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A variational multiscale approach to strain localization – formulation for multidimensional problems. (English) Zbl 1011.74069
This paper examines the strain localization by using a multiscale variational formulation. The idea is to compute on the coarse scale, but still retain (on the coarse scale) the effects of fine scale. This extends former one-dimensional approach to weak discontinuities [the authors, ibid. 159, No. 3-4, 193-222 (1998; Zbl 0961.74009)]. This multiscale approach results in a non-local constitutive law at the coarse scale, thus avoiding ill-posed mesh-dependent solutions. Both the variational formulation and numerical implementation are presented. The paper concludes with some numerical examples.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
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