The main emphasis of these Lecture Notes is on constructing solutions to specific viscoelastic boundary value problems; however properties of the equations of viscoelasticity that provide the theoretical underpinnings for constructing such solutions are also covered. Particular attention is paid to the solution of crack and contact problems. This work is of interest in the context of polymer fracture, modelling of material behaviour, rebound testing of polymers and the phenomenon of hysteretic friction.

This carefully edited book offers a state-of-the-art overview on formulation, mathematical analysis and numerical solution procedures of contact problems. The contributions collected in this volume summarize the lectures presented by leading scientists in the area of contact mechanics, during the 4th Contact Mechanics International Symposium (CMIS) held in Hannover, Germany, 2005.

This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

This book presents current trends in Mechanics of Time Dependent Materials. It covers a number of cutting-edge themes, such as characterization of linear and nonlinear mechanical behavior of viscoelastic materials and their composites, taking into consideration large deformations, low, moderate and large strain rates, as well as failure and fracture phenomena. The contributions are inspired by advanced applications in modern technologies, such as injection molding and extrusion.

This book concerns the mathematical analysis OCo modeling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, etc. OCo involved in predicting complex mechanical/acoustical behavior/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or of the boundary conditions, all of which are often affected by random perturbations, forms the class of related inverse or control problems."

The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).

Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (1919–2000) was the main architect for the renaissance of - tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The ?rst ?ve essays by B. D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will ?nd personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as “conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.