Related papers: Covariant Hysteretic Constitutive Theory for Maxwe…
The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a…
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic…
In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure…
We propose a general hybrid physics-informed machine learning framework for modeling nonlinear, history-dependent viscoelastic behavior under multiaxial cyclic loading. The approach is built on a generalized internal state variable-based…
In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using…
In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…
Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely…
To have a closed system, the Maxwell equations should be supplemented by constitutive relations which connect the primary electromagnetic fields $(\bE,\bB)$ with the secondary ones $(\bD,\bH)$ induced in a medium. Recently [Opt. Commun.…
Biological soft tissues exhibit substantial inter-subject variability, making the automation of constitutive material modeling essential for patient-specific analysis and design. Such materials are not only highly nonlinear but also display…
Electromagnetic properties of a simple polarisable medium may be parameterised in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial (accelerating) frames and in the presence of…
A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic…
In this paper the constitutive relations for moving media with homogeneous and isotropic electric and magnetic properties are presented as the connections between the generalized magnetization-polarization bivector $%\mathcal{M}$ and the…
A self-consistent extended Einstein-Maxwell model for relativistic non-stationary polarizable-magnetizable anisotropic media is presented. Based on the analogy with relativistic extended irreversible (transient) thermodynamics, the extended…
We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
There has been increasing experimental evidence of non-affine elastic deformation mechanisms in biological soft tissues. These observations call for novel constitutive models which are able to describe the dominant underlying…
This paper presents an analytic model of one dimensional magnetostriction. We show how specific assumptions regarding the symmetry of key micromagnetic energies (magnetocrystalline, magnetoelastic, and Zeeman) reduce a general…
Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these…
Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise…