相关论文: Construction of irreducible integrity basis for an…

Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often…

Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…

In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with…

We define what is a generic separating set of invariant functions (a.k.a. a weak functional basis) for tensors. We produce then two generic separating sets of polynomial invariants for 3D elasticity tensors, one made of 19 polynomials and…

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry ($Z_3$) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry…

We discuss the decomposition of the tensorial relaxation function for isotropic and transversely isotropic Modified Quasi-Linear Viscoelastic models. We show how to formulate the constitutive equation by using a convenient decomposition of…

The fabrication of evermore sophisticated miniaturised soft robotic components made up of Electro-Active Polymers (EAPs) is constantly demanding parallel development from the in-silico simulation point of view. The incorporation of…

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

A key challenge in material theory is the formulation of models that satisfy all common mechanical constitutive conditions while retaining sufficient flexibility. In this context, several important modeling aspects remain unresolved for…

In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual…

The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…

We review nine invariant and dispersion-type anisotropic hyperelastic constitutive models for soft biological tissues based on their fitting performance to experimental data from three different human tissues. For this, we used a hybrid…

For the formulation of machine learning-based material models, the usage of invariants of deformation tensors is attractive, since this can a priori guarantee objectivity and material symmetry. In this work, we consider incompressible,…

A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate…

We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…

Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…