Variationally consistent computational homogenization of transient heat flow

A framework for variationally consistent homogenization, combined with a generalized macrohomogeneity condition, is exploited for the analysis of non-linear transient heat conduction. Within this framework the classical approach of (model-based) first-order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are (in practice) introduced in quadrature points in standard fashion. Along with the classical averages, a higher order conservation quantity is obtained. An iterative FE2-algorithm is devised for the case of non-linear diffusion and storage coefficients, and it is applied to transient heat conduction in a strongly heterogeneous particle composite. Parametric Studies are carried Out, in particular with respect to the influence of the 'internal length' associated with the second-order conservation quantity. Copyright (C) 2009 John Wiley & Sons, Ltd.

[1]  Jacob Fish,et al.  Composite grid method for hybrid systems , 1996 .

[2]  Jacob Fish,et al.  Bridging the scales in nano engineering and science , 2006 .

[3]  Denis Aubry,et al.  Adaptive strategy for transient/coupled problems applications to thermoelasticity and elastodynamics , 1999 .

[4]  Jacob Fish,et al.  Toward realization of computational homogenization in practice , 2008 .

[5]  J. Schröder,et al.  Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials , 1999 .

[6]  Jacob Fish,et al.  Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials , 2007 .

[7]  C. Miehe,et al.  Computational micro-to-macro transitions of discretized microstructures undergoing small strains , 2002 .

[8]  Bernhard A. Schrefler,et al.  Thermo‐mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach , 2007 .

[9]  V. Kouznetsova,et al.  Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme , 2002 .

[10]  Sylvie Aubry,et al.  A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials , 2003 .

[11]  M. Geers,et al.  Computational homogenization for heat conduction in heterogeneous solids , 2008 .

[12]  Peter Wriggers,et al.  A model for simulating the deterioration of structural-scale material responses of microheterogeneous solids , 2001 .

[13]  Jacob Fish,et al.  Multiscale enrichment based on partition of unity for nonperiodic fields and nonlinear problems , 2007 .

[14]  C. Miehe,et al.  On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers , 2007 .

[15]  Jacob Fish,et al.  Non‐local dispersive model for wave propagation in heterogeneous media: one‐dimensional case , 2002 .

[16]  Stabilized nonlocal model for dispersive wave propagation in heterogeneous media , 2004 .

[17]  Fredrik Larsson,et al.  Adaptive Bridging of Scales in Continuum Modeling Based on Error Control , 2008 .