Finite element error analysis of a viscoelastic Timoshenko beam with thermodiffusion effects

In this paper, a thermomechanical problem involving a viscoelastic Timoshenko beam is analyzed from a numerical point of view. The so-called thermodiffusion effects are also included in the model. The problem is written as a linear system composed of two second-order-in-time partial differential equations for the transverse displacement and the rotational movement, and two first-order-in-time partial differential equations for the temperature and the chemical potential. The corresponding variational formulation leads to a coupled system of first-order linear variational equations written in terms of the transverse velocity, the rotation speed, the temperature and the chemical potential. The existence and uniqueness of solutions, as well as the energy decay property, are stated. Then, we focus on the numerical approximation of this weak problem by using the implicit Euler scheme to discretize the time derivatives and the classical finite element method to approximate the spatial variable. A discrete stability property and some a priori error estimates are shown, from which we can conclude the linear convergence of the approximations under suitable additional regularity conditions. Finally, some numerical simulations are performed to demonstrate the accuracy of the scheme, the behavior of the discrete energy decay and the dependence of the solution with respect to some parameters

CMMSE: numerical analysis of a chemical targeting model

Treating specific tissues without affecting other regions is a difficult task. It is desirable to target the particular tissue where the chemical has its biological effect. To study this phenomenon computationally, in this work we numerically study a mathematical model which is written as a nonlinear system composed by three parabolic partial differential equations. The variables involved in the model are the concentration of the chemical, the concentration of the binding protein and the concentration of the chemical bound to the protein. Our aim is to propose a fully discrete approximation of this problem, using the Finite Element Method and a semi-implicit Euler scheme, in order to solve it numerically. This discrete problem is analysed, obtaining a discrete stability property and some a priori error estimates that show the algorithm converges linearly if the continuous solution is regular enough. Also, some representative examples are shown, as well as the numerical verification of the convergence.Agencia Estatal de Investigación | Ref. PGC2018-096696-B-I00Universidade de Vigo/CISU

Otitis media in the Tgif knockout mouse implicates TGFβ signalling in chronic middle ear inflammatory disease

Otitis media with effusion (OME) is the most common cause of hearing loss in children and tympanostomy to alleviate the condition remains the commonest surgical intervention in children in the developed world. Chronic and recurrent forms of OM are known to have a very significant genetic component, however, until recently little was known of the underlying genes involved. The identification of mouse models of chronic OM has indicated a role of transforming growth factor beta (TGFβ) signalling and its impact on responses to hypoxia in the inflamed middle ear. We have, therefore, investigated the role of TGFβ signalling and identified and characterized a new model of chronic OM carrying a mutation in the gene for transforming growth interacting factor 1 (Tgif1). Tgif1 homozygous mutant mice have significantly raised auditory thresholds due to a conductive deafness arising from a chronic effusion starting at around 3 weeks of age. The OM is accompanied by a significant thickening of the middle ear mucosa lining, expansion of mucin-secreting goblet cell populations and raised levels of vascular endothelial growth factor, TNF-α and IL-1β in ear fluids. We also identified downstream effects on TGFβ signalling in middle ear epithelia at the time of development of chronic OM. Both phosphorylated SMAD2 and p21 levels were lowered in the homozygous mutant, demonstrating a suppression of the TGFβ pathway. The identification and characterization of the Tgif mutant supports the role of TGFβ signalling in the development of chronic OM and provides an important candidate gene for genetic studies in the human population

Finite Element Simulation for Analysing the Design and Testing of an Energy Absorption System

It is not uncommon to use profiles to act as energy absorption parts in vehicle safety systems. This work analyses an impact attenuator based on a simple design and discusses the use of a thermoplastic material. We present the design of the impact attenuator and a mechanical test for the prototype. We develop a simulation model using the finite element method and explicit dynamics, and we evaluate the most appropriate mesh size and integration for describing the test results. Finally, we consider the performance of different materials, metallic ones (steel AISI 4310, Aluminium 5083-O) and a thermoplastic foam (IMPAXX500™). This reflects the car industry’s interest in using new materials to make high-performance, low-mass energy absorbers. We show the strength of the models when it comes to providing reliable results for large deformations and strong non-linearities, and how they are highly correlated with respect to the test results both in value and behaviour

Numerical analysis of an osseointegration model

In this work, we study a bone remodeling model used to reproduce the phenomenon of osseointegration around endosseous implants. The biological problem is written in terms of the densities of platelets, osteogenic cells, and osteoblasts and the concentrations of two growth factors. Its variational formulation leads to a strongly coupled nonlinear system of parabolic variational equations. An existence and uniqueness result of this variational form is stated. Then, a fully discrete approximation of the problem is introduced by using the finite element method and a semi-implicit Euler scheme. A priori error estimates are obtained, and the linear convergence of the algorithm is derived under some suitable regularity conditions and tested with a numerical example. Finally, one- and two-dimensional numerical results are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.Ministerio de Ciencia, Innovación y Universidades | Ref. PGC2018-096696-B-I00Xunta de Galicia | Ref. ED481A-2019/23

Analysis of damage models for cortical bone

Bone tissue is a material with a complex structure and mechanical properties. Diseases or even normal repetitive loads may cause microfractures to appear in the bone structure, leading to a deterioration of its properties. A better understanding of this phenomenon will lead to better predictions of bone fracture or bone-implant performance. In this work, the model proposed by Frémond and Nedjar in 1996 (initially for concrete structures) is numerically analyzed and compared against a bone specific mechanical model proposed by García et al. in 2009. The objective is to evaluate both models implemented with a finite element method. This will allow us to determine if the modified Frémond–Nedjar model is adequate for this purpose. We show that, in one dimension, both models show similar results, reproducing the qualitative behaviour of bone subjected to typical engineering tests. In particular, the Frémond–Nedjar model with the introduced modifications shows good agreement with experimental data. Finally, some two-dimensional results are also provided for the Frémond–Nedjar model to show its behaviour in the simulation of a real tensile test.Ministerio de Ciencia, Innovación y Universidades | Ref. PGC2018-096696-B-I00Xunta de Galicia | Ref. ED481A-2019/230Xunta de Galicia | Ref. ED481A-2017/04

Structural Potting of Large Aeronautic Honeycomb Panels: End-Effector Design and Test for Automated Manufacturing

Structural potting is used to prepare honeycomb panels to fix metallic elements, typical in aircraft doors. In this paper, a full procedure for structural potting using robotic arms is presented for the first time. Automating this procedure requires the integration of, first, machining operations to remove the skin layers and prepare the potting points and, then, resin injection into the honeycomb cells. The paper describes the design, prototyping, and testing of specific end-effectors. Different end-effectors were explored to ensure efficient injection. The results obtained with the prototypes show that the potting quality is adequate to accomplish the required process checks for industrial manufacturing. The injection process time can be reduced by a factor greater than 3.5, together with the extra assets associated with the automation of complex tasks. Therefore, structural potting automation is demonstrated to be feasible with the end-effectors proposed for milling and injection, which are ready for use with conventional robotic arms in manufacturing lines.Ministerio de Ciencia e Innovacion | Ref. PGC2018-099746-B-C2

Analysis of a poro-thermo-viscoelastic model of type III

In this work, we numerically study a thermo-mechanical problem arising in poro-viscoelasticity with the type III thermal law. The thermomechanical model leads to a linear system of three coupled hyperbolic partial differential equations, and its weak formulation as three coupled parabolic linear variational equations. Then, using the finite element method and the implicit Euler scheme, for the spatial approximation and the discretization of the time derivatives, respectively, a fully discrete algorithm is introduced. A priori error estimates are proved, and the linear convergence is obtained under some suitable regularity conditions. Finally, some numerical results, involving one- and two-dimensional examples, are described, showing the accuracy of the algorithm and the dependence of the solution with respect to some constitutive parameters.Ministerio de Ciencia, Innovación y Universidades | Ref. PGC2018-096696-B-I00Xunta de Galicia | Ref. ED431C2019/2

Finite element validation of an energy attenuator for the design of a formula student car

Passive safety systems of cars include parts on the structure that, in the event of an impact, can absorb a large amount of the kinetic energy by deforming and crushing in a design-controlled way. One such energy absorber part, located in the front structure of a Formula Student car, was measured under impact in a test bench. The test is modeled within the Finite Element (FE) framework including the weld characteristics and weld failure description. The continuous welding feature is almost always disregarded in parts included in impact test models. In this work, the FE model is fully defined to reproduce the observed results. The test is used for the qualitative and quantitative validation of the crushing model. On the one hand, the acceleration against time curve is reproduced, and on the other hand, the plying shapes and welding failure observed in the test are also correctly described. Finally, a model that includes additional elements of the car structure is also simulated to verify that the energy absorption system is adequate according to the safety regulations.Ministerio de Ciencia, Innovación y Universidades | Ref. PGC2018-096696-B-I00Xunta de Galicia | Ref. beca ED431C 2019/21Xunta de Galicia | Ref. ED481A-2019/23