn.* **15**, 21-32, 2003.

[70] Random formation, inelastic response, and scale effects in paper, with J. Castro, *Phil. Trans. Roy. Soc. Lond. A* (special issue on ‘*Micromechanics of Fluid Suspensions and Solid Composites*‘), **361**(1806), 965-986, 2003.

[71] Elasto-plasticity of paper, with J. Castro, *Int. J. Plast.* (in honour of Z. Mróz) **19**(12), 2083-2098, 2003.

[72] Spectral finite elements for vibrating rods and beams with random field properties, A.N. Woods, *J. Sound Vib.* **268**(1), 779-797, 2003.

[73] Thermoelastic waves in a helix with parabolic or hyperbolic heat conduction, *J. Thermal Stresses* **26**, 1205-1219, 2003.

[74] On the reduction of constants in planar Cosserat elasticity with eigenstrains and eigencurvatures, with I. Jasiuk, *J. Thermal Stresses* **26**, 1221-1228, 2003.

[75] Effects of microscale material randomness on the attainment of optimal structural shapes, with T. Liszka, *Struct. Multidiscipl. Optimization* **26**(1-2), 67-76, 2004.

[76] Friction and scratch resistance of Polyamide 6 modified with ionomeric Ethylene/Methacrylic Acid Copolymer, with M. Jaklewicz, A. Litak, *J. Appl. Polymer Sci.* **91**(6), 3866-3870, 2004.

[77] Fracture of brittle micro-beams, *ASME J. Appl. Mech.* **71**, 424-427, 2004.

[78] A numerical study of plume dispersion motivated by a mesoscale atmospheric flow over a complex terrain, with G. Wang, *Appl. Math. Modell.* **28**, 957-981 , 2004.

[79] Influence of topography on the Phoenix CO2 dome: a computational study, with G. Wang, *Atmos. Sci. Lett.* **5**, 103-107, 2004.

[80] Modeling of bone at a single lamella level, with I. Jasiuk, *Biomech. Modeling Mechanobiology* **3**, 67-74, 2004.

[81] Spectral finite element of a helix, with R. Shahsavari, *Mech. Res. Comm*. **32**, 147-152, 2005.

[82] Scale effects in plasticity of random media: status and challenges, *Intl. J. Plast.* **21**, 1119-1160, 2005.

[83] Particle modeling of dynamic fragmentation – I: Theoretical considerations, with G. Wang, *Comput. Mater. Sci.* **33**(4), 429-442, 2005.

[84] Thermoelastic damping in nanomechanical resonators with finite wave speeds, with Z. Khisaeva, *J. Thermal Stresses* **29**, 201-216, 2005.

[85] On the admissibility of an isotropic, smooth elastic continuum, *Arch. Mech.* **57**(4), 345-355, 2005.

[86] Homogenization of a micro-periodic helix, with J.M. Vivar-Pèrez, J. Bravo-Castillero and R. Rodriguez-Ramos, G.A. Maugin special issue of *Phil. Mag.* **85**(33-35), 4201-4212, 2005.

[87] On elastic and viscoelastic helices, with H. Shahsavari, G.A. Maugin special issue of *Phil. Mag*. **85**(33-35), 4213-4230, 2005.

[88] Particle modeling of dynamic fragmentation – II: Fracture in single- and multi-phase materials, with G. Wang, P. Radziszewski and M. Ourriban, *Comput. Mater. Sci.* **35**(2), 116-133, 2005.

[89] Mesoscale bounds in finite elasticity and thermoelasticity of random composites, with Z. Khisaeva, *Proc. R. Soc. Lond. – A* **462**, 1167-1180, 2006.

[90] Homogenization of a micro-periodic helix with parabolic or hyperbolic heat conduction, with J.M. Vivar-Pèrez, J. Bravo-Castillero and R. Rodriguez-Ramos, *J. Thermal Stresses* **29**, 467-483, 2006.

[91] Material spatial randomness – from statistical to representative volume element, *Probab. Eng. Mech.* **21**(2), 112-132, 2006.

[92] Stochastic dynamics of acceleration wavefronts in random media, with J. Trebicki, S. Torquato special issue of *Mech. Mater.* **38**, 840-848, 2006.

[93] On the scaling from statistical to representative volume element in thermoelasticity of random materials, *Networks and Heterogeneous Media*, **1**(2), 259-274, 2006.

[94] On the size of representative volume element for Darcy law in random media, with X. Du, *Proc. R. Soc. Lond. A* **462**, 2949-2963, 2006.

[95] Particle modeling of random crack patterns in epoxy plates, with G. Wang, *Probab. Eng. Mech*. **21(3)**, 267-275, 2006.

[96] Mesoscale simulations of atmospheric flow and tracer transport in the Phoenix, Arizona, airshed, with G. Wang, *Meteorological Applications* **13**, 235-241, 2006.

[97] On the size of RVE in finite elasticity of random composites, with Z.F. Khisaeva, *J. Elasticity* **85**, 153-173, 2006.

[98] Yield of random elasto-plastic materials, with W. Li, *J. Mech. Mater. Struct.* **1**, 1055-1073, 2006.

[99] Lithic raw material physical properties and use wear accrual, with H. Lerner, X. Du & A. Costopoulos, *J. Archaeological Science* **34**(5), 711-722, 2007.

[100] Large eddy simulation of sheet/cloud cavitation on a NACA0015 hydrofoil, with G. Wang, *Appl. Math. Modelling* **31**, 417-447, 2007.

[101] On the size of representative volume element in elastic, plastic, thermoelastic, and permeable random microstructures, with X. Du, Z.F. Khisaeva and W. Li, *Materials Science Forum* **539-543**, 201-206, 2007.

[102] Scale effects in infinitesimal and finite thermoelasticity of random composites, with Z.F. Khisaeva, *J. Thermal Stresses* **30**, 587-603, 2007.

[103] Towards thermomechanics of fractal media, *J. Appl. Math. Phys. (ZAMP)* **58**, 1085-1096, 2007.

[104] Towards thermoelasticity of fractal media, *J. Thermal Stresses* **30**, 889-896, 2007.

[105] Comparisons of the size of representative volume element in elastic, plastic, thermoelastic, and permeable random microstructures, with X. Du, Z. Khisaeva and W. Li, *Int. J. Multiscale Comp. Eng.* **5**(2), 73-82, 2007.

[106] On a helix made of a fractional viscoelastic material, with H. Shahsavari, *ASME J. Appl. Mech.* **75**, 011012-1-4, 2008.

[107] The effect of imperfect contact on the homogenization of a micro-periodic helix, with J.M. Vivar-Pèrez, J. Bravo-Castillero, R. Rodriguez-Ramos, *Math. Mech. Solids* **13**, 431-446, 2008.

[108] On turbulence in fractal porous media, *J. Appl. Math. Phys. (ZAMP)* **59**(6), 1111-1117, 2008.

[109] Scale-dependent homogenization of inelastic random polycrystals, with S.I. Ranganathan, *ASME J. Appl. Mech. ***75**, 051008-1-9, 2008.

[110] The electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium, with R.J. Hill, *Phys. Rev. E* **77**, 011404-1-12, 2008.

[111] On the geodesic property of strain field patterns in elasto-plastic composites, with D. Jeulin and W. Li, *Proc. R. Soc. Lond. A* **464**, 1217-1227, 2008.

[112] Scaling function, anisotropy and the size of RVE in elastic random polycrystals, with S.I. Ranganathan, *J. Mech. Phys. Solids* **56**, 2773-2791, 2008.

[113] Mesoscale conductivity and scaling function in aggregates of cubic, trigonal, hexagonal, and tetragonal crystals, with S.I. Ranganathan, *Phys. Rev. B*** 77**, 214308-1-10, 2008.

[114] Universal elastic anisotropy index, with S.I. Ranganathan, *Phys. Rev. Lett.* **101**, 055504-1-4, 2008.

[115] Continuum mechanics models of fractal porous media: Integral relations and extremum principles, *JoMMS* **4**(5), 901-912, 2009.

[116] Extremum and variational principles for elastic and inelastic media with fractal geometries, *Acta Mech.* **205**, 161-170, 2009. (doi:10.1007/s00707-009-0169-0)

[117] Fractal materials, beams and fracture mechanics, with J. Li, *J. Appl. Math. Phys. (ZAMP) ***60**, 1-12, 2009 (doi:10.1007/s00033-009-8120-8).

[118] Fractal pattern formation at elastic-plastic transition in heterogeneous materials, with J. Li, *ASME J. Appl. Mech.* **77**, 021005-1-7, 2010. **computer movies: **ukbc.avi usbc.avi

[119] A derivation of the Maxwell-Cattaneo equation from the free energy and dissipation potentials, *Int. J. Eng. Sci.* **47**, 807–810, 2009. (doi:10.1016/j.ijengsci.2009.03.002)

[120] Towards scaling laws in random polycrystals, with S. I. Ranganathan, *Int. J. Eng. Sci. *(A.J.M. Spencer special issue), **47**, 1322–1330, 2009.

[121] Fractal solids, product measures and fractional wave equations, with J. Li, *Proc. R. Soc. Lond. A* **465**, 2521-2536, 2009.

[122] Fractals in elastic-hardening plastic materials, with J. Li, *Proc. R. Soc. Lond. A* **466**, 603-621, 2010; online Nov. 2009.

[123] MRI-based finite element modeling of head trauma: Spherically focusing shear waves, with Y. Chen, *Acta Mech*., in press, 2010. **computer movies: **free-BC.avi fixed-BC.avi

[124] Hybrid lattice particle modelling approach for polymeric materials subject to high strain rate loads, with G. Wang, A. H.-D. Cheng, A. Al-Ostaz and P. Radziszewski, *Polymers ***2010**, 2, 3-30, 2010.

[125] Dissipation function in hyperbolic thermoelasticity, *J. Thermal Stresses* **34**(1), 68–74, 2010.

[126] Macrohomogeneity condition in dynamics of micropolar media, *Arch. Appl. Mech.*, **81**(7), 899-906, 2011.

[127] Fractals in thermo-elasto-plastic materials, with J. Li, *JoMMS* (C.R. and M.-L. Steele special issue) **6**(1-4), 351-359, 2011.

[128] On the objective rate of change of heat and stress fluxes. Connection with micro/nano-scale convection, with R.E. Khayat, *Discrete and Continuous Dynamical Systems – Series B (DCDS-B)* **15**(4), 991-998, 2011.

[129] Quantifying the anisotropy in biological materials, with S.I. Ranganathan and M. Ferrari, *ASME J. Appl. Mech.* **78**, 064501-1-4, 2011.

[130] Waves in fractal media, with P.N. Demmie, to appear in *J. Elast.* (*D.E. Carlson special issue*) **104**, 187-204, 2011.

[131] On the wave propagation in isotropic fractal media, with H. Joumaa, online *J. Appl. Math. Phys. (ZAMP).*

[132] Micropolar continuum mechanics of fractal media, with J. Li, *Int. J. Eng. Sci*. (*A.C. Eringen special issue*) **49**, 1302-1310, 2011.

[133] Stress and couple-stress invariance in non-centrosymmetric micropolar planar elasticity, with H. Joumaa, *Proc. R. Soc. Lond. A*, online, May, 2011.

[134] Powerless fluxes and forces, and change of scale in irreversible thermodynamics, with A. Zubelewicz, *J. Phys. A: Math. & Theor.* **44**, 335002, 2011.

[135] Fractal solids, product measures and fractional wave equations, (revised reprint of 1.121), with J. Li, *FormaMente* **VI**, 93-113, 2011.

[136] Stochastic finite elements: Where is the physics?, *Theoretical and Applied Mechanics* **38**(4), 379-396, 2011.

[137] Brain deformation under mild impact: Magnetic resonance imaging-based assessment and finite element study, with Y. Chen, B. Sutton, C. Conway and S.P. Broglio, special issue “Brain Neuro-Mechanics” of *International Journal of Numerical Analysis and Modeling Series B* **3**(1), 20-35, 2012.

[138] Shock waves in random viscoelastic media, with L. Costa, *Acta Mechanica* **223**, 1777-1788, 2012.

[139] New classes of spectral densities for lattice processes and random fields built from simple univariate margins, with E. Porcu, P. Gregori, J. Mateu, *Stochastic Environmental Research and Risk Assessment* **26**(4), 479-492, 2012.

[140] Elastic-plastic transition in 3D random materials: Massively parallel simulations, fractal morphogenesis and scaling function, with J. Li, A. Saharan and S. Koric, *Phil. Mag.* **92**(22), 2733-2758, 2012.

[141] Edges of Saturn’s rings are fractal, with J. Li, *Arxiv 1207.0155*, 2012; *SpringerPlus* **4**, 158, 2015.

[142] From random fields to classical or generalized continuum models, *Procedia IUTAM* **6**, 31–34, 2013.

[143] Electromagnetism on anisotropic fractal media, *ZAMP* **64**(2), 381-390, 2013.

[144] On thermodynamic restrictions in peridynamics, with P.N. Demmie and A. Zubelewicz, * ASME J. Appl. Mech*.

**80**, 014502, 2013.

[145] Fracture model for cemented aggregates, with A. Zubelewicz, A. Ionita, D. Thompson, D. Shunk, M.W. Lewis, J. Lawson, S. Kale and S. Koric, *AIP Advances ***3**, 012119 (2013).

[146] From fractal media to continuum mechanics, with J. Li, H. Joumaa and P.N. Demmie, invited review,* Zeit. Angew. Math. Mech. (ZAMM)* **93**, 1-29, 2013.

[147] Fractal geometric characterization of functionally graded materials, with A. Saharan and S. Koric, *ASCE Journal of Nanomechanics and Micromechanics* **3**(4), 04013001-1-13, 2013.

[148] Scaling function in conductivity of planar random checkerboards, with Ahmed Saleh Dalaq and S.I. Ranganathan, *Computational Materials Science*, **79**, 252-261, 2013.

[149] Acoustic-elastodynamic interaction in isotropic fractal media, with H. Joumaa, *Europ. Phys. J.*, t**222**, 1949–1958, 2013.

[150] Stiffness tensor random fields through upscaling of planar random materials, with M.P. Sena and L. Costa,* Probabilistic Eng. Mech*. **34**, 131-156, 2013.

[151] Tensor random fields in conductivity and classical or micropolar elasticity, with L. Shen and A. Malyarenko, *Math. Mech. Solids*, **20**(4), 418-432, 2015.

[152] Comment on “*Hydrodynamics of fractal continuum flow*” and “*Map of fluid flow in fractal porous medium into fractal continuum flow*“, with J. Li, *Physical Review E* **88**(5), 005700-01-04, 2013.

[153] Elastodynamics in micropolar fractal solids, with H. Joumaa and P.N. Demmie, *Mathematics and Mechanics of Solids* **19**(2) 117–134, 2013.

[154] Fractal shear bands at elastic-plastic transitions in random Mohr-Coulomb materials, with J. Li, *ASCE Journal of Engineering Mechanics ***140**(9), 04014072-1-12, 2013.

[155] Viscothermoelasticity with finite wave speeds: Thermomechanical laws, *Acta Mech.* **225**(4-5), 1277-1285, 2014.

[156] Statistically isotropic tensor random fields: Correlation structures, with A. Malyarenko, *Mathematics and Mechanics of Complex Systems (MEMOCS)*, **2**(2), 201-231, 2014.

[157] Elastic-plastic-brittle transitions and avalanches in disordered media, with S. Kale, *Phys. Rev. Lett.* **112**, 045503-1-5, 2014.

[158] Bernoulli-Euler beams with random field properties under random field forcings: fractal and Hurst effects, with L. Shen and E. Porcu, *Arch. Appl. Mech. 84, *1595-1626, 2014.

[159] Particulate random composites homogenized as micropolar materials, with P. Trovalusci, A.M. de Bellis, and A. Murrali, *Meccanica ***49**, 2719-2727, 2014.

[160] Homogenization of random composites as micropolar continua, P. Trovalusci, A.M. de Bellis, and A. Murrali, *Eur. J. Mech./A: Solids* **49**, 396-407, 2014.

[161] Continuum mechanics beyond the second law of thermodynamics, with A. Malyarenko, *Proc. Roy. Soc. **A* **470**, 20140531, 2014.

[162] Morphological study of elastic-plastic-brittle transitions in disordered media, with S. Kale, *Phys. Rev. E* **90**, 042405-1-15, 2014.

[163] A mechanism based model for dynamic behavior and fracture of geomaterials, with A. Zubelewicz, E. Rougier, E.E. Knight, C. Bradley and H.S. Viswanathan, *Int. J. Rock Mech. & Mining Sci*. **72**, 277-282, 2014.

[164] Electrical properties of random checkerboards at finite scales, with B. Raghavan and S. Ranganathan, *AIP Advances* **5**, 017131, 2015.

[165] Responses of first-order dynamical systems to Matérn, Cauchy, or Dagum excitations, with L. Shen and E. Porcu. *Mathematics and Mechanics of Complex Systems (MEMOCS)* **3**(1), 27-41, 2015.

[166] Elastic rods and shear beams with random field properties under random field loads: fractal and Hurst effects, with L. Shen and E. Porcu, *ASCE J. Eng. Mech*., on line, 04015002-1-8, 2014.

[167] Scale-dependent homogenization of random hyperbolic thermoelastic solids, with L. Costa and S.I. Ranganathan, *J. Elast.* **118**, 243-250, 2014.

[168] Scaling and bounds in thermal conductivity of planar Gaussian correlated microstructures, with S. Kale, A. Saharan and S. Koric, *J. Appl. Phys.* **117**, 104301, 2015.

[169] A 3D model of fine particle retention during percolation through a fiber mat, with T. Bliss, J. Castro, *TAPPI Journal* **14**(8), 546-554, 2015.

[170] Harmonic oscillator driven by random processes having fractal and Hurst effects, with L. Shen and E. Porcu, *Acta Mechanica* **226**(11), 3653-3672, 2015.

[171] Mesoscale bounds in viscoelasticity of random composites, with J. Zhang, *Mechanics Research Communications* **68**, 98-104, 2015.

[172] Tunneling-percolation behavior of polydisperse prolate and oblate ellipsoids, with S. Kale, F. Sabet, I. Jasiuk, *J. Appl. Phys.* **118**(15), 154306, 2015. cover

[173] Pirouette launch and energy storage system, *Journal of the British Interplanetary Society* **68**, 406-407, 2015.

[174] Local and nonlocal material models, spatial randomness, and impact loading, with P.N. Demmie, *Arch. Appl. Mech ***86**(1), 39-58,* 85 ^{th} Anniversary Special Issue*, 2016.

[175] Second law violations, continuum mechanics, and permeability, *Continuum Mechanics and Thermodynamics* **28**, 489-501, 2015.

[176] Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments, with V. Nishawala, M. Leamy and P.N. Demmie, *Wave Motion* **60**, 73-83, 2015.

[177] Finite element solutions to the bending stiffness of a single-layered helically wound cable with internal friction, with D. Zhang, *ASME J. Appl. Mech.* **83**, 031003-1-8, 2016. DOI:10.1115/1.4032023

[178] Continuum mechanics versus violations of the second law of thermodynamics, with B. Raghavan, *J. Thermal Stresses* **39**:6, 734-749, 2016.

[179] Peristatic solutions for finite one and two dimensional systems, with V. Nishawala, *Mathematics and Mechanics of Solids*, in press, 2016.

[180] Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites, with J. Zhang, *Proceedings of the Royal Society A*, on line, 2016.

[181] Spectral expansions of homogeneous and isotropic tensor-valued random fields, with A. Malayrenko, arXiv:1402.1648, *ZAMP*, online, 2016. arXiv:1402.1648

[182] On the dilatational wave motion in anisotropic fractal solids, with H. Joumaa, in press,* Mathematics and Computers in Simulation (C. Christov special issue)*

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[183] Representing stochastic damage evolution in disordered media as a jump Markov process using the fiber bundle model, with S. Kale, *International Journal of Damage Mechanics*, on line, 2016. DOI: 10.1177/1056789516650249

[184] Effect of filler alignment on percolation in polymer nanocomposites using tunneling-percolation model, with S. Kale, F. Sabet, I. Jasiuk, *J. Appl. Phys.* **120**, 045105-1-10, 2016.

[185] Lamb’s problem on random mass density fields with fractal and Hurst effects, with V. Nishawala, M. Leamy and E. Porcu, *Proceedings of the Royal Society A*, online, 2016. Electronic supplementary material

[186] A random field formulation of Hooke’s law in all elasticity classes, with A. Malayrenko, *J. Elast.*, open access, 2016. http://arxiv.org/abs/1602.09066

[187] Experimental and computational study of shielding effectiveness of polycarbonate carbon nanocomposites, with P. Karimi, M. Ostoja-Starzewski and I. Jasiuk, *J. Appl. Phys.* **120**, 145103-1-11, 2016. Doi: 10.1063/1.4964691

[188] Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations, with D. Zhang and K.A. Dahmen, *Physical Review E ***95***, *032902, 2017.

[189] Shear-thinning characteristics of molecular fluids undergoing planar Couette flow, with B. Raghavan, *Physics of Fluids* **29**, 023103-1-7, 2017.

[190] Admitting spontaneous violations of the second law in continuum thermomechanics, *Entropy* **19**, 78, 10 pages, 2017. doi:10.3390/e19020078.

[191] Shear wave patterns in mild traumatic brain injury, with Y. Chen and A. Madhukar, on line, *International Journal for Numerical Methods in Biomedical Engineering*, 2017.

[192] Dynamic interaction of plates in an inhomogeneous transversely isotropic space weakened by a crack, with A. Amiri-Hezaveh, H. Moghaddasi, P. Karimi, *ZAMM*, in press, 2017.

[193] Three-dimensional vibrations of a helically wound cable modeled as a Timoshenko rod, with L. Le Marrec and D. Zhang, *Acta Mechanica* (“Franz Ziegler memorial issue”), in press, 2017.

[194] Fractal planetary rings: Energy inequalities and random field model, with A. Malyarenko, *Int. J. Modern Physics B ***31**, 1750236 (13 pages), 2017*. *

[195] Acceleration waves on random fields with fractal and Hurst effects, with V. Nishawala, *Wave Motion*, in press, 2017.