Formulation and Finite Element Implementation of Dynamically Consistent Gradient Elasticity

2009 ◽  
Author(s):  
H. Askes ◽  
I.M. Gitman ◽  
T. Bennett
Keyword(s):  
Finite Element ◽  
Gradient Elasticity ◽  
Finite Element Implementation

scholarly journals A finite element implementation of the stress gradient theory

Meccanica ◽  
2021 ◽  
Author(s):  
Tobias Kaiser ◽  
Samuel Forest ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Stress Gradient ◽  
Gradient Elasticity ◽  
Field Variable ◽  
Gradient Theory ◽  
Weak Formulation ◽  
Finite Element Implementation ◽  
Valued Field ◽  
Normal Projection

AbstractIn this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Finite element implementation of an improved conservative level set method for two-phase flow

2014 ◽  
Vol 100 ◽  
pp. 138-154 ◽  
Author(s):  
Lanhao Zhao ◽  
Jia Mao ◽  
Xin Bai ◽  
Xiaoqing Liu ◽  
Tongchun Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Finite Element Implementation ◽  
Conservative Level Set

Finite Element Implementation of Gent-Gent Hyperelastic Model for Swollen Elastomers

2020 ◽  
Vol 2020 (0) ◽  
pp. J03139
Author(s):  
Shotaro KIKUCHI ◽  
Hiroaki MIYOSHI ◽  
Seishiro MATSUBARA ◽  
Dai OKUMURA
Keyword(s):  
Finite Element ◽  
Finite Element Implementation ◽  
Hyperelastic Model
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