Will and his friend are risking their lives and have escaped the plantation. They are on the run; but before Will took off, the old conjure woman warned him, "Evil spirits creeps 'round at night, and tricky spirits kin hex people--even da smart ones likes you."Evil spirits are not the only problem; slave hunters, patrollers, and a mercenary detective are all after Will and Tom, and his childhood companion, Teeny. Luckily, the three friends encounter a group of abolitionists--a lawyer, a riverboat captain, a businessman, and a wealthy heiress--who want nothing more than to help them escape to freedom. But slaves are valuable property, and owners will go to any lengths to get them back.What transpires for these three slaves borders on the implausible, but is rooted in historical fact. They all flee in different directions and make their way north by steamboat on the Mississippi and Missouri rivers. This harrowing journey involves wearing disguises, finding new love, and risking a fortune in a poker game. But the real gamble is a slave betting he can escape and be free...he pays the ultimate price if he loses.
This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the relatedconfigurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.
This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the relatedconfigurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.
This book illustrates the deep roots of the geometrically nonlinear kinematics ofgeneralized continuum mechanics in differential geometry. Besides applications to first-order elasticity and elasto-plasticity an appreciation thereof is particularly illuminatingfor generalized models of continuum mechanics such as second-order (gradient-type)elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second-order crystal plasticity in Part I several concepts from differential geometry, relevantfor what follows, such as connection, parallel transport, torsion, curvature, and metricfor holonomic and anholonomic coordinate transformations are reiterated in Part II.Then, in Part III, the kinematics of geometrically nonlinear continuum mechanicsare considered. There various concepts of differential geometry, in particular aspectsrelated to compatibility, are generically applied to the kinematics of first- and second-order geometrically nonlinear continuum mechanics. Together with the discussion onthe integrability conditions for the distortions and double-distortions, the conceptsof dislocation, disclination and point-defect density tensors are introduced. Forconcreteness, after touching on nonlinear first- and second-order elasticity, a detaileddiscussion of the kinematics of (multiplicative) first- and second-order elasto-plasticityis given. The discussion naturally culminates in a comprehensive set of different typesof dislocation, disclination and point-defect density tensors. It is argued, that thesecan potentially be used to model densities of geometrically necessary defects and theaccompanying hardening in crystalline materials. Eventually Part IV summarizes theabove findings on integrability whereby distinction is made between the straightforwardconditions for the distortion and the double-distortion being integrable and the moreinvolved conditions for the strain (metric) and the double-strain (connection) beingintegrable. The book addresses readers with an interest in continuum modelling of solids fromengineering and the sciences alike, whereby a sound knowledge of tensor calculus andcontinuum mechanics is required as a prerequisite.
