@Article{icces.2021.08043,
AUTHOR = {Jurica Sorić, Boris Jalušić, Tomislav Lesičar, Filip Putar, Zdenko Tonković},
TITLE = {Numerical Modeling of Material Deformation Responses Using Gradient  Continuum Theory},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {23},
YEAR = {2021},
NUMBER = {1},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v23n1/42019},
ISSN = {1933-2815},
ABSTRACT = {In modeling of material deformation responses, the physical 
phenomena such as stress singularity problems, strain localization and modeling 
of size effects cannot be properly captured by means of classical continuum 
mechanics. Therefore, various regularization techniques have been developed to 
overcome these problems. In the case of gradient approach the implicit gradient 
formulations are usually used when dealing with softening. Although the 
structural responses are mesh objective, they suffer from spurious damage 
growth. Therefore, a new formulation based on the strain gradient continuum 
theory, which includes both strain gradients and their stress conjugates, has been 
proposed. In this way, a physically correct structural response can be captured.
The C1 continuity displacement based finite element formulation employing that
theory has been derived. The element consists of three nodes and 36 degrees of 
freedom, and displacement field is approximated by a condensed fifth order 
polynomial. By employing an appropriate softening low, the damage evolution 
may be modeled [1]. This element formulation may be also used in the 
multiscale computational approach as shown in [2]. As an alternative to finite 
element method (FEM), a relatively new meshless approach is used for the 
discretization of higher-order continuum. In comparison to FEM, it possesses
real advantages in a simpler construction of shape functions of arbitrarily highorder continuity as well as in formulation with fewer nodal unknowns at the 
global level. In this contribution, the mixed meshless Local Petrov- Galerkin 
method will be presented. The governing equations of gradient elasticity are 
solved using two different operator-split approaches, and the problem is 
considered as an uncoupled sequence of two sets of second-order differential 
equations [3]. The performance of the presented methods is demonstrated using 
appropriate numerical examples.},
DOI = {10.32604/icces.2021.08043}
}