engleski

Meshfree Methods for Modeling of Material Deformation Using Higher-Order Continuum Theories

In this contribution, meshfree methods are applied for the modeling of gradient elasticity and hyperelasticity using higher-order theories based on only one microstructural parameter. Both the Mixed Meshless Local Petrov-Galerkin (MLPG) approach and the Optimal Transportation Method (OTM) are considered. Firstly, the MLPG collocation method based on the staggered solution strategy is utilized for structures undergoing small strain. Thereafter, the OTM based on the weak-form of gradient continuum for finite strain is considered. Both methods are used for the modeling of homogeneous and heterogeneous structures. In the mixed collocation approach the fourth-order equilibrium equations are solved as an uncoupled sequence of two sets of second-order differential equations, while in the OTM method the weak-form of the original fourth-order equilibrium equations is employed. The independent variables in both approaches are approximated using meshless interpolating functions enabling the satisfaction of the boundary conditions in a simple and straightforward manner without the need for the calculation of additional parameters. The Interpolation Moving Least Squares (IMLS) are utilized in the mixed MLPG methods and the Maximum-Entropy functions are used in the OTM method. The analysis of accuracy and numerical performance of both approaches are demonstrated by a set of suitable numerical examples.

meshfree methods, higher-order continuum

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