Fernando P. Duda

Compatibility conditions for the Cauchy-Green strain fields: Solutions for the plane case

This paper considers the issues related to uniqueness and existence of a finite deformation generated by prescribed right or left Cauchy-Green strain tensor field in the plane. First, the questions of uniqueness and existence to a pre-assigned right strain field C are discussed. It is shown that the existence condition, in the context of continuum mechanics, are naturally posed using the field corresponding to the square root of C instead of C, the latter a classical approach. Then, the corresponding questions for the left strain field are considered, which is more involved. The analysis of uniqueness gives rise to an appropriate classification of the deformation fields. The question of existence is discussed and a complete solution is presented. In both the right and left cases, we stress the techniques for obtaining the corresponding deformation fields.

The influence of the loading mode on the stress distribution on the connector region of metal-ceramic and all-ceramic fixed partial denture.

Studies pertaining to the mechanical behavior of fixed partial dentures (FPDs) frequently found the highest tensile stress values at the connector region when load is applied at the pontic central region. The connector region is considered the weakest point of the prosthesis with the greatest potential of fractures, regardless of the material used. This 2D finite element study compared the stress distribution on three-element all-ceramic and metal-ceramic FPDs with different loading conditions. Three FPD models were designed: (i) metal-ceramic FPD; (ii) all-ceramic FPD with the veneering porcelain only on the occlusal face; and (iii) all-ceramic FPD with the veneering porcelain on the occlusal and cervical face of the pontic. Loads of 100 N were applied following these simulations: (i) distributed on all working cusps; (ii) only on the abutment teeth; and (iii) only on the pontic. There is a significant change on the stress distribution and on the tensile stress values when the load configuration is changed. The stress distribution from the load applied on the abutments was significantly better compared with the other two load simulations. When the loads were applied on the pontic and distributed on all working cusps, the highest tensile stress values appeared on the cervical region of the connectors between the abutments and the pontic. However, when the load was applied on the abutment teeth, the maximum tensile stress value significantly decreased and was located on the occlusal region of the connectors. In fact, the load applied on the pontic region does not simulate the clinical situation. Studies using this load configuration have overestimated the connector regions as having the highest probability of failures.

On a continuum theory of brittle materials with microstructure

This paper deals with a finite strain continuum theory of elastic-brittle solids with microstructure. A single scalar microstructural field is introduced, meant to represent - even if in a summary way - the concentration of microdefects within the material. A system of microforces, dual to the microstructural field, is axiomatically introduced. The corresponding balance, augmented with suitable constitutive information, yields, inter alia, a kinetic equation for the microstructural field, criteria for damage nucleation, growth and healing as well as a failure criterion based on attainment of a critical value of the microstructural field. The theory is applied for the description of the Mullins effect.

Influence of Substructure Design and Occlusal Reduction on the Stress Distribution in Metal Ceramic Complete Crowns: 3D Finite Element Analysis

PURPOSE Occlusal reduction is considered a fundamental step for providing adequate and uniform space for the ceramic prosthesis; however, a flat occlusal surface is usually found. The prosthesis design influences the resistance to deformation and the stress state within the ceramic. This finite element (FE) study analyzes the influence of changing the substructure design on the stress distribution of a metal-ceramic crown in a premolar tooth with three types of occlusal reduction. MATERIALS AND METHODS Each part of three-dimensional metal ceramic complete crown models was designed according to the space provided by different levels of occlusal reduction and the same external morphology of the tooth. Three models were designed: (1) correct occlusal reduction with a uniform thickness of the substructure (0.3 mm) and the veneering porcelain (1.5 mm); (2) flat occlusal reduction with different thicknesses of veneering porcelain to produce a uniform substructure; and (3) a flat occlusal reduction with different thicknesses of substructure for a uniform thickness of veneering porcelain. RESULTS Stress distributions were very similar in the three models. The highest tensile stresses were concentrated immediately below the midline fissure in both the veneering porcelain and the metal alloy substructure. Although models with flat occlusal reduction had lower stress values, this preparation results from a reduction that removes a greater amount of sound tissue, which may increase the probability of dental pulp injury. CONCLUSIONS Occlusal reduction must be anatomic; however, when a flat occlusal reduction already exists, the substructure must reproduce the correct anatomic form to allow a uniform thickness of the veneering porcelain.

On the Modeling of Deformation-Diffusion-Damage Coupling in Elastic Solids

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion-damage in elastic solids. The formulation is carried out within the framework of continuum mechanics, where, in addition to the standard fields, extra fields are introduced in order to describe diffusion and damage processes. The governing equations are then obtained after supplementing the basic balances with a thermodynamically consistent constitutive theory. The couplings are implemented via the free energy response and include both deformation and damage assisted diffusion. It is worth mentioning that a gradient damage theory is obtained, which allows the modeling of fracture problems. The numerical implementation is based on the finite element method and a Euler implicit scheme for spatial and temporal discretizations, respectively. A numerical algorithm is presented to solve the discrete system of equations. In order to illustrate the potentiality of the proposed model, applications in the context of hydrogen embrittlement are presented.

A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems

This paper presents a new consistent and stabilized finite-element formulation for fourth-order incompressible flow problems. The formulation is based on the C^0-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf-sup condition, and considers discontinuous pressure interpolations. A stability analysis through a lemma establishes that the proposed formulation satisfies the inf-sup condition, thus confirming the robustness of the method. This lemma indicates that, at the element level, there exists an optimal or quasi-optimal GLS stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, the geometry of the finite element, and the fluid viscosity term. Numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure, and to stabilize large pressure gradients.

On the Representation of the Stored Energy for Elastic Materials with Full Transverse Response-Symmetry

We solve the representation problem for the stored energy of both transversely-isotropic and transversely-hemitropic elastic materials. Our method is based on giving the problem a form allowing application of a modified version of the classical representation theorem by Cauchy for scalar-valued mappings over the Nth power of a vector space.

Maximal Classes of Stored Energies Compatible with Cylindrical Inflations

We consider a family of deformations describing cylindrical inflations within the context of finite, compressible, isotropic elasticity. We pose the problem of finding the maximal class of materials for which these deformations are possible at equilibrium under surface tractions only. We solve this problem for families of cylindrical inflations whose principal strain invariants have a special dependence on the radius. These families comprise and extend all cases considered by Murphy [2].

Stress effects on the kinetics of hydride formation and growth in metals

Although metal hydrides are considered promising candidates for solidstate hydrogen storage, their use for practical applications remains a challenge due to the limitation imposed by the slow kinetics of hydrogen uptake and release, which has driven the interest in using metal nanoparticles as advanced materials of new hydrogen-storage systems since they display fast hydrogenation and dehydrogenation kinetics. Nevertheless, the understanding of the adsorption/release kinetics requires the investigation of the role played by the stress which appears to accommodate the misfit between the metal and hydride phases. In this paper, we present a continuum theory capable of assessing how the misfit stress affects the kinetics of hydride formation and growth in metallic nanoparticles. The theory is then applied to study the kinetics of adsorption/release in spherical particles. This work extends Duda and Tomassetti (2015, 2016) by considering stress-dependent hydrogen mobility.

Experimental-theoretical thermal and electrical analyses of insulated gate bipolar transistors (IGBT) power module

Applications of high-power insulated gate bipolar transistor (IGBT) modules include railway traction, motor drives, and hybrid electric vehicles. The reliability of these semiconductor devices is tightly linked to the operating junction temperatures of IGBT and diode chips present in them. Since these temperatures are very difficult to measure, accurate models and simulation tools are required to compute the instantaneous temperature of the devices under different load conditions. In this paper, we describe a transient 3D heat transfer numerical model of an IGBT power device with many layers of varying cross-sectional areas, distinct materials, and heat sources. Two cases were evaluated according to the total power dissipation considered. In the first case, a non-switching constant conduction scenario was considered in which a power dissipation of 6.15 W based on experiments was adopted and the calculated results were validated against experimental data obtained via infrared thermography, and excellent agreement between the results was observed. For the second case, IGBT switching — along with power losses due to the gate-closing and gate-opening transitions between conducting and non-conducting states — was taken into consideration. For this case, a higher power of 27.23 W was considered to represent the average power dissipation associated with a typical real-life application of the IGBT unit at a switching at frequency of 1 kHz. For this case, the power dissipation on the IGBT chip was obtained from an electrical simulation and used in the heat transfer problem as a strongly time-dependent heat source. The temperature distributions for both cases were then critically compared.