Publication: A continuum mechanics framework for hyperelastic materials: connecting experiments and modelling
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2016-11
Defense date
2016-11-30
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Abstract
La investigación llevada a cabo en esta Tesis Doctoral proporciona nuevas ideas y
metodologías para el desarrollo de modelos constitutivos con base hiperelástica, con
fundamentación física y basados en evidencias experimentales. Estos modelos han sido
aplicados al estudio del comportamiento termomecánico de polímeros termoplásticos y
tejidos blandos en un amplio intervalo de condiciones de trabajo. La simulación de este
tipo de sólidos debe considerar grandes desplazamientos, rotaciones y deformaciones,
efectos inerciales, cambios de condiciones de contorno durante el proceso de
deformación, generación de calor por deformación plástica, y requieren de leyes de
comportamiento de material complejas. Con objeto de proporcionar un marco general del
continuo para la formulación de modelos constitutivos, se han desarrollado las siguientes
actividades:
(i) Se ha realizado un análisis experimental y numérico del comportamiento mecánico de
materiales hiperelásticos. Este estudio proporciona nuevas observaciones sobre los
mecanismos que gobiernan el proceso de deformación de este tipo de sólidos.
(ii) Se ha desarrollado un nuevo modelo constitutivo para predecir el comportamiento de
polímeros semicristalinos. La formulación de este modelo se basa en evidencias físicas
observadas durante el análisis del comportamiento mecánico de polímeros termoplásticos,
conectando de esta manera técnicas experimentales con la modelización constitutiva. El
modelo ha sido formulado en hipótesis de grandes deformaciones dentro de un marco
termodinámicamente consistente que considera: la dependencia del comportamiento
mecánico con la presión y la deformación plástica volumétrica; el endurecimiento del
material asociado a la sensibilidad con la velocidad de deformación; la generación de
calor en el proceso de deformación inducida por disipación plástica y la evolución de la
temperatura debida al flujo térmico; el ablandamiento térmico y la expansión térmica del
material. Los parámetros del modelo han sido identificados para el polímero poliéter-étercetona
(PEEK) y la capacidad predictiva del modelo ha sido verificada para un amplio
intervalo de condiciones de carga.
(iii) El marco constitutivo del modelo propuesto para polímeros semicristalinos ha sido
generalizado para la formulación de modelos transversalmente isótropos con base
hiperelástica. Este marco general considera: viscoelasticidad; viscoplasticidad;
hiperelasticidad; expansión térmica y anisotropía debida a la orientación de las fibras. El
marco general del continuo ha sido particularizado dando lugar a modelos constitutivos para dos materiales específicos: materiales compuestos de matriz termoplástica PEEK
reforzados con fibra corta de carbono; y la materia blanca del cerebro.
(iv) Finalmente, los modelos constitutivos y las herramientas numéricas desarrolladas en
esta tesis doctoral han sido implementados en un código comercial de elementos finitos y
se han aplicado al estudio de un problema real: el análisis del comportamiento mecánico
de implantes craneales fabricados con polímeros termoplásticos que están expuestos a
cargas de impacto. Para este propósito, se ha desarrollado un modelo de cabeza humana
en elementos finitos a partir de resonancias magnéticas que incluye tejido dérmico,
cráneo, líquido cefalorraquídeo y el tejido cerebral, incluyendo un implante craneal
termoplástico que sustituye parte del cráneo.
The research carried out in this Doctoral Thesis provides new ideas and methodologies on the development of hyperelastic-based constitutive models and may motivate future contributions within this line of investigation. To achieve the main objective of providing a general continuum mechanics framework, the methodology has been divided into the following specific activities: (i) With the aim of supporting the modelling assumptions of the framework, an experimental and numerical analysis of the mechanical behaviour of hyperelastic materials has been conducted. This study provides new insights into the mechanisms that govern the deformation process. (ii) A new constitutive model for semi-crystalline thermoplastic polymers has been developed. The formulation of this model is based on physical evidence from the analysis of the mechanical behaviour of thermoplastic polymers, thereby connecting experiments with modelling. In this sense, the model accounts for strain rate and temperature dependencies, and pressure sensitivity within a thermodynamically consistent framework formulated in finite deformations. The model parameters have been identified for polyether-ether-ketone (PEEK) and the model has been validated for a wide range of loading conditions. (iii) The constitutive framework of the model proposed for semi-crystalline polymers has been generalized for transversely isotropic hyperelastic-based models. This general framework allows for the formulation of constitutive models taking into account: viscoelasticity, viscoplasticity, hyperelasticity, thermal expansion and anisotropy induced by fibre orientation. The general continuum framework has been particularized, providing constitutive models for two materials: short carbon fibre reinforced PEEK composites; and white matter of brain. (iv) Finally, the constitutive and numerical tools developed in this thesis have been implemented in finite element commercial codes and applied to study a real problem, the analysis of the mechanical behaviour of thermoplastic cranial implants subjected to impact loading. For this purpose, a finite element head model comprising scalp, skull, cerebral falx, cerebrospinal fluid and brain tissue, with a cranial implant replacing part of the skull, has been developed from magnetic resonance imaging data.
The research carried out in this Doctoral Thesis provides new ideas and methodologies on the development of hyperelastic-based constitutive models and may motivate future contributions within this line of investigation. To achieve the main objective of providing a general continuum mechanics framework, the methodology has been divided into the following specific activities: (i) With the aim of supporting the modelling assumptions of the framework, an experimental and numerical analysis of the mechanical behaviour of hyperelastic materials has been conducted. This study provides new insights into the mechanisms that govern the deformation process. (ii) A new constitutive model for semi-crystalline thermoplastic polymers has been developed. The formulation of this model is based on physical evidence from the analysis of the mechanical behaviour of thermoplastic polymers, thereby connecting experiments with modelling. In this sense, the model accounts for strain rate and temperature dependencies, and pressure sensitivity within a thermodynamically consistent framework formulated in finite deformations. The model parameters have been identified for polyether-ether-ketone (PEEK) and the model has been validated for a wide range of loading conditions. (iii) The constitutive framework of the model proposed for semi-crystalline polymers has been generalized for transversely isotropic hyperelastic-based models. This general framework allows for the formulation of constitutive models taking into account: viscoelasticity, viscoplasticity, hyperelasticity, thermal expansion and anisotropy induced by fibre orientation. The general continuum framework has been particularized, providing constitutive models for two materials: short carbon fibre reinforced PEEK composites; and white matter of brain. (iv) Finally, the constitutive and numerical tools developed in this thesis have been implemented in finite element commercial codes and applied to study a real problem, the analysis of the mechanical behaviour of thermoplastic cranial implants subjected to impact loading. For this purpose, a finite element head model comprising scalp, skull, cerebral falx, cerebrospinal fluid and brain tissue, with a cranial implant replacing part of the skull, has been developed from magnetic resonance imaging data.
Description
Mención Internacional en el título de doctor
Keywords
Ensayo de materiales, Mecánica de sólidos, Resistencia de materiales, Plasticidad, Polímeros termoplásticos, Hyperelastic materials, Thermoplastic polymers, Numerical methods, Mechanical behaviour, Mechanical behavior