## 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. - M. Ostoja-Starzewski, “Continuum physics with violations of the second law of thermodynamics,” (invited)
*Mathematical Modelling in Solid Mechanics**– Proceedings ETAMM*(eds. F. dell’Isola, M. Sofonea and D. Steigmann), pp. 181-192, Springer, 2017. DOI 10.1007/978-981-10-3764-1 - M. Ostoja-Starzewski, J. Li and P.N. Demmie, “Continuum Homogenization of Fractal Media” in
*Handbook of Nonlocal Continuum Mechanics for Materials and Structures*, pp. 1-31, Springer, 2017. doi:10.1007/978-3-319-22977-5_18-1 - A. Malyarenko and M. Ostoja-Starzewski, “Random fields related to the symmetry classes of second-order symmetric tensors,”
*Stochastic Processes and Algebraic Structures — From Theory Towards Applications (**SPAS 2017**)*on the occasion of the 70^{th}birthday of Prof. Dmitrii Silvestrov, Mälardalen University and Stockholm University, 2017.

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

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

[69] 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.

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

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

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

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

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

[75] 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.

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

[77] 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.

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

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

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

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

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

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

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

[85] 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.

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

[87] 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.

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

[89] 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.

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

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

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

[93] 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.

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

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

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

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

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

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

[100] 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.

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

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

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

[104] 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.

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

[106] 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.

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

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

[109] 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.

[110] 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.

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

[112] 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.

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

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

[115] 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)

[116] 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).

[117] Fractal pattern formation at elastic-plastic transition in heterogeneous materials, with J. Li, *ASME J. Appl. Mech.* **77**, 021005-1-7, 2010.

[118] S.I. Ranganathan and M. Ostoja-Starzewski, “Towards scaling laws in random polycrystals,” *Int. J. Engineering Science *(A.J.M. Spencer special issue) **47**, 1322-1330, 2009.

[119] J. Li and M. Ostoja-Starzewski, “Fractal solids, product measures and fractional wave equations,” *Proceedings of the Royal Society, London A* **465**, 2521-2536, 2009. Errata (2010) doi:10.1098/rspa.2010.0491.

[120] J. Li and M. Ostoja-Starzewski, “Fractal pattern formation at elastic-plastic transition in heterogeneous materials,” *ASME Journal of Applied Mechanics* **77**, 021005-1-7, 2010.

[121] J. Li and M. Ostoja-Starzewski, “Fractals in elastic-hardening plastic materials,” *Proceedings of the Royal Society, London A* **466**, 603-621, 2010.

[122] Y. Chen and M. Ostoja-Starzewski, “MRI-based finite element modeling of head trauma: spherically focusing shear waves,” *Acta Mechanica* **213** (1-2), 155-167, 2010. DOI 10.1007/s00707-009-0274-0

[123] G. Wang, A. H.-D. Cheng, M. Ostoja-Starzewski, A. Al-Ostaz and P. Radziszewski, “Hybrid lattice particle modelling approach for polymeric materials subject to high strain rate loads,” *Polymers* **2010**, *2*, 3-30, 2010. doi: 10.3390/polym2010003

[124] M. Ostoja-Starzewski, “Dissipation function in hyperbolic thermoelasticity,” *Journal of Thermal Stresses* **34**(1), 68–74, 2011.

[125] M. Ostoja-Starzewski, “Macrohomogeneity condition in dynamics of micropolar media,” *Archive of Applied Mechanics*** 81**(7), 899-906, 2011. DOI: 10.1007/s00419-010-0456-1

[126] J. Li and M. Ostoja-Starzewski, “Fractals in thermoelastoplastic materials,” *Journal of Mechanics of Materials and **Structures* (*Charles and Marie-Louise Steele commemorative issue*) **6**(1-4), 351-359, 2011.

[127] R.E. Khayat and M. Ostoja-Starzewski, “On the objective rate of change of heat and stress fluxes,” Connection with micro/nano-scale convection,” *Discrete and Continuous Dynamical Systems – Series B (DCDS-B)* **15**(4), 991-998, 2011. 10.3934/dcdsb.2011.15.991

[128] S.I. Ranganathan, M. Ostoja-Starzewski and M. Ferrari, “Quantifying the anisotropy in biological materials,” *ASME Journal of Applied Mechanics*, **78**, 064501-1-4, 2011. DOI: 10.1115/1.4004553

[129] P.N. Demmie and M. Ostoja-Starzewski, “Waves in fractal media,” *Journal of Elasticity* (*D.E. Carlson special issue*) **104**, 187-204, 2011. DOI 10.1007/s10659-011-9333-6

[130] H. Joumaa and M. Ostoja-Starzewski, “On the wave propagation in isotropic fractal media,” *ZAMP* **62**, 1117-1129, 2011. DOI: 10.1007/s00033-011-0135-2

[131] J. Li and M. Ostoja-Starzewski, “Micropolar continuum mechanics of fractal media,” *International Journal of **Engineering* *Science* (*A.C. Eringen special issue*) **49**, 1302-1310, 2011. doi: 10.1016/jijengsci.2011.03.010

[132] H. Joumaa and M. Ostoja-Starzewski, “Stress and couple-stress invariance in non-centrosymmetric micropolar planar elasticity,” *Proceedings of the Royal Society A* **467**(2134), 2896-2911, 2011. doi: 101098/rspa2010.0660

[133] M. Ostoja-Starzewski and A. Zubelewicz, “Powerless fluxes and forces, and change of scale in irreversible thermodynamics,” *Journal of Physics A: Mathematical and Theoretical* **44**, 335002, 2011.

[134] J. Li and M. Ostoja-Starzewski, “Fractal solids, product measures and fractional wave equations,” (invited and revised reprint of 1.120) *Formamente* **VI**, 93-113, 2011.

[135] M. Ostoja-Starzewski, “Stochastic finite elements: Where is the physics?” *Theoretical and Applied Mechanics* **38**(4), 379-396, 2011.

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

[137] M. Ostoja-Starzewski and L. Costa, “Shock waves in random viscoelastic media,” *Acta Mechanica* **223**, 1777-1788, 2012. DOI 10.1007/s00707-012-0658-4

[138] E. Porcu, P. Gregori, J. Mateu and M. Ostoja-Starzewski, “New classes of spectral densities for lattice processes and random fields built from simple univariate margins,” *Stochastic Environmental Research and Risk Assessment* **26**(4), 479-490, 2012. DOI: 10.1007/s00477-012-0572-2

[139] J. Li, A. Saharan, S. Koric and M. Ostoja-Starzewski, “Elastic-plastic transition in three-dimensional random materials: Massively parallel simulations, fractal morphogenesis and scaling function,” *Philosophical Magazine* **92**(22), 2733-2758, 2012. DOI: 10.1080/14786435.2012.674223

[140] J. Li and M. Ostoja-Starzewski, “Edges of Saturn’s rings are fractal,” *arXiv: 1207.0155*, 2012. *SpringerPlus* **4**, 158, 2015. DOI:10.1186/s40064-015-0926-6.

[141] M. Ostoja-Starzewski, “From random fields to classical or generalized continuum models,” *Procedia IUTAM* **6**, 31–34, 2013.

[142] M. Ostoja-Starzewski, “Electromagnetism on anisotropic fractal media,” *ZAMP* **64**(2), 381-390, 2013. (DOI) 10.1007/s00033-012-0230-z.

[143] M. Ostoja-Starzewski, P.N. Demmie, A. Zubelewicz, “On thermodynamic restrictions in peridynamics,” *ASME Journal of Applied Mechanics* **80**, 014502, 2013. DOI: 10.1115/1.4006945

[144] A. Zubelewicz, D.G. Thompson, M. Ostoja-Starzewski, A. Ionita, D. Shunk, M.W. Lewis, J.C. Lawson, S. Kale and S. Koric, “Fracture model for cemented aggregates,” *AIP Advances* **3**, 012119-1-10, 2013.

[145] A. Saharan, M. Ostoja-Starzewski and S. Koric, “Fractal geometric characterization of functionally graded materials,” *ASCE Journal of Nanomechanics and Micromechanics* **3**(4), 04013001-1-13, 2013. DOI: 10.1061/(ASCE)NM.2153-5477.0000058.

[146] Ahmed Saleh Dalaq, S.I. Ranganathan and M. Ostoja-Starzewski, “Scaling function in conductivity of planar random checkerboards,” *Computational Materials Science* **79**, 252-261, 2013.

[147] H. Joumaa and M. Ostoja-Starzewski, “Acoustic-elastodynamic interaction in isotropic fractal media,” *European Physical Journal Special Topics* **222**, 1949–1958, 2013. DOI: 10.1140/epjst/e2013-01976-x

[148] M.P. Sena, M. Ostoja-Starzewski and L. Costa, “Stiffness tensor random fields through upscaling of planar random materials,” *Probabilistic Eng. Mech*. **34**, 131-156, 2013. http://dx.doi.org/10.1016/j.probengmech.2013.08.008

[149] J. Li and M. Ostoja-Starzewski, “Comment on “*Hydrodynamics of fractal continuum flow*” and “*Map of fluid flow in fractal porous medium into fractal continuum flow*“,” *Physical Review E* **88**(5), 057001, 2013.

[150] H. Joumaa, M. Ostoja-Starzewski and P.N. Demmie, “Elastodynamics in micropolar fractal solids,” *Mathematics and Mechanics of Solids* **19**(2), 117–134, 2014. DOI: 10.1177/1081286512454557

[151] M. Ostoja-Starzewski, J. Li, H. Joumaa and P.N. Demmie, “From fractal media to continuum mechanics,” invited review, *ZAMM* **94**(5), 373-401, 2014. DOI 10.1002/zamm.201200164

[152] J. Li and M. Ostoja-Starzewski, “Fractal shear bands at elastic-plastic transitions in random Mohr-Coulomb materials,” *ASCE Journal of Engineering Mechanics* **140**(9), 04014072-1-12, 2014.

[153] M. Ostoja-Starzewski, “Viscothermoelasticity with finite wave speeds: Thermomechanical laws,” *Acta Mechanica* **225**(4-5), 1277-1285, 2014. DOI 10.1007/s00707-013-1075-z

[154] A. Malyarenko and M. Ostoja-Starzewski, “Statistically isotropic tensor random fields: Correlation structures,” *Mathematics and Mechanics of Complex Systems (MEMOCS)* **2**(2), 209-231, 2014. dx.doi.org/10.2140/memocs.2014.2.209

[155] S. Kale and M. Ostoja-Starzewski, “Elastic-plastic-brittle transitions and avalanches in disordered media,” *Physical Review Letters* **112**, 045503-1-5, 2014. DOI: 10.1103/PhysRevLett.112.045503

[156] L. Shen, M. Ostoja-Starzewski and E. Porcu, “Bernoulli-Euler beams with random field properties under random field forcings: fractal and Hurst effects,” *Archive of Applied Mechanics* **84**, 1595-1626, 2014.

[157] P. Trovalusci, M.L. De Bellis, M. Ostoja-Starzewski and A. Murrali, “Particulate random composites homogenized as micropolar materials,” *Meccanica* **49**, 2719-2727, 2014. DOI:10.1007/s11012-014-0031-x

[158] P. Trovalusci, M. Ostoja-Starzewski, M.L. De Bellis and A. Murrali, “Scale-dependent homogenization of random composites as micropolar continua,” *European Journal of Mechanics/A: Solids* **49**, 396-407, 2014. DOI: 10.1016/j.euromechsol.2014.08.010

[159] M. Ostoja-Starzewski and A. Malyarenko, “Continuum mechanics beyond the second law of thermodynamics,” *Proceedings of the Royal Society A* **470**, 20140531, 2014. DOI: 10.1098/rspa.2014.0531

[160] S. Kale and M. Ostoja-Starzewski, “Morphological study of elastic-plastic-brittle transitions in disordered media,” *Physical Review E* **90**, 042405-1-15, 2014. DOI: 10.1103/PhysRevE.90.042405

[161] A. Zubelewicz, E. Rougier, M. Ostoja-Starzewski, E.E. Knight, C. Bradley and H.S. Viswanathan, “A mechanism-based model for dynamic behavior and fracture of geomaterials,” *International Journal of Rock Mechanics & Mining Sciences* **72**, 277-282, 2014. DOI: 10.1016/j.ijrmms.2014.09.015

[162] M. Ostoja-Starzewski, L. Shen and A. Malyarenko, “Tensor random fields in conductivity and classical or microcontinuum theories,” *Mathematics and Mechanics of Solids* **20**(4), 418-432, 2015. DOI:10.1177/1081286513498524

[163] B. Raghavan, S.I. Ranganathan and M. Ostoja-Starzewski, “Electrical properties of random checkerboards at finite scales,” *AIP Advances* **5**, 017131-1-12, 2015.

[164] L. Shen, M. Ostoja-Starzewski and E. Porcu, “Responses of first-order dynamical systems to Matérn, Cauchy, or Dagum excitations,” *Mathematics and Mechanics of Complex Systems (MEMOCS)* **3**(1), 27-41, 2015. dx.doi.org/10.2140/memocs.2015.3.27

[165] “Elastic rods and shear beams with random field properties under random field loads: fractal and Hurst effects,” with L. Shen and E. Porcu, *ASCE Journal of Engineering Mechanics*, **141**(7), 04015002-1-8, 2015. doi: 10.1061/(ASCE)EM.1943-7889.0000906.

[166] “Scale-dependent homogenization of random hyperbolic thermoelastic solids,” with L. Costa and S.I. Ranganathan, *Journal of Elasticity* **118**, 243-250, 2015. DOI 10.1007/s10659-014-9483-4

[167] “Scaling and bounds in thermal conductivity of planar Gaussian correlated microstructures,” with S. Kale, A. Saharan and S. Koric, *Journal of Applied Physics* **117**, 104301, 2015. http://dx.doi.org/10.1063/1.4914128

[168] “A three-dimensional model of fine particle retention during percolation through a fiber mat,” with T. Bliss and J. Castro, *TAPPI Journal* **14**(8), 546-554, 2015.

[169] “Harmonic oscillator driven by random processes having fractal and Hurst effects,” with L. Shen and E. Porcu, *Acta Mechanica* **226**(11), 3653-3672, 2015. DOI 10.1007/s00707-015-1385-4

[170] “Mesoscale bounds in viscoelasticity of random composites,” with J. Zhang, *Mechanics Research Communications* **68**, 98-104, 2015. doi:10.1016/j.mechrescom.2015.05.005

[171] “Tunneling-percolation behavior of polydisperse prolate and oblate ellipsoids,” with S. Kale, F. Sabet and I. Jasiuk, *Journal of Applied Physics* **118**(15), 154306, 2015. DOI: 10.1063/1.4933100 cover

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

[173] “Local and nonlocal material models, spatial randomness, and impact loading,” with P.N. Demmie, *Archive of Applied Mechanics* **86**(1), 39-58, *85 ^{th} Anniversary Special Issue*, 2016. DOI 10.1007/s00419-015-1095-3

[174] “Second law violations, continuum mechanics, and permeability,” *Continuum Mechanics and Thermodynamics* **28**, 489-501, 2016. DOI: 10.1007/s00161-015-0451-4; *Erratum* **29**, 359, 2017. DOI: 10.1007/s00161-016-0534-x

[175] “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, 2016. https://doi.org/10.1016/j.wavemoti.2015.08.005

[176] “Finite element solutions to the bending stiffness of a single-layered helically wound cable with internal friction,” with D. Zhang, *ASME Journal of Applied Mechanics* **83**, 031003-1-8, 2016. DOI:10.1115/1.4032023

[177] “Continuum mechanics versus violations of the second law of thermodynamics,” (invited) with B. Raghavan, *J. Thermal Stresses* **39**:6, 734-749, 2016. http://www.tandfonline.com/doi/full/10.1080/01495739.2016.1169140

[178] “Peristatic solutions for finite one and two dimensional systems,” with V.V. Nishawala, *Mathematics and Mechanics of Solids*, in press, 2016. DOI: 10.1177/1081286516641180

[179] “Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites,” with J. Zhang, *Proceedings of the Royal Society A* **472**, 20150801, 2016. DOI: 10.1098/rspa.2015.0801

[180] “Spectral expansions of homogeneous and isotropic tensor-valued random fields,” with A. Malyarenko, arXiv:1402.1648, *Journal of Applied Mathematics and Physics (ZAMP)* **67**(3), paper 59, 2016. DOI 10.1007/s00033-016-0657-8

[181] “On the dilatational wave motion in anisotropic fractal solids,” with H. Joumaa, *Mathematics and Computers in Simulation (C. Christov issue)* **127**, 114-130, 2016. DOI: 10.1016/j.matcom.2013.03.012

[182] “Representing stochastic damage evolution as a jump Markov process,” with S. Kale, *International Journal of Damage Mechanics*, on line, 2016. DOI: 10.1177/1056789516650249

[183] “Effect of filler alignment on percolation in polymer nanocomposites using tunneling-percolation model,” with S. Kale, F. Sabet and I. Jasiuk, *Journal of Applied Physics* **120**, 045105-1-10, 2016.

[184] “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* **472** (2196), 2016. DOI: 10.1098/rspa.2016.0638. Electronic supplementary material

[185] “A random field formulation of Hooke’s law in all elasticity classes,” with A. Malyarenko, *Journal of Elasticity* **127**(2), 269-302, 2017; arXiv:1602.09066

[186] “Experimental and computational study of shielding effectiveness of polycarbonate carbon nanocomposites,” with P. Karimi and I. Jasiuk, *Journal of Applied Physics* **120**, 145103-1-11, 2016. DOI: 10.1063/1.4964691

[187] “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**, 032902-1-12, 2017. DOI: 10.1103/PhysRevE.95.032902

[188] “Shear-thinning characteristics of molecular fluids undergoing planar Couette flow,” with B.V. Raghavan, *Physics of Fluids* **29**, 023103-1-7, 2017. doi: 10.1063/1.4976319

[189] “Admitting spontaneous violations of the second law in continuum thermomechanics,” *Entropy* **19**, 78, 10 pages, 2017.

[190] “Effect of cerebrospinal fluid modelling on spherically convergent shear waves during blunt head trauma,” with A. Madhukar and Y. Chen, *International Journal for Numerical Methods in Biomedical Engineering* **33**(12), 11 pages, 2017.

[191] “Dynamic interaction of plates in an inhomogeneous transversely isotropic space weakened by a crack,” with A. Amiri-Hezaveh, H. Moghaddasi and P. Karimi, *ZAMM*, on line, 2017.

[192] “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. DOI: 10.1007/s00707-017-1992-3

[193] A. Malyarenko and M. Ostoja-Starzewski, “Fractal planetary rings: Energy inequalities and random field model,” *Int. J. Modern Physics B* **31**(30), 1750236 (14 pages), 2017.

[194] V. Nishawala and M. Ostoja-Starzewski, “Acceleration waves on random fields with fractal and Hurst effects,” *Wave Motion* **74**, 134-150, 2017. doi: 10.1016/j.wavemoti.2017.07.004

[195] “Electromagnetic characteristics of systems of prolate and oblate ellipsoids with focus on CNT and GNP,” with P. Karimi, A. Amiri-Hezaveh, and J.-M. Jin, *Journal of Applied Physics*, in press, 2017. DOI: 10.1063/1.5000045

[196] “Oldroyd fluids with hyperbolic heat conduction,” with R.E. Khayat, *Mechanics Research Communications* **93**, 108-113, 2017 – special issue “*Mechanics from the 20th to the 21st Century: The Legacy of Gérard A. Maugin*“.

[197] “Stochastic characteristics and Second-Law violations of atomic fluids in Couette flow,” with B.V. Raghavan, P. Karimi, *Physica A* **496**, 90-107, 2018. doi: 10.1016/j.physa.2017.11.007

[198] “Ignaczak equation of elastodynamics,” *Mathematics and Mechanics of Solids*, in press, 2018. DOI: 10.1177/1081286518757284

[199] “Tunneling-percolation model of multicomponent nanocomposites,” with S. Kale, P. Karimi, F. Sabet, I. Jasiuk, *Journal of Applied Physics*, **123**, 085104, 2018. featured on cover. 10.1063/1.5019945

[200] “Does a fractal microstructure require a fractional viscoelastic model?” with J. Zhang, *Fractal & Fractional*, **2**(1), 12, 2018. DOI: 10.3390/fractalfract2010012

[201] “Anti-plane shear Lamb’s problem on random mass density fields with fractal and Hurst effects,” with X. Zhang, V. Nishawala, *Evolution Equations and Control Theory* [special issue “*Nonlinear Wave Phenomena in Continuum Physics: Some Recent Findings*“], **8**(1), 231-246, 2019. doi:10.3934/eect.2019013

[202] “Shielding effectiveness and bandgaps of interpenetrating phase composites based on the Schwarz Primitive surface,” with D.W. Abueidda, P. Karimi, J.-J. Jin, N.A. Sobh, I.M. Jasiuk, *Journal of Applied Physics ***124**, 175102, 2018. DOI: 10.1063/1.5046105

[203] “Telegraph equation: two types of harmonic waves, a discontinuity wave, and a spectral finite element,” with D. Zhang, *Acta Mechanica* **230**, 1725-1743, 2019.

[204] “Finite element methods in head impact simulations: A review,” with A. Madhukar, *Annals of Biomedical Engineering*, online, 2019.

[205] P. Karimi, X. Zhang, S. Yan, M. Ostoja-Starzewski and J.-J. Jin, “Electrostatic and magnetostatic properties of random materials,” *Physical Review E ***99**(2), 022120-1-9, 2019. DOI: 10.1103/PhysRevE.99.022120

[206] D. Zhang, M. Ostoja-Starzewski and L. Le Marrec, “Mechanical and thermal couplings in helical strands,” *Journal of Thermal Stresses* **42**(1), 185-212, 2019.

[207] P. Karimi, A. Amiri-Hezaveh, H. Moghaddasi, F. A Sabet and M. Ostoja-Starzewski, “Elastodynamics of a multilayered transversely isotropic half-space due to rigid motion of foundation,” *Wave Motion* **88**, 106-128, 2019.

[208] A. Malyarenko and M. Ostoja-Starzewski, “Towards stochastic continuum damage mechanics,” *International Journal of Solids and Structures*, on line, 2019.

[209] A. Amiri-Hezaveh, P. Karimi and M. Ostoja-Starzewski, “Stress field formulation of linear electro-magneto-elastic materials,” *Math. Mech. Solids* **24**(12), 3806-3822, 2019.

[210] B.V. Raghavan and M. Ostoja-Starzewski, “On the hydrodynamic stability of a Lennard-Jones molecular fluid,” *Journal of Statistical Physics*, on line, 2019.

[211] D. Zhang and M. Ostoja-Starzewski, “Thermoelastic waves in helical strands with Maxwell-Cattaneo heat conduction,” *Theoretical and Applied Mechanics Letters* **9**(5), 2019.

[212] P. Karimi, A. Malyarenko, M. Ostoja-Starzewski and X. Zhang, “RVE problem, random fields, and stochastic mechanics,” *International Journal of Engineering Science*, on line, 2019.

[213] A. Madhukar, Y. Park, W. Kim, H.J., R. Berlin, L.P. Chamorro, J. Bentsman, and M. Ostoja-Starzewski, “Heat conduction in porcine muscle and blood: Experiments and time-fractional telegraph equation model,” *Journal of the Royal Society Interface*, to appear, 2019.