Paul Steinmann - Böcker

The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de­ ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math­ ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con­ tinuum mechanics. It is more or less clear that seemingly different phe­ nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten­ sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com­ mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "driving force" causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.

This book covers new theoretical and numerical developments in the mechanics of material forces. Conceptually speaking, common continuum mechanics in the sense of Newton -- which gives rise to the notion of spatial (mechanical) forces -- considers the response to variations of spatial placements of "physical particles" with respect to the ambient space, whereas continuum mechanics in the sense of Eshelby -- which gives rise to the notion of material (configurational) forces -- is concerned with the response to variations of material placements of "physical particles" with respect to the ambient material. Well-known examples of material forces are driving forces on defects like the Peach-Koehler force, the J-Integral in fracture mechanics, and energy release. The consideration of material forces goes back to the works of Eshelby, who investigated forces on defects; therefore this area of continuum mechanics is sometimes denoted Eshelbian mechanics.

This book gives a comprehensive account of the formulation and computational treatment of basic geometrically linear models in 1D. On the one hand, this allows, in the true sense of a catalogue, to consult each of the basic material models separately without the need to refer to other basic material models.

This book gives a comprehensive account of the formulation and computational treatment of basic geometrically linear models in 1D. On the one hand, this allows, in the true sense of a catalogue, to consult each of the basic material models separately without the need to refer to other basic material models.

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.

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.

From fabrication to testing and modeling this monograph covers all aspects on the materials class of magneto active polymers. The focus is on computational modeling of manufacturing processes and material parameters. As other smart materials, these elastomers have the ability to change electrical and mechanical properties upon application of magnetic fields. This allows for novel applications ranging from biomedical engineering to mechatronics.

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.

Con?gurational mechanics has attracted quite a bit of attention from various - search ?elds over the recent years/decades. Having been regarded in its infancy of the early years as a somewhat obscureand almost mystic ?eld of researchthat could only be understood by a happy few of insiders with a pronounced theoretical inc- nation, con?gurational mechanics has developed by now into a versatile tool that can be applied to a variety of problems. Since the seminal works of Eshelby a general notion of con?gurational - chanics has been developed and has successfully been applied to many pr- lems involving various types of defects in continuous media. The most pro- nent application is certainly the use of con?gurational forces in fracture - chanics. However, as con?gurational mechanics is related to arbitrary mat- ial inhomogeneities it has also very successfully been applied to many ma- rials science and engineering problems such as phase transitions and inelastic deformations. Also the modeling of materials with micro-structure evolution is an important ?eld, in which con?gurational mechanics can provide a better understanding of processes going on within the material. Besides these mechanically, physically, and chemically motivated applications, ideas from con?gurational mechanics are now increasingly applied within computational mechanics.