scholarly journals Coupling BEM and VEM for the Analysis of Composite Materials with Damage

2021 ◽  
Author(s):  
Marco Lo Cascio ◽  
Ivano Benedetti
Keyword(s):  
Damage Mechanics ◽  
Numerical Technique ◽  
Matrix Material ◽  
Heterogeneous Materials ◽  
Continuum Damage Mechanics ◽  
Computational Effort ◽  
Polygonal Mesh ◽  
Analysis And Design ◽  
Surrounding Matrix ◽  
Element Method

Numerical tools which are able to predict and explain the initiation and propagation of damage at the microscopic level in heterogeneous materials are of high interest for the analysis and design of modern materials. In this contribution, we report the application of a recently developed numerical scheme based on the coupling between the Virtual Element Method (VEM) and the Boundary Element Method (BEM) within the framework of continuum damage mechanics (CDM) to analyze the progressive loss of material integrity in heterogeneous materials with complex microstructures. VEM is a novel numerical technique that, allowing the use of general polygonal mesh elements, assures conspicuous simplification in the data preparation stage of the analysis, notably for computational micro-mechanics problems, whose analysis domain often features elaborate geometries. BEM is a widely adopted and efficient numerical technique that, due to its underlying formulation, allows reducing the problem dimensionality, resulting in substantial simplification of the pre-processing stage and in the decrease of the computational effort without affecting the solution accuracy. The implemented technique has been applied to an artificial microstructure, consisting of the transverse section of a circular shaped stiff inclusion embedded in a softer matrix. BEM is used to model the inclusion that is supposed to behave within the linear elastic range, while VEM is used to model the surrounding matrix material, developing more complex nonlinear behaviors. Numerical results are reported and discussed to validate the proposed method.

Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme

2020 ◽  
Vol 11 (04) ◽  
pp. 2050008
Author(s):  
Marco Lo Cascio ◽  
Marco Grifò ◽  
Alberto Milazzo ◽  
Ivano Benedetti
Keyword(s):  
Numerical Technique ◽  
Matrix Material ◽  
Heterogeneous Materials ◽  
Computational Effort ◽  
Computational Homogenization ◽  
Surrounding Matrix ◽  
Unit Cells ◽  
Virtual Element ◽  
Solution Accuracy ◽  
Element Method

The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the problem, resulting in substantial simplification of the pre-processing stage and in the reduction of the computational effort, without jeopardizing the solution accuracy. In this contribution, we explore the possibility of a coupling VEM and BEM for computational homogenization of heterogeneous materials with complex microstructures. The test morphologies consist of unit cells with irregularly shaped inclusions, representative e.g., of a fiber-reinforced polymer composite. The BEM is used to model the inclusions, while the VEM is used to model the surrounding matrix material. Benchmark finite element solutions are used to validate the analysis results.

scholarly journals Creep crack simulations using continuum damage mechanics and extended finite element method

2017 ◽  
Vol 28 (1) ◽  
pp. 3-34 ◽  
Author(s):  
VB Pandey ◽  
I V Singh ◽  
BK Mishra ◽  
S Ahmad ◽  
AV Rao ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Growth ◽  
Damage Mechanics ◽  
Extended Finite Element Method ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Extended Finite Element ◽  
Creep Crack ◽  
Element Method

In the present work, elasto-plastic creep crack growth simulations are performed using continuum damage mechanics and extended finite element method. Liu–Murakami creep damage model and explicit time integration scheme are used to evaluate the creep strain and damage variable for various materials at different temperatures. Compact tension and C-shaped tension specimens are selected for the simulation of crack growth analysis. For damage evaluation, both local and nonlocal approaches are employed. The accuracy of the extended finite element method solutions is checked by comparing with experimental results and finite element solutions. These results show that the extended finite element method requires a much coarser mesh to effectively model crack propagation. It is also shown that mesh independent results can be achieved by using nonlocal implementation.

scholarly journals On Continuum Damage Modeling of Fiber Reinforced Viscoelastic Composites with Microcracks in terms of Invariants

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Melek Usal
Keyword(s):  
Damage Mechanics ◽  
Transverse Isotropy ◽  
Matrix Material ◽  
Damage Model ◽  
Viscoelastic Behavior ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Symmetric Tensors ◽  
The Matrix ◽  
Linear Viscoelastic Behavior

A continuum damage model is developed for the linear viscoelastic behavior of composites with microcracks consisting of an isotropic matrix reinforced by two arbitrarily independent and inextensible fiber families. Despite the fact that the matrix material is isotropic, the model in consideration bears the characteristic of directed media included in the transverse isotropy symmetry group solely due to its fibers distributions and the existence of microcracks. Using the basic laws of continuum damage mechanics and equations belonging to kinematics and deformation geometries of fibers, the constitutive functions have been obtained. It has been detected as a result of the thermodynamic constraints that the stress potential function is dependent on two symmetric tensors and two vectors, whereas the dissipative stress function is dependent on four symmetric tensors and two vectors. To determine arguments of the constitutive functionals, findings relating to the theory of invariants have been used as a method because of the fact that isotropy constraint is imposed on the material. As a result the linear constitutive equations of elastic stress, dissipative stress, and strain energy density release rate have been written in terms of material coordinate description. Using these expressions, total stress has been found.

Fatigue Life of the Human Teeth: A Continuum Damage Approach

2019 ◽  
Vol 43 ◽  
pp. 1-19
Author(s):  
Theddeus Tochukwu Akano
Keyword(s):  
Fatigue Life ◽  
Damage Mechanics ◽  
Stress Amplitude ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Elastoplastic Model ◽  
Human Teeth ◽  
Proposed Model ◽  
Number Of Cycles ◽  
Cycles To Failure

Normal oral food ingestion processes such as mastication would not have been possible without the teeth. The human teeth are subjected to many cyclic loadings per day. This, in turn, exerts forces on the teeth just like an engineering material undergoing the same cyclic loading. Over a period, there will be the creation of microcracks on the teeth that might not be visible ab initio. The constant formation of these microcracks weakens the teeth structure and foundation that result in its fracture. Therefore, the need to predict the fatigue life for human teeth is essential. In this paper, a continuum damage mechanics (CDM) based model is employed to evaluate the fatigue life of the human teeth. The material characteristic of the teeth is captured within the framework of the elastoplastic model. By applying the damage evolution equivalence, a mathematical formula is developed that describes the fatigue life in terms of the stress amplitude. Existing experimental data served as a guide as to the completeness of the proposed model. Results as a function of age and tubule orientation are presented. The outcomes produced by the current study have substantial agreement with the experimental results when plotted on the same axes. There is a notable difference in the number of cycles to failure as the tubule orientation increases. It is also revealed that the developed model could forecast for any tubule orientation and be adopted for both young and old teeth.

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