TY - BOOK

T1 - On the formulation and numerical implementation of anisotropic elasto-plasticity with application to fibre-reinforced composites

AU - Gaddikere Nagaraja, Swaroop

N1 - no embargo

PY - 2019

Y1 - 2019

N2 - The mechanics of highly anisotropic materials, such as composites, has raised many questions in solid mechanics which in turn have led to an improved understanding of the subject. For the effective use of such materials, it is important to have suitable and reliable mathematical models that describe their behaviour. In this context, the overall objective of this work is to develop physically motivated and sufficiently general constitutive equations that describe the non-linear material response of fibre-reinforced composites from the continuum perspective. Macroscopically, a composite may be regarded as an anisotropic material which exhibits a highly direction-dependent mechanical response. These materials can be characterised by different symmetry groups based on their inherent micro-structure. If the material is reinforced by fibres in one direction, then the composite has only a single preferred direction and is characterised by the transversely isotropic system. Typical example is a unidirectional fibre-reinforced composite. It is also conceivable for a composite material to be reinforced by fibres in more than one direction. For example, a woven fabric has fibres aligned in two perpendicular directions. Such materials belong to the orthorhombic system and are characterised by the existence of two preferred directions. While composite materials show a variety of mechanical responses, this thesis presents a framework for the description of elastic and plastic response. For the two selected symmetry groups, relatively general models of elastoplasticity are developed within the geometrically linear framework, and aspects of the finite element implementation are outlined. A key aspect is the formulation of anisotropic elastic and plastic constitutive response functions with the aid of general representation theorems, where additional (symmetric second-order) tensorial arguments which reflect the microstructural information on the macroscopic level are incorporated. A further core ingredient is the set-up of a canonical and non-conventional constitutive structure, with respect to associated and non-associated flow response, where the use of latter is motivated by the physical inconsistencies induced by the former under shear dominated loads. A rate-dependent approximation of the rate-independent setting is also outlined. The performance of the proposed models is evaluated qualitatively and quantitatively by means of representative numerical simulations.

AB - The mechanics of highly anisotropic materials, such as composites, has raised many questions in solid mechanics which in turn have led to an improved understanding of the subject. For the effective use of such materials, it is important to have suitable and reliable mathematical models that describe their behaviour. In this context, the overall objective of this work is to develop physically motivated and sufficiently general constitutive equations that describe the non-linear material response of fibre-reinforced composites from the continuum perspective. Macroscopically, a composite may be regarded as an anisotropic material which exhibits a highly direction-dependent mechanical response. These materials can be characterised by different symmetry groups based on their inherent micro-structure. If the material is reinforced by fibres in one direction, then the composite has only a single preferred direction and is characterised by the transversely isotropic system. Typical example is a unidirectional fibre-reinforced composite. It is also conceivable for a composite material to be reinforced by fibres in more than one direction. For example, a woven fabric has fibres aligned in two perpendicular directions. Such materials belong to the orthorhombic system and are characterised by the existence of two preferred directions. While composite materials show a variety of mechanical responses, this thesis presents a framework for the description of elastic and plastic response. For the two selected symmetry groups, relatively general models of elastoplasticity are developed within the geometrically linear framework, and aspects of the finite element implementation are outlined. A key aspect is the formulation of anisotropic elastic and plastic constitutive response functions with the aid of general representation theorems, where additional (symmetric second-order) tensorial arguments which reflect the microstructural information on the macroscopic level are incorporated. A further core ingredient is the set-up of a canonical and non-conventional constitutive structure, with respect to associated and non-associated flow response, where the use of latter is motivated by the physical inconsistencies induced by the former under shear dominated loads. A rate-dependent approximation of the rate-independent setting is also outlined. The performance of the proposed models is evaluated qualitatively and quantitatively by means of representative numerical simulations.

KW - Anisotropie

KW - Repräsentationstheoremen

KW - Faserverstärkte Verbundwerkstoffe

KW - Elastizität

KW - Plastizität

KW - Finite-Elemente-Implementierung

KW - Anisotropy

KW - Representation theorems

KW - Fibre-reinforced composites

KW - Elasticity

KW - Plasticity

KW - Finite element implementation

M3 - Doctoral Thesis

ER -