TY - EJOU
AU - Sorić, Jurica
AU - Jalušić, Boris
AU - Lesičar, Tomislav
AU - Putar, Filip
AU - Tonković, Zdenko
TI - Numerical Modeling of Material Deformation Responses Using Gradient Continuum Theory
T2 - The International Conference on Computational \& Experimental Engineering and Sciences
PY - 2021
VL - 23
IS - 1
SN - 1933-2815
AB - 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.
KW - Strain gradient theory; finite element method; meshless method
DO - 10.32604/icces.2021.08043