Related papers: A texture tensor to quantify deformations

This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…

Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more…

This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…

Mutual information between local stress and local non-affine deformation is proposed as a collective field variable quantifying the {\em local softness} of soft materials. The liquid-solid transition in a simple liquid is considered as a…

A fundamental assumption in our understanding of material rheology is that when microscopic deformations are reversible, the material responds elastically to external loads. Plasticity, i.e. dissipative and irreversible macroscopic changes…

Traditionally, the deformation of continuum is divided into elastic, plastic, and flow. For a large deformation with cracking, they are combined together. So, for complicated deformation, a formulation to express the evolution of…

Understanding and harnessing the coupling between lubrication pressure and elasticity provides materials design strategies for applications such as adhesives, coatings, microsensors, and biomaterials. Elastic deformation of compliant solids…

This thesis presents a two-layer uniform facet elastic object for real-time simulation based on physics modeling method. It describes the elastic object procedural modeling algorithm with particle system from the simplest one-dimensional…

The problem of surface effects at a fluid/force field boundary is investigated. A classical simple fluid with a locally introduced field simulating a solid is considered. For the case of a hard-core field, rigid, exponential, realistic, and…

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…

We develop a supervised-learning-based approach for monitoring and diagnosing texture-related defects in manufactured products characterized by stochastic textured surfaces that satisfy the locality and stationarity properties of Markov…

Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…

A generalized notion of a nonlocal tensor order parameter is introduced within the framework of the phenomenological approach. This parameter has the form of a traceless tensor correlation function or a tensor integral operator. Based on…

In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representation of the classical curvature tensor and by exploiting some…

As we enter the age of designer matter - where objects can morph and change shape on command - what tools do we need to create shape-shifting structures? At the heart of an elastic deformation is the combination of dilation and distortion,…

A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is…

We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in…

A sessile liquid drop can deform the substrate on which it rests if the solid is sufficiently "soft". In this paper we compute the detailed spatial structure of the capillary forces exerted by the drop on the solid substrate using a model…

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while…

The plastic flow of a polycrystal is analyzed assuming grains as fine that the rate limiting process is grain boundary sliding, and grains readily accommodate their shapes by slip to preserve spatial continuity. It is shown that thinking of…