Related papers: An Energy-Deformation Decomposition for Morphoelas…
This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order $\delta$, which takes into account the specific geometry of such beams. A deformation $v$ is split into an elementary…
Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue…
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…
Biological growth is often driven by mechanical cues, such as changes in external pressure or tensile loading. Moreover, it is well known that many living tissues actively maintain a preferred level of mechanical internal stress, called the…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting,…
In this article, we propose a general framework to study the dynamics and topology of cellular networks that capture the geometry of cell packings in two-dimensional tissues. Such epithelia undergo large-scale deformation during…
Accretion and ablation, i.e. the addition and removal of mass at the surface, is important in a wide range of physical processes including solidification, growth of biological tissues, environmental processes, and additive manufacturing.…
A fundamental challenge for disordered solids is predicting macroscopic yield from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic…
Poroelasticity can be classified with geophysics and describes the interaction between solids deformation and the pore pressure in a porous medium. The investigation of this effect is anywhere interesting where a porous medium and a fluid…
Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters…
Searches for modified gravity in the large-scale structure try to detect the enhanced amplitude of density fluctuations caused by the fifth force present in many of these theories. Neutrinos, on the other hand, suppress structure growth…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
A continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model can include finite…
Second gradient theories have to be used to capture how local micro heterogeneities macroscopically affect the behavior of a continuum. In this paper a configurational space for a solid matrix filled by an unknown amount of fluid is…
In recent years there has been a growing interest in the statistical properties of surfaces growing under deposition of material. Yet it is clear that a theory describing the evolution of a surface should at the same time describe the…
Large deformations play a central role in the shape transformations of slender active and biological structures. A classical example is the eversion of the Volvox embryo, which demonstrates the need for shell theories that can describe…