Related papers: Structured Deformations of Continua: Theory and Ap…
This paper is devoted to the mechanics of fractal materials. A continuum framework accounting for the topological and metric properties of fractal domains in heterogeneous media is developed. The kinematics of deformations is elucidated and…
An attempt is made to bring into harmony two of the paradigms commonly used in the theory of continuous distributions of defects. It is shown that the common differential geometric apparatus is provided neatly by the theory of G-structures.…
Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…
The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
This dissertation is founded on the central notion that structural correlations in dense fluids, such as dense gases, liquids, and glasses, are directly related to fundamental interatomic forces. This relationship was identified early in…
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
This chapter reviews four notions of system structure, three of which are contextual and classic (i.e. the complete computational structure linked to a state space model, the sparsity pattern of a transfer function, and the interconnection…
In this paper, we study a deformation theory of rigid analytic spaces. We develop a theory of cotangent complexes for rigid geometry which fits in with our deformations. We then use the complexes to give a cohomological description of…
A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to…
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
Understanding crack propagation in structures subjected to fluid loads is crucial in various engineering applications, ranging from underwater pipelines to aircraft components. This study investigates the dynamic response of structures,…
In the present work, the overall nonlinear elastic behavior of a 1D multi-modular structure incorporating possible imperfections at the discrete (micro-scale) level, is derived with respect to both tensile and compressive applied loads. The…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were…
Within the context of finite deformation elasticity theory the problem of deforming an open sector of a thick-walled circular cylindrical tube into a complete circular cylindrical tube is analyzed. The analysis provides a means of…
We use energetic considerations to deduce the form of a previously uncertain coupling term in the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. As in the earlier versions of the STZ theory, the onset of…
This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied.