Constitutive equations for Ca2+ -alginate gels

Correlative image learning of chemo-mechanics in phase-transforming solids

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li_XFePO₄, a technologically relevant battery positive electrode material. We uncovered the functional form of the composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 ≤ X ≤ 1), including inside the thermodynamically unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

Examining the contribution of cell wall polysaccharides to the mechanical properties of apple parenchyma tissue using exogenous enzymes

The viscoelastic mechanical properties of water-rich plant tissues are fundamental for many aspects of organ physiology and plant functioning. These properties are determined partly by the water in cellular vacuole and partly by the mechanical properties of the cell wall, the latter varying according to the composition and organization of its polysaccharides. In this study, relationships between the viscoelastic properties of apple cortex parenchyma tissue and cell wall pectin, hemicelluloses, and cellulose structures were studied by infusing the tissue with selected sets of purified enzymes in a controlled osmoticum. The results showed that tissue elasticity and viscosity were related, and controlled to variable extents by all the targeted polysaccharides. Among them, pectic homogalacturonan domains, crystalline cellulose, and fucosylated xyloglucan were revealed as being of prime importance in determining the viscoelastic mechanical properties of apple cortex tissue.

Mechanical stimulations on human bone marrow mesenchymal stem cells enhance cells differentiation in a three-dimensional layered scaffold

Scaffolds laden with stem cells are a promising approach for articular cartilage repair. Investigations have shown that implantation of artificial matrices, growth factors or chondrocytes can stimulate cartilage formation, but no existing strategies apply mechanical stimulation on stratified scaffolds to mimic the cartilage environment. The purpose of this study was to adapt a spraying method for stratified cartilage engineering and to stimulate the biosubstitute. Human mesenchymal stem cells from bone marrow were seeded in an alginate (Alg)/hyaluronic acid (HA) or Alg/hydroxyapatite (Hap) gel to direct cartilage and hypertrophic cartilage/subchondral bone differentiation, respectively, in different layers within a single scaffold. Homogeneous or composite stratified scaffolds were cultured for 28 days and cell viability and differentiation were assessed. The heterogeneous scaffold was stimulated daily. The mechanical behaviour of the stratified scaffolds were investigated by plane-strain compression tests. Results showed that the spraying process did not affect cell viability. Moreover, cell differentiation driven by the microenvironment was increased with loading: in the layer with Alg/HA, a specific extracellular matrix of cartilage, composed of glycosaminoglycans and type II collagen was observed, and in the Alg/Hap layer more collagen X was detected. Hap seemed to drive cells to a hypertrophic chondrocytic phenotype and increased mechanical resistance of the scaffold. In conclusion, mechanical stimulations will allow for the production of a stratified biosubstitute, laden with human mesenchymal stem cells from bone marrow, which is capable in vivo to mimic all depths of chondral defects, thanks to an efficient combination of stem cells, biomaterial compositions and mechanical loading.

Thermodynamical journey in plant biology

Nonequilibrium irreversible thermodynamics constitute a meaningful point of view suitable to explore life with a rich paradigm. This analytical framework can be used to span the gap from molecular processes to plant function and shows great promise to create a holistic description of life. Since living organisms dissipate energy, exchange entropy and matter with their environment, they can be assimilated to dissipative structures. This concept inherited from nonequilibrium thermodynamics has four properties which defines a scale independent framework suitable to provide a simpler and more comprehensive view of the highly complex plant biology. According to this approach, a biological function is modeled as a cascade of dissipative structures. Each dissipative structure, corresponds to a biological process, which is initiated by the amplification of a fluctuation. Evolution of the process leads to the breakage of the system symmetry and to the export of entropy. Exporting entropy to the surrounding environment corresponds to collecting information about it. Biological actors which break the symmetry of the system and which store information are by consequence, key actors on which experiments and data analysis focus most. This paper aims at illustrating properties of dissipative structure through familiar examples and thus initiating the dialogue between nonequilibrium thermodynamics and plant biology.

On a staggered iFEM approach to account for friction in compression testing of soft materials

An inverse finite element method (iFEM) to estimate material parameters from compression tests of soft materials is presented, where alginate hydrogel was used as a phantom material. The method applies if the boundary conditions at the loaded surfaces are not ideal, i.e. neither free of friction nor fully constrained, as it may be the case in most realistic testing set-ups. Assuming a linear friction law, the friction coefficient μ was considered unknown and estimated in a first step by minimising the difference between the contours of the sample, obtained by optical measurements, and the simulated shape. Force-displacement data were used in a second step to determine the parameters of the constitutive law. Staggering these two steps, both friction and material parameters were identified by optimisation. Skipping the first step and predefining μ instead, a unique parameter set could only be clearly identified if the deviations of the contours were considered in addition to the deviations in the force-displacement data. Finally, forward FEM calculations with differently shaped specimens were used to verify the goodness of the obtained parameter sets.