Related papers: A unifying perspective: the relaxed linear micromo…
In the present contribution we show that the relaxed micromorphic model is the only non-local continuum model which is able to account for the description of band-gaps in metamaterials for which the kinetic energy accounts separately 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…
We derive and analyze a novel approach for modeling and computing the mechanical relaxation of incommensurate 2D heterostructures. Our approach parametrizes the relaxation pattern by the compact local configuration space rather than real…
The quantitative understanding of membranes is still rooted in work performed in the 1970s by Helfrich and others, concerning amphiphilic bilayers. However, most biological membranes contain a wide variety of nonamphiphilic molecules too.…
The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe…
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
A new relaxation approach is proposed which allows for the description of stress- and strain-softening at finite strains. The model is based on the construction of a convex hull replacing the originally non-convex incremental stress…
We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new…
A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant…
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…
We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…
In this paper we model the size-effects of metamaterial beams under bending with the aid of the relaxed micromorphic continuum. We analyze first the size-dependent bending stiffness of heterogeneous fully discretized metamaterial beams…
Models of adhesion of extended particles on linear and planar substrates are of interest in interpreting surface deposition in colloid, polymer, and certain biological systems. An introduction is presented to recent theoretical advances in…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues.…
We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…
Through experiments, we idealise a plant leaf as a flexible, thin, rectangular plate clamped at the midpoint and positioned perpendicular to an airflow. Flexibility of the structure is considered as an advantage at moderate flow speed…
The Cosserat continuum is used in this paper to regularize the ill-posed governing equations of the Cauchy/Maxwell continuum. Most available constitutive models adopt yield and plastic potential surfaces with a circular deviatoric section.…