From bulk to structural failure: fracture of hyperelastic materials

This thesis investigates the fracture of nearly incompressible hyperelastic media. It covers the different characteristics of bulk material failure under dilatational or distortional loads and develops a unified description of the corresponding failure surface. It proposes a coupled strain and energy failure criterion for the assessment of notch-induced crack nucleation and presents a weak interface model that allows for efficient stress, strain and failure analyses of hyperelastic adhesive lap joints. Theoretical concepts for the measurement of fracture properties of nonlinear elastic materials are provided. The methodology is developed using two exemplary hyperelastic silicones, DOWSIL 993 Structural Glazing Sealant and DOWSIL Transparent Structural Silicone Adhesive, and is validated using large sets of experiments of different loading conditions

Instabilities in the free inflation of a nonlinear hyperelastic toroidal membrane

Study on an incompressible nonlinear hyperelastic thin-walled toroidal mem- brane of circular cross-section subjected to inflation due to a uniform pressure is conducted in this work. Comparisons are made for three elastic constitutive mod- els (neo-Hookean, Mooney–Rivlin, and Ogden) and for different geometric aspect ratios (ratio of the radius of cross-section to the radius of revolution). A variational approach is used to derive the equations of equilibrium and bifurcation. An analysis of the pressure–deformation plots shows occurrence of the well-known limit point (snap through) instabilities in membrane. Calculations are performed to study the elastic buckling point to predict bifurcation of solution corresponding to loss of symmetry. Tension field theory is employed to study the wrinkling instability that, in this case, typically occurs near the inner regions of tori with large aspect ratios

Computational Modeling of Tires

This document contains presentations and discussions from the joint UVA/NASA Workshop on Computational Modeling of Tires. The workshop attendees represented NASA, the Army and Air force, tire companies, commercial software developers, and academia. The workshop objectives were to assess the state of technology in the computational modeling of tires and to provide guidelines for future research

Modeling fracture in polymeric material using phase field method based on critical stretch criterion

In this work, the phase field method (PFM) is applied for modeling fracture in the polymeric type of materials. Considering the large extensibility of polymer chains before fracture, a crack initiation criteria based on a critical stretch value is proposed. The tensile stretches in the material contribute to the active strain energy, which is responsible for driving fracture. Additive decomposition of strain energy into active and passive parts is adopted based on the critical stretch value of polymer chains in a phase-field setting. This critical value is determined by assuming an equivalent uniaxial tensile state of stress in front of the crack tip at the onset of fracture. The stretch of individual polymeric chains is determined by using a polymer network model. The critical fracture toughness of the polymer is kept constant up to the onset of fracture and a gradually reducing value of it is adopted in front of the crack tip beyond the critical stretch. A hybrid phase-field formulation with a staggered solver is used owing to its numerical efficiency and robustness. The effectiveness and applicability of the present model are demonstrated through various numerical examples

Constitutive modeling for biodegradable polymers for application in endovascular stents

Percutaneous transluminal balloon angioplasty followed by drug-eluting stent implantation has been of great benefit in coronary applications, whereas in peripheral applications, success rates remain low. Analysis of healing patterns in successful deployments shows that six months after implantation the artery has reorganized itself to accommodate the increase in caliber and there is no purpose for the stent to remain, potentially provoking inflammation and foreign body reaction. Thus, a fully biodegradable polymeric stent that fulfills the mission and steps away is of great benefit. Biodegradable polymers have a widespread usage in the biomedical field, such as sutures, scaffolds and implants. Degradation refers to bond scission process that breaks polymeric chains down to oligomers and monomers. Extensive degradation leads to erosion, which is the process of mass loss from the polymer bulk. The prevailing mechanism of biodegradation of aliphatic polyesters (the main class of biodegradable polymers used in biomedical applications) is random scission by passive hydrolysis and results in molecular weight reduction and softening. In order to understand the applicability and efficacy of biodegradable polymers, a two pronged approach involving experiments and theory is necessary. A constitutive model involving degradation and its impact on mechanical properties was developed through an extension of a material which response depends on the history of the motion and on a scalar parameter reflecting the local extent of degradation and depreciates the mechanical properties. A rate equation describing the chain scission process confers characteristics of stress relaxation, creep and hysteresis to the material, arising due to the entropy-producing nature of degradation and markedly different from their viscoelastic counterparts. Several initial and boundary value problems such as inflation and extension of cylinders were solved and the impacts of the constitutive model analyzed. In vitro degradation of poly(L-lactic acid) fibers under tensile load was performed and degradation and reduction in mechanical properties was dependent on the mechanical environment. Mechanical testing of degraded fibers allowed the proper choice of constitutive model and its evolution. Analysis of real stent geometries was made possible with the constitutive model integration into finite element setting and stent deformation patterns in response to pressurization changed dramatically as degradation proceeded

Dynamic stiffness and damping prediction on rubber material parts, FEA and experimental correlation

The final objective of the present work is the accurate prediction of the dynamic stiffness behaviour of complex rubber parts using finite element simulation tools. For this purpose, it becomes necessary to perform a complex rubber compound material characterisation and modelling work; this needs two important previous steps. These steps are detailed in the present document together with a theoretical review of viscoelastic visco-elasto-plastic models for elastomers. Firstly, a new characterisation method is proposed to determine the degree of cure of rubber parts. It is known that the degree of cure of rubbers bears heavily on their mechanical properties. This method consists of the correlation of swelling results to rheometer data achieving a good agreement. Secondly, the influence of the strain rate used in static characterisation tests is studied. In this step, a new characterisation method is proposed. The latter characterisation method will be used to fit extended hyperelastic models in Finite Element Analysis (FEA) software like ANSYS. The proposed method improves the correlation of experimental data to simulation results obtained by the use of standard methods. Finally, the overlay method proposed by Austrell concerning frequency dependence of the dynamic modulus and loss angle that is known to increase more with frequency for small amplitudes than for large amplitudes is developed. The original version of the overlay method yields no difference in frequency dependence with respect to different load amplitudes. However, if the element in the viscoelastic layer of the finite element model are given different stiffness and loss properties depending on the loading amplitude level, frequency dependence is shown to be more accurate compared to experiments. The commercial finite element program Ansys is used to model an industrial metal rubber part using two layers of elements. One layer is a hyper viscoelastic layer and the other layer uses an elasto-plastic model with a multi-linear kinematic hardening rule. The model, being intended for stationary cyclic loading, shows good agreement with measurements on the harmonically loaded industrial rubber part

Doctor of Philosophy

dissertationWhile the healthy hip provides decades of pain free articulation, the cartilage and labrum may degenerate during the process of osteoarthritis (OA). Most hip OA is caused by subtle pathomorphologies, including acetabular dysplasia and acetabular retroversion. The link between pathomorphology and OA is thought to be mechanical, but the mechanics have not been quantified. The aim of this dissertation was to provide insight into the pathogenesis of hip OA via finite element (FE) modeling. The objectives were two-fold: to validate a subject-specific modeling protocol for a series of specimens and assess the effects of assumptions on model predictions, and to use the modeling protocol to evaluate soft tissue mechanics in pathomorphologic hips in comparison to normal hips. For the first objective, FE predictions of contact stress and contact area were directly validated for five cadaveric specimens, and the specimen- and region-specific hyperelastic material behavior of cartilage was determined. FE predictions of contact stress and contact area were in good agreement with experimental results, and were relatively insensitive to the assumed cartilage constitutive model. There were distinct regional differences in the hyperelastic material behavior of human hip cartilage, with stiffer lateral than medial cartilage and stiffer acetabular than femoral cartilage. In order to investigate the mechanical link between pathomorphology and hip OA, FE models of ten hips with normal morphology, ten hips with acetabular dysplasia and ten hips with acetabular retroversion were generated. FE models of dysplastic acetabula demonstrated the importance of the acetabular labrum in load support in the dysplastic hip. FE models of retroverted acetabula demonstrated distinct superomedial contact patterns in comparison to distributed contact patterns in the normal hip. Finally, the effects of cartilage constitutive model on predictions of transchondral maximum shear stress and first principal strain were evaluated. In contrast to contact stress and contact area, maximum shear stress and first principal strain were sensitive to the cartilage constitutive model. Overall, this dissertation provides novel insights into the contact mechanics of pathomorphologic hips that may be important in the pathogenesis of OA, as well as the technical foundation for studies evaluating additional mechanical variables in the human hip