An Equivalent Constitutive Model of Cancellous Bone With Fracture Prediction

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Mohammad Salem ◽  
Lindsey Westover ◽  
Samer Adeeb ◽  
Kajsa Duke
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cast Iron ◽  
Constitutive Model ◽  
Cancellous Bone ◽  
Equivalent Model ◽  
Plasticity Model ◽  
Microscale Model ◽  
Computational Resources ◽  
Element Method

Abstract To simulate the mechanical and fracture behaviors of cancellous bone in three anatomical directions and to develop an equivalent constitutive model. Microscale extended finite element method (XFEM) models of a cancellous specimen were developed with mechanical behaviors in three anatomical directions. An appropriate abaqus macroscale model replicated the behavior observed in the microscale models. The parameters were defined based on the intermediate bone material properties in the anatomical directions and assigned to an equivalent nonporous specimen of the same size. The equivalent model capability was analyzed by comparing the micro- and macromodels. The hysteresis graphs of the microscale model show that the modulus is the same in loading and unloading; similar to the metal plasticity models. The strength and failure strains in each anatomical direction are higher in compression than in tension. The microscale models exhibited an orthotropic behavior. Appropriate parameters of the cast iron plasticity model were chosen to generate macroscale models that are capable of replicating the observed microscale behavior of cancellous bone. Cancellous bone is an orthotropic material that can be simulated using a cast iron plasticity model. This model is capable of replicating the microscale behavior in finite element (FE) analysis simulations without the need for individual trabecula, leading to a reduction in computational resources without sacrificing model accuracy. Also, XFEM of cancellous bone compared to traditional finite element method proves to be a valuable tool to predict and model the fractures in the bone specimen.

A numerical approach based on finite element method for the wrinkling analysis of dielectric elastomer membranes

2021 ◽  
pp. 1-37
Author(s):  
Guoyong Mao ◽  
Wei Hong ◽  
Martin Kaltenbrunner ◽  
Shaoxing Qu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thickness Distribution ◽  
Numerical Approach ◽  
Dielectric Elastomer ◽  
Equivalent Model ◽  
Maxwell Stress ◽  
Buckling Mode ◽  
Post Buckling ◽  
Element Method

Abstract Dielectric elastomer (DE) actuators are deformable capacitors capable of a muscle-like actuation when charged. When subjected to voltage, DE membranes coated with compliant electrodes may form wrinkles due to the Maxwell stress. Here, we develop a numerical approach based on the finite element method (FEM) to predict the morphology of wrinkled DE membranes mounted on a rigid frame. The approach includes two steps, I) pre-buckling and II) post-buckling. In step I, the first buckling mode of the DE membrane is investigated by substituting the Maxwell stress with thermal stress in the built-in function of the FEM platform SIMULIA Abaqus. In step II, we use this first buckling mode as an artificial geometric imperfection to conduct the post-buckling analysis. For this purpose, we develop an equivalent model to simulate the mechanical behavior of DEs. Based on our approach, the thickness distribution and the thinnest site of the wrinkled DE membranes subjected to voltage are investigated. The simulations reveal that the crests/troughs of the wrinkles are the thinnest sites around the center of the membrane and corroborate these findings experimentally. Finally, we successfully predict the wrinkles of DE membranes mounted on an isosceles right triangle frame with various sizes of wrinkles generated simultaneously. These results shed light on the fundamental understanding of wrinkled dielectric elastomers but may also trigger new applications such as programmable wrinkles for optical devices or their prevention in DE actuators.

Numerical Simulation of Polymer Flows in Coat-Hanger Die Using Wagner Constitutive Model

2011 ◽  
Vol 189-193 ◽  
pp. 1941-1945
Author(s):  
Yong Li ◽  
Jian Rong Zheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Computing Time ◽  
Three Dimensional ◽  
Die Design ◽  
Dimensional Simulation ◽  
Element Method

An understanding of flow behavior of polymer melts through a slit die is extremely important for optimizing die design. In this paper numerical simulations have been undertaken for the flow of linear low-density polyethylene through Coat-hanger sheet dies. A new finite element method is proposed to simulate the flow in slit channel using Wagner constitutive model. This is one kind of finite element semi-analytical method by which the velocity distributions in thickness direction is approach by Fourier series. Numerical results of volumetric flow and pressure in coat-hanger dies are given to compare to the three-dimensional simulation using the finite element method. It appears that numerical solutions are as accurate as the complete 3D calculations and the computing time can be saved.

Finite element method applied to the quenching of steel cylinders using a multi-phase constitutive model

2013 ◽  
Vol 83 (7) ◽  
pp. 1013-1037 ◽  
Author(s):  
Wendell P. de Oliveira ◽  
Marcelo A. Savi ◽  
Pedro Manuel C. L. Pacheco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Multi Phase ◽  
Element Method

scholarly journals Finite Element Method Analysis of Stress Distribution to Supporting Tissues in a Class IV Aramany Removable Partial Denture (Part II: Bone and Mucosal Membrane)

2008 ◽  
Vol 9 (7) ◽  
pp. 49-56 ◽  
Author(s):  
Jafar Gharechahi ◽  
Esmael Sharifi ◽  
Saeid Nosohian ◽  
Nafiseh Asadzadeh Aghdaee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Distribution ◽  
Cancellous Bone ◽  
Removable Partial Denture ◽  
Posterior Teeth ◽  
Mucosal Membrane ◽  
Method Analysis ◽  
Class Iv ◽  
Element Method

Abstract Aim One of the most important issues in the design of removable partial dentures (RPD) is the location of retentive arms to provide sufficient support. This is a critical factor in patients with less supporting tissue and abutment teeth. Patients classified as Class IV Aramany need special attention in this area of RPD design to minimize the stress distribution in bone and mucosal membrane. Using the finite element method, the aim of this study was to analyze the distribution stress to supporting tissues when a Class IV Aramany RPD is worn. The data presented in this report are the effects of the stress on bone and mucosal membranes. Results on teeth and the periodontal ligament have been previously reported. Methods and Materials Three dimensional finite element models were constructed using normal dimensions. Exact physiology and morphology of teeth and the remaining palate were simulated to that of a maxillectomy patient. Three RPD designs with circumferential cast retainers were examined: buccal retention and palatal reciprocation (P1); palatal retention and buccal reciprocation (P2); and buccal and palatal retention (P3). After completion of the models and remaining palate, each RPD design was loaded under 53N and stress was applied in three different directions: vertical to the posterior teeth (premolar and first molars) of the RPD (F1); at a 33° angle to the posterior teeth (premolar and first molars) of the RPD (F2); and vertically on the anterior teeth (central incisors) of the RPD (F3). The stress distribution in the RPD models on cortical and cancellous bone and the mucosal membrane was analyzed using von Mises criterion. Results The maximum tension in cortical bone (70.84 Mpa) was observed when a 53N force was applied in a vertical direction to posterior teeth (F2) using buccal and palatal retention (P3). Minimum tension (15.73 Mpa) in cortical bone was observed using the F3 load on the P2 design. Similar results were seen in cancellous bone, with the highest stress (8.01 Mpa) observed using F2 load on the P3 design and the lowest stress (3.04 Mpa) observed using the F3 load on the P2 design. For mucosal membrane, the maximum (3.57 Mpa) and minimum (3.05 Mpa) stress was observed using the F3 load on the P3 design and the F1 load on the P2 design, respectively. The average stress in all RPD designs was 3 Mpa. Conclusion The design demonstrating the least tension in cortical and cancellous bone and mucosal membrane was the P2 design, a RPD with palatal retention and buccal reciprocation. Clinical Significance Palatal retention and buccal reciprocation (P2 design) is recommended for patients with maxillofacial RPDs. Citation Gharechahi J, Sharifi E, Nosohian S, Aghdaee NA. Finite Element Method Analysis of Stress Distribution to Supporting Tissues in a Class IV Aramany Removable Partial Denture (Part II: Bone and Mucosal Membrane). J Contemp Dent Pract 2008 November; (9)7:049-056.

An equivalent model for sandwich panel with double-directional trapezoidal corrugated core

2019 ◽  
Vol 22 (7) ◽  
pp. 2445-2465
Author(s):  
Huimin Li ◽  
Lei Ge ◽  
Baosheng Liu ◽  
Haoran Su ◽  
Tianyi Feng ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Sandwich Panel ◽  
Equivalent Model ◽  
Geometrical Parameters ◽  
Detailed Model ◽  
Novel Structure ◽  
Homogeneous Method ◽  
Element Method

A novel sandwich panel with double-directional corrugated core is proposed in this paper. This complex-corrugated core makes the conventional detailed finite element analysis of large structures a tough work. Thus, an equivalent homogeneous method is proposed, the key of which is to obtain the equivalent property of this novel structure. The equivalent elastic modulus considering the effect of geometrical parameters is analytically derived and verified by finite element method. Besides, equivalent shear modulus and Poisson’s ratios are obtained by finite element method. Three-dimensional detailed and equivalent models are established for further validation of this equivalent homogeneous method. Results show that elastic modulus predicted by analytical formulas is in good agreement with that by finite element method no matter how geometrical parameters change. It has been proved that stretching deformation is dominating in thickness direction, and only corrugation along loading direction can bear the load. The proposed novel sandwich structure owns better mechanical property than the conventional one with single-corrugated core. The result by equivalent model agrees well with that by detailed model, which means that this equivalent homogeneous method can well predict the macroscopic property of this novel structure.

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