Rapid development and stiff competition in material related industries such as the automotive, demand very high precision in end products in very quick time. The transformation of raw material into an intricate-shaped final product involves various intermediate steps like design, material selection, manufacturing processes, etc. In all these steps, an in-depth understanding of material behavior plays an important role. The available traditional methods such as trial-and-error, especially in the case of die design, become highly inefficient in terms of time and money. This, there is a growing interest in simulation of the final product in order to predict different parameters which are important in design and manufacturing. Currently available simulation techniques are based on existing theories of plasticity or large deformation. These theories have been developed over several decades and many theoretical and practical issues have been debated over the years. Though the theories have great utility in understanding and solving some practical problems, there are ranges of applications for which no acceptable models are available. Most of these theories are either materials or process-specific with oversimplified real physical situations using assumptions and empirical relations. Development of field equations from first principles to stimulate elasto-plastic deformation is one such, still a subject of on-going discussion. Materials and composites exhibit hysteresis even at very low stresses, i.e., inelasticity is always present under all types of loading. This observation shows that the representing constitutive relation cannot treat the elastic and plastic deformations separately. The deformation is due to changes in size and shape, and studies with varying strain rates show considerable material sensitivity to the rate of deformation. Therefore, a generalized field equation is developed from first principles in the Eulerian coordinate system using material resistance to changes in size and shape, and their rates. The formulation uses a unified approach representing continuous effect of elastic and plastic strains and strain rates. The field equation involves eight material parameters, viz. bulk modulus, shear modulus, material shear velocity, material bulk viscosity, and four more constants associated with activation points related to deviatoric and volumetric strains and plastic strain rates. The elastic moduli, bulk and shear, are constants, and so also the material viscosities, while plastic stain rates are functions of elastic strain rates. The field equation redces to Cauchy’s equation in the solid limit and Navier-Stokes equation in the fluid limit. Simple experimental measurements are suggested to obtain the numerical values of the material parameters. Uniaxial tension tests are carried out on commercially available mild steel and aluminium alloy at different strain rates to quantify any variations in the values of material parameters during large deformation. Experimental results and the classical understanding of material deformation reveal the constant nature of elastic moduli during large deformation and, from fluids, the viscosities seem to remain constant. Around the yield region, materials experience a sharp increase in absorbed energy which is modeled to represent the plastic strain rates. The variations and contributions from elastic and plastic strains, both volumetric and deviatoric, and the corresponding stresses are observed. The effects of strain rate on plastic stress and energy absorbed are investigated. The model is checked for different materials and loading conditions to ascertain the proposed changes to earlier theories. Available experimental data in the literature are used for this purpose. The analysis shows that, though the overall stress-strain relations of different materials look similar, their internal responses differ. The internal response of a material depends on various microstructural factors, like alloying elements, impurities, etc. The present model is able to capture those internal differences between various materials. Numerical solution of different plasticity problems have to be undertaken to ascertain the applicability, generality, realism, accuracy and feasibility of the model.

Este trabalho apresenta uma modelagem de placas laminadas com sensores/atuadores piezoelétricos integrados e conectados a circuitos tipo shunt resistivo-indutivo (RL). O modelo faz uso de duas teorias de placa, FSDT (First-order Shear Deformatíon Theory) e TSDT (Third-order Shear Deformatíon Theory), e considera a possibilidade de inserção de pastilhas piezoelétricas trabalhando nos modos de extensão e cisalhamento. Um modelo de elementos finitos para placas laminadas piezoelétricas, em camada equivalente (Equivalent Single Layer), foi desenvolvido usando como graus de liberdade os deslocamentos mecânicos generalizados e a carga elétrica gerada nos circuitos acoplados. Após, uma implementação computacional foi realizada e validada através de comparações com resultados encontrados na literatura. Então, foram realizados estudos para configurações de placa laminada com diferentes quantidades de pastilhas piezoelétricas através de uma análise paramétrica para obtenção das posições de maior acoplamento entre pastilhas e estrutura para os primeiros modos de vibração da placa. Estes resultados possibilitaram a otimização da eficiência do acoplamento eletromecânico através da distribuição das pastilhas piezoelétricas para uma placa com maior quantidade de pastilhas bem como a comparação dos resultados obtidos entre as duas teorias utilizadas. / This work presents the modeling of laminate plates with embedded piezoelectric sensors and actuators connected to resistive-inductive (RL) shunt circuits. The model considers two plate theories, FSDT (First-order Shear Deformation Theory) and TSDT (Third-order Shear Deformation Theory) and allows embedded piezoelectric patches in extension and thickness-shear modes. A finite element model for piezoelectric laminate plates, using equivalent single layer (ESL), was developed considering the generalized mechanical displacements and the electric charges induced in the coupled electric circuits as degrees of freedom. Then, the model was implemented and validated by means of comparisons with results found in the literature. Thereafter, some laminate plate configurations with different numbers of piezoelectric patches were studied through a parametric analysis to obtain the positions that maximize the electromechanical coupling between patches and structure for the first vibration modes. These results allowed the optimization of the electromechanical coupling efficiency through piezoelectric patches distribution for a plate with a larger number of patches and the comparison between the results obtained with the two plate theories considered.

Este trabalho apresenta uma modelagem de placas laminadas com sensores/atuadores piezoelétricos integrados e conectados a circuitos tipo shunt resistivo-indutivo (RL). O modelo faz uso de duas teorias de placa, FSDT (First-order Shear Deformatíon Theory) e TSDT (Third-order Shear Deformatíon Theory), e considera a possibilidade de inserção de pastilhas piezoelétricas trabalhando nos modos de extensão e cisalhamento. Um modelo de elementos finitos para placas laminadas piezoelétricas, em camada equivalente (Equivalent Single Layer), foi desenvolvido usando como graus de liberdade os deslocamentos mecânicos generalizados e a carga elétrica gerada nos circuitos acoplados. Após, uma implementação computacional foi realizada e validada através de comparações com resultados encontrados na literatura. Então, foram realizados estudos para configurações de placa laminada com diferentes quantidades de pastilhas piezoelétricas através de uma análise paramétrica para obtenção das posições de maior acoplamento entre pastilhas e estrutura para os primeiros modos de vibração da placa. Estes resultados possibilitaram a otimização da eficiência do acoplamento eletromecânico através da distribuição das pastilhas piezoelétricas para uma placa com maior quantidade de pastilhas bem como a comparação dos resultados obtidos entre as duas teorias utilizadas. / This work presents the modeling of laminate plates with embedded piezoelectric sensors and actuators connected to resistive-inductive (RL) shunt circuits. The model considers two plate theories, FSDT (First-order Shear Deformation Theory) and TSDT (Third-order Shear Deformation Theory) and allows embedded piezoelectric patches in extension and thickness-shear modes. A finite element model for piezoelectric laminate plates, using equivalent single layer (ESL), was developed considering the generalized mechanical displacements and the electric charges induced in the coupled electric circuits as degrees of freedom. Then, the model was implemented and validated by means of comparisons with results found in the literature. Thereafter, some laminate plate configurations with different numbers of piezoelectric patches were studied through a parametric analysis to obtain the positions that maximize the electromechanical coupling between patches and structure for the first vibration modes. These results allowed the optimization of the electromechanical coupling efficiency through piezoelectric patches distribution for a plate with a larger number of patches and the comparison between the results obtained with the two plate theories considered.