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

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

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 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

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

The Rock Processing Sector: Part I: Cutting Technology Tools, Anew Diamond Segment Band Saw Part II: Study Of Cutting Forces

This article presents the state of the art in cutting procedures used for ornamental stone processing: primarily diamond segment discs, diamond wires and frame saws. In all these, a reduction in cutting thickness has a direct repercussion on profitability. A new tool is presented with a cutting thickness half that of the best achieved in conventional tools: a band saw with welded diamond segments. The first prototypes are built, cutting tests are carried out and the features of the cut are studied. In the second part, existing studies on measurement of cutting force in conventional tools are reviewed and the prototype band saw machine is monitored. Cutting forces in this new process are studied, with measurement of tangential force and feed force under various working conditionsEl artículo presenta el estado del arte de los procedimientos de corte empleados en la transformación de roca ornamental, principalmente, disco con segmentos de diamante, hilo diamantado y los telares. En todos ellos, una reducción en el espesor de corte, repercute de forma directa en la rentabilidad. Se presenta una herramienta novedosa, con un espesor de corte la mitad del mejor conseguido en herramientas convencionales: una sierra de cinta sobre la que se sueldan segmentos de diamante. Se construyen los primeros prototipos, se realizan pruebas de corte y se estudian las características del corte realizado. En una segunda parte se revisan los estudios que existen en la actualidad sobre la medición de fuerzas de corte en granito con herramientas convencionales, y se monitoriza una máquina prototipo de sierra de cinta. Se estudian las fuerzas de corte para este nuevo proceso de corte, se mide la fuerza tangencial, y la fuerza de avance, bajo diferentes condiciones de trabajo

The rock processing sector: part i: cutting technology tools, a new diamond segment band saw part ii: study of cutting forces

This article presents the state of the art in cutting procedures used for ornamental stone processing: primarily diamond segment discs, diamond wires and frame saws. In all these, a reduction in cutting thickness has a direct repercussion on profitability. A new tool is presented with a cutting thickness half that of the best achieved in conventional tools: a band saw with welded diamond segments. The first prototypes are built, cutting tests are carried out and the features of the cut are studied. In the second part, existing studies on measurement of cutting force in conventional tools are reviewed and the prototype band saw machine is monitored. Cutting forces in this new process are studied, with measurement of tangential force and feed force under various working conditions