Influence of the course boundary value problem on length scale parmeters for second-gradient continuum theories

Conference · Mon Dec 20 04:00:00 EST 2010

OSTI ID:1044900

Luscher, Darby J ^[1]; Bronkhorst, Curt A ^[1]; Mc Dowell, David L ^[2]

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1. Los Alamos National Laboratory
2. GEORGIA TECH

All nonlocal continuum descriptions of inelastic material response involve length scale parameters that either directly or implicitly quantify the physical dimensions of a neighborhood of response which influences the behavior at a particular point. The second-gradient continuum theories such as those developed by Germain, Toupin and Mindlin, and Eringen, and giving rise to strain-gradient plasticity, is becoming a common coarse-scale basis for homogenization of material response that respects the non local nature of heterogeneous material response. Ideally, the length scale parameters involved in such homogenization would be intrinsically associated with dominant aspects of the microstructure. However, these parameters, at least in some cases, are inextricably linked to the details of the coarse scale boundary value problem. Accordingly, they cannot be viewed as pure constitutive parameters. An example problem of multiscale homogenization is presented to underscore the dependence of second-gradient length scale parameters on the coarse scale boundary value problem, namely the multiscale response of an idealized porous microstructure. The fine scale (microstructure) comprises elastic perfectly plastic matrix with a periodic array of circular voids. This fine scale description of the problem is identical for two separate classes of coarse scale boundary value problem, viz. an extruded channel subject to compression and eventually developing plastic shear bands and a thin layer of material with larger (coarse scale) elliptical voids subject to shear deformation. Implications of the relationship between length scale parameters and the details of the coarse scale boundary value problem are discussed and ideas to ascertain such length parameters from evolving response fields are presented.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 1044900
• Report Number(s): LA-UR-10-08378; LA-UR-10-8378
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPRESSION
DEFORMATION
DIMENSIONS
MICROSTRUCTURE
PLASTICITY
PLASTICS
SHEAR