A Continuum-Microscopic Algorithm for Modeling Fibrous, Heterogeneous Media with Dynamic Microstructures

Many materials undergo reconfiguration of microscopic structure in response to applied stress. Computing the mechanical behavior of such materials at the continuum level requires a locally valid stress-strain relation. Due to the dynamic microstructure reconfiguration, such relations are difficult to obtain analytically. Numerical simulation of the microscopic dynamics is an alternative, albeit one that is computationally expensive. Continuum-microscopic (CM) interaction algorithms seek to reduce computational cost by microscopic simulation over some small fraction of the continuum time step of interest, enough to determine the locally valid stress-strain relationship, assumed to hold over the entire continuum time step. One difficulty with this approach is the problem of recreating a valid microscopic configuration at the start of the next continuum time step. In most previous CM algorithms, the microscopic structure at the beginning of a new continuum time step is assumed to obey some predefined statist...

[1]  H. Callen Thermodynamics and an Introduction to Thermostatistics , 1988 .

[2]  W. T. Grandy,et al.  Kinetic theory : classical, quantum, and relativistic descriptions , 2003 .

[3]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[4]  E Weinan,et al.  The heterogeneous multiscale method* , 2012, Acta Numerica.

[5]  D. Wirtz,et al.  Strain Hardening of Actin Filament Networks , 2000, The Journal of Biological Chemistry.

[6]  J. Michel,et al.  Effective properties of composite materials with periodic microstructure : a computational approach , 1999 .

[7]  Daniel A. Fletcher,et al.  Reversible stress softening of actin networks , 2007, Nature.

[8]  C. Bert,et al.  The behavior of structures composed of composite materials , 1986 .

[9]  J. Oden,et al.  Analysis and adaptive modeling of highly heterogeneous elastic structures , 1997 .

[10]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[11]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[12]  M. G. RUSBRIDGE,et al.  Kinetic Theory , 1969, Nature.

[13]  Kun Xu,et al.  Numerical Navier-Stokes solutions from gas kinetic theory , 1994 .

[14]  Jurij Kotar,et al.  The nonlinear mechanical response of the red blood cell , 2007, Physical biology.

[15]  Jacob Fish,et al.  Multigrid method for periodic heterogeneous media Part 1: Convergence studies for one-dimensional case , 1995 .

[16]  Ioannis G. Kevrekidis,et al.  Equation-free multiscale computations for a lattice-gas model: coarse-grained bifurcation analysis of the NO+CO reaction on Pt(1 0 0) , 2004 .

[17]  R. LeVeque Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[18]  Ilpo Vattulainen,et al.  Strain hardening, avalanches, and strain softening in dense cross-linked actin networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  W Alt,et al.  Cytoplasm dynamics and cell motion: two-phase flow models. , 1999, Mathematical biosciences.

[20]  B. Alberts,et al.  Molecular Biology of the Cell (Fifth Edition) , 2008 .

[21]  Yu Zou,et al.  An equation-free approach to analyzing heterogeneous cell population dynamics , 2007, Journal of mathematical biology.

[22]  Robert Lipton Homogenization and Field Concentrations in Heterogeneous Media , 2006, SIAM J. Math. Anal..

[23]  Dominic Welsh,et al.  Probability: An Introduction , 1986 .

[24]  A. N. Guz On Two-Scale Model of Fracture Mesomechanics of Composites with Cracks under Compression , 2005 .

[25]  I. Kevrekidis,et al.  Coarse molecular dynamics of a peptide fragment: Free energy, kinetics, and long-time dynamics computations , 2002, physics/0212108.

[26]  Jennifer J. Young,et al.  Cytoskeleton micromechanics: A continuum-microscopic approach , 2010 .

[27]  김척기,et al.  Dynamic Mechanical Properties of filled PP , 1986 .

[28]  Damien Durville A finite element approach of the behaviour of woven materials at microscopic scale , 2008 .

[29]  E. Weinan,et al.  Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics , 2005 .

[30]  E. Morozov,et al.  Mechanics and analysis of composite materials , 2001 .

[31]  A. Abdulle ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY , 2006 .

[32]  R. J. Arsenault,et al.  Metal matrix composites : mechanisms and properties , 1991 .

[33]  C. W. Gear,et al.  Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[34]  Tsu-Wei Chou,et al.  Microstructural design of fiber composites: Nonlinear elastic finite deformation of flexible composites , 1992 .

[35]  Alejandro L. Garcia,et al.  Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo , 1999 .

[36]  Ioannis G. Kevrekidis,et al.  Equation-free: The computer-aided analysis of complex multiscale systems , 2004 .

[37]  Thomas Y. Hou,et al.  Multiscale Modeling and Computation of Incompressible Flow , 2002 .