## Continuum models for materials with microstructureContinuum Models for Materials with Microstructure Edited by H. B. Mühlhaus, CSIRO, Nedlands, Australia When the characteristic length-scale (‘fabric dimension') of the microstructure of materials is not small when compared to the macroscopic dimensions, the well established framework for the modelling of deformation processes for simple materials needs enhancement. To introduce an internal length scale, one has to resort to continuum models such as Nonlocal Theories, Cosserat or Gradient-type Models, Discrete Element and Lattice Theories or modified Viscoplastic Models. These new approaches are addressed in this volume. It includes contributions from research areas as diverse as bio-mechanics, concrete engineering and solid state physics. Generalised continuum models and its applications are presented and complemented by numerical and analytical tools for the solution of boundary value problems. |

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### Contents

A Micromechanicsbased Continuum Theory | 27 |

Bibliography | 65 |

Nonlocal Damage | 105 |

Copyright | |

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Aifantis analysis assumed beams behavior bending bifurcation boundary conditions characteristic length classical compression computed concrete confining pressure considered constitutive equations constitutive model continua Continuum Models continuum theory corresponding Cosserat elastic couple stress crack growth critical curve damage model deformation density dependence derived Desai deviatoric dipole asymptotics discontinuous discretization dislocation displacement effect experimental failure Figure finite element fracture mechanics function incremental intact integration interaction lattice lattice model linear linear elastic loading localisation localization matrix MBCT Mech Mechanics mesh method microcracks micropolar microstructure mode modulus Muhlhaus nonlocal normal numerical observed obtained particle phase velocity plane plane strain plastic strain Poisson's ratio Portevin-Le Chatelier predicted problem rotation shear band shear modulus shear stress shown simulations solid solution spatial specimen stiffness strain softening strain tensor stress tensor stress-strain stress-strain curve structure surface tensile tension tests uniaxial Vardoulakis vector velocity wave yield Young's modulus zero zone