Related papers: Well-posedness for the microcurl model in both sin…
This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the…
The influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution, based on a recently developed yield…
Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a…
Based on the Stokes complex with vanishing boundary conditions and its dual complex, we reinterpret a grad-curl problem arising from the quad-curl problem as a new vector potential formulation of the three-dimensional Stokes system. By…
Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been…
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…
This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the…
Size-dependence of plastic flow is studied by discrete dislocation dynamical simulation of systems with various numbers of interacting linear edge dislocations while the stress is slowly increased. Regions between avalanches in the…
A micromechanical model based on the theory of elasticity has been developed to study the configuration of self-assembled impurity nanostructures in high temperature superconducting YBCO films. With the calculated equilibrium strain and…
Efficient and precise prediction of plasticity by data-driven models relies on appropriate data preparation and a well-designed model. Here we introduce an unsupervised machine learning-based data preparation method to maximize the…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
It is shown here that fracture after a brief plastic strain, typically of a few percents, is a necessary consequence of the polycrystalline nature of the materials. The polycrystal undergoing plastic deformation is modeled as a flowing…
We present an experimental approach to discriminate hyper-elastic models describing the mechanical behavior of rubber-like materials. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the…
(Abridged, full abstract available in the text) The main goal of the study presented in this thesis was to perform in-situ investigations on deformation structures in plastically deformed polycrystalline copper at low degrees (<5%) of…
A hyperbolic type integro-differential equation with two weakly singular kernels is considered together with mixed homogeneous Dirichlet and non-homogeneous Neumann boundary conditions. Existence and uniqueness of the solution is proved by…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
A standard elasto-plasto-dynamic model at finite strains based on the Lie-Liu-Kr\"oner multiplicative decomposition, formulated in rates, is here enhanced to cope with spatially inhomogeneous materials by using the reference (called also…
A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse concrete structures subjected to dynamic loading. The aim is to obtain a model, which requires input parameters with clear physical…