Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 198, Issue 15-16, Pages 1401-1412Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2008.12.031
Keywords
Generalized continua; Strain gradient theory; Multiscale methods; Scale effects; Meshfree methods
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This work follows a generalized continuum framework [C. Sansour, A unified concept of elastic-visco-plastic cosserat and micromorphic continua, J. Phys. IV Proc. 8 (1998) 341-348] to derive a first strain gradient formulation which features a generalized deformation description, new strain and stress measures. As a consequence of these new quantities a corresponding generalized variational principle is formulated and its underlying equilibrium equations are derived. The approach is completed by Dirichlet boundary conditions for the displacement held and its derivatives. The basic idea behind this generalized continuum theory is the consideration of a micro- and a macro-space which span together the generalized space. The approach is appealing from theoretical as well as numerical point of view as it allows for the consideration of classical material laws and circumvents the use of otherwise cumbersome representation theorems. The resulting expressions for first and second order stresses are obtained by numerical integration over the micro-space. In this way material information of the micro-space, which is here only the geometrical specifications of the micro-continuum, can naturally enter the constitutive law. Moreover, non-linear material behaviour can be considered in a straightforward manner. In this work conventional hyperelasticity will be considered. Four applications in the context of linear and non-linear hyperelasticity demonstrate the potential of the proposed method. In particular, the use of a moving least square-based meshfree method facilitates a pure displacement-based approximation scheme, as it can provide C(1) continuity which is required for this strain gradient formulation. (C) 2009 Elsevier B.V. All rights reserved.
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