年間 6 号発行
ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352
Indexed in
EFFECTIVE DISPLACMENTS OF PERIDYNAMIC HETEROGENEOUS BAR LOADED BY BODY FORCE WITH COMPACT SUPPORT
要約
A statistically homogeneous random bar with the bond-based peridynamic properties of constituents is considered for a static case. For both statistically homogeneous 1D composites and homogeneous remote loading, the effective properties of both the peridynamic composites and locally elastic ones are described by constant tensor of the local effective moduli. However, even for locally elastic composites subjected to inhomogeneous loading, the effective deformations are described by a nonlocal (either the differential or integral) operator. Estimation of this effective displacement is performed by exploitation of the most popular tools and concepts used in conventional elasticity of composite materials with their adaptation to peridynamics. This is extraction from the material properties of a constituent of the matrix properties. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts. The current paper is dedicated to the estimation of effective deformations of a 1D statistically homogeneous peridynamic composite bar for the prescribed self-equilibrated body forces. The method is based on estimation of a perturbator introduced by one inclusion inside an infinite homogeneous bar. The statistical averages of the total displacements are estimated by summation of these perturbators for all possible locations of inclusions in the framework of a generalized effective field method.
-
Alali, B. and Lipton, R., Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation, J. Elast., vol. 106, no. 1, pp. 71-103,2012.
-
Askari, E., Bobaru, F., Lehoucq, R.B., Parks, M.L., Siling, S.A., and Weckner, O., Peridynamics for Multiscale Materials Modeling, J. Phys.: Conf. Ser., vol. 125, p. 012078,2008.
-
Askari, E., Xu, J., and Siling, S.A., Peridynamic Analysis of Damage and Failure in Composites, 44th AIAA Aerospace Sciences Meeting and Exhibition, AIAA 2006-88, pp. 1-12, Reno, NV, 2006.
-
Askari, A., Azdoud, Y., Han, F., Lubineau, G., and Siling, S., Peridynamics for Analysis of Failure in Advanced Composite Materials, in Numerical Modeling of Failure in Advanced Composite Materials, Soston, UK: Woodhead Publishing, pp. 331-350,2015.
-
Bobaru, F., Foster, J., Geubelle, P., and Siling, S., Eds., Handbook of Peridynamic Modeling, Boca Raton, FL: CRC Press, 2017.
-
Bobaru, F., Yang, M., Alves, L.F., Siling, S.A., Askari, A., and Xu, J., Convergence, Adaptive Refinement, and Scaling in 1D Peridynamics, Int. J. Numer. Methods Eng, vol. 77, pp. 852-877,2009.
-
Buryachenko, V.A., Micromechanics ofHeterogeneous Materials, New York, NY: Springer, 2007.
-
Buryachenko, V.A., Some General Representations in Thermoperistatics of Random Structure Composites, Int. J. Multiscale Comput. Eng., vol. 12, no. 4, pp. 331-350,2014a.
-
Buryachenko, V., Effective Elastic Modulus of Heterogeneous Peristatic Bar of Random Structure, Int. J. Solids Struct., vol. 51, no. 17, pp. 2940-2948,2014b.
-
Buryachenko, V.A., Effective Thermoelastic Properties of Heterogeneous Thermoperistatic Bar of Random Structure, Int. J. Multiscale Comput. Eng., vol. 13, no. 1, pp. 55-71,2015.
-
Buryachenko, V.A., Effective Properties of Thermoperistatic Random Structure Composites: Some Background Principles, Math. Mech. Solids, vol. 22, no. 6, pp. 366-386,2017.
-
Buryachenko, V., Modeling of One Inclusion in the Infinite Peristatic Matrix, J. Peridynam. Nonlocal Model., vol. 1, pp. 75-87, 2019.
-
Buryachenko, V., Generalized Effective Fields Method in Peridynamic Micromechanics of Random Structure Composites, Int. J. Solids Struct., vol. 202, pp. 765-786,2020a.
-
Buryachenko, V., Effective Deformation of Peridynamic Random Structure Bar Subjected to Inhomogeneous Body Force, Int. J. Multiscale Comput. Eng., vol. 18, pp. 569-585,2020b.
-
Buryachenko, V.A., Local and Nonlocal Micromechanics of Heterogeneous Materials, New York, NY: Springer, 2022.
-
Dayal, K. and Bhattacharya, K., Kinetics of Phase Transformations in the Peridynamic Formulation of Continuum Mechanics, J. Mech. Phys. Solids, vol. 54, pp. 1811-1842,2006.
-
Du, Q., Gunzburger, M., Lehoucq, R.B., and Zhou, K., Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints, SIAMRev., vol. 54, no. 4, pp. 667-696,2012.
-
Emmrich, E. and Weckner, O., Analysis and Numerical Approximation of an Integro-Differential Equation Modeling Nonlocal Effects in Linear Elasticity, Math. Mech. Solids, vol. 12, no. 4, pp. 363-384,2007.
-
Gerstle, W., Sau, N., and Siling, S.A., Peridynamic Modeling of Plain and Reinforced Concrete Structures, in 18th Intern. Conf. on Structural Mechanics in Reactor Technology (SMiRT 18), Beijing, China, No. SMIRT18-B01-2, pp. 54-68,2005.
-
Hu, W., Ha, Y.D., and Bobaru, F., Peridynamic Model for Dynamic Fracture in Unidirectional Fiber-reinforced Composites, Comput. Methods Appl. Mech. Engrg., vols. 217-220, pp. 247-261,2012.
-
Javili, A., McBride, A.T., and Steinmann, P., Continuum-Kinematics-Inspired Peridynamics. Mechanical Problems, J. Mech. Phys. Solids, vol. 131, pp. 125-146,2019.
-
Javili, A., Morasata, R., and Oterkus, E., Peridynamics Review, Math Mech Solids, vol. 24, no. 11, pp. 3714-3739,2019.
-
Kilic, B., Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials, PhD, Department Mechanical Engineering, The University of Arisona, Tucson, AZ, USA, 2009.
-
Lax, M., Multiple Scattering of Waves II. The Effective Fields Dense Systems, Phys. Rev., vol. 85, no. 4, pp. 621-629,1952.
-
Madenci, E. and Oterkus, E., Peridynamic Theory and Its Applications, New York, NY: Springer, 2014.
-
Macek, R.W. and Siling, S.A., Peridynamics via Finite Element Analysis, Finite Elements Anal. Design, vol. 43, no. 15, pp. 1169-1178,2007.
-
Mikata, Y., Analytical Solutions of Peristatic and Peridynamic Problems for a 1D Infinite Rod, Int. J. Solids Struct., vol. 49, no. 21, pp. 2887-2897,2012.
-
Mori, T. and Tanaka, K., Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions, Acta Metal., vol. 21, no. 5, pp. 571-574,1973.
-
Siling, S., Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces, J. Mech. Phys. Solids, vol. 48, no. 1, pp. 175-209,2000.
-
Siling, S.A., Origin and Effect of Nonlocality in a Composite, J. Mech. Mater. Struct., vol. 9, pp. 245-258,2014.
-
Siling, S.A. and Askari, E., A Meshfree Method Based on the Peridynamic Model of Solid Mechanics, Comput. Struct., vol. 83, nos. 17-18, pp. 1526-1535,2005.
-
Siling, S.A., Epton, M., and Weckner, O., Peridynamic States and Constitutive Modeling, J. Elast., vol. 88, pp. 151-184,2007.
-
Siling, S.A. and Lehoucq, R.B., Peridynamic Theory of Solid Mechanics, Adv. Appl. Mech, vol. 44, pp. 73-168,2010.
-
Siling, S.A., Zimmermann, M., and Abeyaratne, R., Deformation of a Peridynamic Bar, J. Elast., vol. 73, pp. 173-190,2003.
-
Weckner, O. and Abeyaratne, R., The Effect of Long-Range Forces on the Dynamics of a Bar, J. Mech. Phys. Solids, vol. 53, no. 3, pp. 705-728,2005.
-
Weckner, O. and Emmrich, E., Numerical Simulation of the Dynamics of a Nonlocal, Inhomogeneous, Infinite Bar, J. Comput. Appl. Mech., vol. 6, no. 2, pp. 311-319,2005.
-
Yang, Y., Ragnvaldsen, O., Bai, Y., Yi, M., and Xu, B.X., 3D Nonisothermal Phase-Field Simulation of Microstructure Evolution during Selective Laser Sintering, npj Comput. Mater., vol. 5, p. 81, 2019.
-
Yilbas, B.S., Laser Heating Applications: Analytical Modeling, Amsterdam, Netherlands: Elsevier, 2012.
-
You, H., Yu, Y., Siling, S., and D'Elia, M., Data-Driven Learning of Nonlocal Models: From High-Fidelity Simulations to Constitutive Laws, 2020. arXiv: 2012.04157.
-
You, H., Yu, Y., Siling, S., and D'Elia, M., A Data-Driven Peridynamic Continuum Model for Upscaling Molecular Dynamics, Comput. Meth. Appl. Mech. Eng., vol. 389, p. 114400,2022.