scholarly journals ON MULTISCALE DAMAGE MODELLING OF HETEROGENEOUS MATERIALS USING NONLOCAL CONTINUUM THEORY

Brodogradnja ◽  
2021 ◽  
Vol 72 (4) ◽  
pp. 121-139
Author(s):  
Jurica Sorić ◽  
◽  
Tomislav Lesičar ◽  
Filip Putar ◽  
Zdenko Tonković ◽  
...  
Keyword(s):  
Finite Element ◽  
Equivalent Plastic Strain ◽  
Continuum Theory ◽  
Material Point ◽  
Ductile Damage ◽  
Element Formulation ◽  
State Variables ◽  
Nonlocal Continuum ◽  
Element Discretization ◽  
Nonlocal Continuum Theory

An overview of the modelling of quasi-brittle as well as ductile damage is given. The multiscale procedure employing the nonlocal continuum theory is described in more detail. The softening is introduced at the microlevel in the microstructural volume element and after that the homogenization procedure state variables are mapped at the macrolevel material point via the scale transition approach. In the case of quasi-brittle softening the C1 continuous finite element discretization is applied at both micro- and macrolevel. At the modelling of ductile damage response, the macrolevel is also discretized by the C1 finite element formulation, while the microscale utilizes quadrilateral mixed finite elements employing the nonlocal equivalent plastic strain and gradient-enhanced elastoplasticity. All approaches presented are verified in the standard examples.

Nonlocal Continuum Theory Based Modeling of Carbon Nanotube Composites

2008 ◽  
Author(s):  
Ali Alavinasab ◽  
Goodarz Ahmadi ◽  
Ratneshwar Jha
Keyword(s):  
Finite Element ◽  
Carbon Nanotube ◽  
Continuum Theory ◽  
Nonlocal Theory ◽  
Total Force ◽  
Stress Distributions ◽  
Nonlocal Continuum ◽  
Element Analysis ◽  
Nonlocal Continuum Theory ◽  
Nanotube Composites

Analytical modeling of Carbon Nanotube (CNT) composite based on the nonlocal continuum theory is investigated. This approach accounts for nonlocal stress-strain relationships, that is, stress at any point in a structure is a function of strain in the entire structure. Finite element analysis of a representative volume element (RVE) of CNT composite is used to evaluate unknown constant in the nonlocal theory based solution. Stress distributions are obtained from finite element method (FEM), nonlocal theory, and standard (local) elasticity. Nonlocal theory and FEM stress distributions yield the same total force and first moment, whereas standard elasticity gives less accurate results.

A finite element study on effect of frictional heating in the taylor rod impact problem

2014 ◽  
Vol 11 (6) ◽  
pp. 529-542 ◽  
Author(s):  
Sachin Gautam ◽  
Ravindra Saxena
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
High Strain ◽  
Frictional Heating ◽  
Equivalent Plastic Strain ◽  
Surface Friction ◽  
Effect Of Temperature ◽  
Element Formulation ◽  
Strain Rates ◽  
High Strain Rates

In an impact phenomenon the material is subjected to very short duration high force levels resulting large plastic deformations and rise in temperature at high strain rates. A circular rod impacting against a rigid surface called as Taylor rod impact test is widely used for determining the mechanical behaviour of materials subjected to high strain rates with associated increase in temperature. A three-dimensional large deformation, thermo-elasto-plastic, dynamic, contact, finite element formulation is developed to study the effect of temperature rise due to plastic deformation and surface friction on the deformation and stress fields. It is found that the predicted equivalent plastic strain values are influenced by temperature generated due to plastic deformation and surface friction. The values of the coefficient of friction have a profound effect on the location of fracture initiation on the impacting face in a circular rod.

Implicit finite element formulation of multiresolution continuum theory

2015 ◽  
Vol 293 ◽  
pp. 114-130 ◽  
Author(s):  
Hao Qin ◽  
Lars-Erik Lindgren ◽  
Wing Kam Liu ◽  
Jacob Smith
Keyword(s):  
Finite Element ◽  
Continuum Theory ◽  
Finite Element Formulation ◽  
Element Formulation

A Damage Identification Method Using Vibration Modal Parameters Through Finite Element Discretization

2003 ◽  
Author(s):  
Xiaoping Zhou ◽  
Abhijit Gupta
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Damage Identification ◽  
Least Squares Method ◽  
Modal Testing ◽  
Mode Shapes ◽  
Element Formulation ◽  
Element Discretization ◽  
Damage Indices ◽  
Actual Damage

Natural frequencies and mode shapes of a structure will change whenever the structure has any kind of damage. This paper introduces a technique to quantify and locate the damage when the natural frequencies and mode shapes of undamaged and damaged structure are known. Aluminum beams (with and without damage) are used for numerical simulation and experimental verification. To establish the theoretical basis of this method, finite element formulation is used. A set of undetermined equations involving damage indices and natural frequencies and mode shapes of undamaged and damaged structures are obtained. The damage indices are computed using non-negative least squares method. Impact modal testing was conducted with three aluminum beams and damage indices based on experimental data are compared with actual damage cases to establish the effectiveness of this method to identify the damage.

scholarly journals Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 1: Theory and validation

2003 ◽  
Vol 217 (4) ◽  
pp. 289-304 ◽  
Author(s):  
M. J. A. Holmes ◽  
H. P. Evans ◽  
T. G. Hughes ◽  
R. W. Snidle
Keyword(s):  
Finite Element ◽  
Point Contact ◽  
Detailed Comparison ◽  
Element Formulation ◽  
Element Discretization ◽  
Discretization Methods ◽  
Temporal Discretization ◽  
Analysis Technique ◽  
Full Coupling ◽  
Comparison Of The Results

The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential deflection formulation. The way in which the differential deflection is incorporated into the overall solution method for a point contact is discussed. A range of spatial and temporal discretization methods are incorporated and compared. The method is validated under transient conditions by a detailed comparison with published work produced using a different, independent method incorporating a moving roughness feature. A comparison of the results with different discretization methods leads to the conclusion that spatial central differencing with a Crank-Nicolson temporal discretization is the most effective finite difference scheme, and this is generally equivalent to the finite element discretization given in detail in the paper. A comparison of the results produced for moving rough surfaces suggests that the finite element formulation is preferred.

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