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Regularization of material instabilities of meshfree approximations with intrinsic length scales. (English) Zbl 0987.74079
Summary: Meshfree approximation, such as moving least square (MLS) and reproducing kernel (RK) approximations, possess intrinsic non-local properties. Here these non-local properties of meshfree approximations are exploited to incorporate an intrinsic length scale which regularizes problems with material instabilities. The discrete equilibrium equation is obtained by employing an assumed strain method in Galerkin approximation. This proposed method is essentially uniformly non-local, but, in contrast to non-local finite elements, no kinematics modes are observed. Gradient-type regularization can also be modelled by this method without additional boundary conditions and other complications of the conventional gradient methods. Numerical examples show that the displacement-based MLS/RK formulation (1-level regularization) is sufficient to remedy mesh sensitivity in damage-induced strain localization. For strain localization associated with plasticity, a two-level MLS/RK regularization in displacement and strain is shown to be effective.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74R05 Brittle damage
74R20 Anelastic fracture and damage
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