Lattice Spring Models

Solid mechanics can be addressed by a Lattice Spring Model whose major ingredients are briefly described. It is applied to solve the dynamic equations of motions and the static equations derived by homogenization. Results relative to the macroscopic properties of solids are successfully compared to the ones obtained by analytical methods and by other techniques of numerical calculations. Wave velocities derived by direct simulations are in good agreement with the ones derived by homogenization.

[1]  G. Rodin.  The overall elastic response of materials containing spherical inhomogeneities , 1993 .

[2]  Ashok V. Kumar,et al.  Implicit boundary method for determination of effective properties of composite microstructures , 2009 .

[3]  Feng,et al.  Behavior of depleted elastic networks: Comparison of effective-medium and numerical calculations. , 1985, Physical review. B, Condensed matter.

[4]  I. Webman,et al.  Vibration properties of a percolating cluster , 1984 .

[5]  Joseph B. Keller,et al.  Effective elasticity tensor of a periodic composite , 1984 .

[6]  J. Thovert,et al.  Wave propagation through saturated porous media. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  T. Iwakuma,et al.  Composites with periodic microstructure , 1983 .

[8]  Arbabi,et al.  Test of universality for three-dimensional models of mechanical breakdown in disordered solids. , 1990, Physical review. B, Condensed matter.

[9]  E. Sanchez-Palencia.  Non-Homogeneous Media and Vibration Theory , 1980 .

[10]  John H. Kinney,et al.  Elastic constants of cellular structures , 1997 .

[11]  Pierre M. Adler,et al.  Porous media : geometry and transports , 1992 .

[12]  D. Srolovitz,et al.  Brittle fracture in materials with random defects. , 1989, Physical review. B, Condensed matter.

[13]  A. Sangani,et al.  Elastic coefficients of composites containing spherical inclusions in a periodic array , 1987 .

[14]  Anna C Balazs,et al.  Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Pierre M. Adler,et al.  The effective mechanical properties of random porous media , 1996 .

[16]  van der Erik Giessen,et al.  Scaling of the failure stress of homophase and heterophase three-dimensional spring networks , 2002 .

[17]  P. N. Keating,et al.  Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure , 1966 .

[18]  Martin Ostoja-Starzewski,et al.  Lattice models in micromechanics , 2002 .

[19]  John H. Kinney,et al.  DEFORMATION AND FAILURE IN CELLULAR MATERIALS , 1997 .

[20]  Jian Wang,et al.  The bond-bending model in three dimensions , 1989 .