Modelling and simulations of hydrogels with coupled solvent diffusion and large deformation

textSwelling of a polymer gel is a kinetic process coupling mass transport and mechanical deformation. A comparison between a nonlinear theory for polymer gels and the classical theory of linear poroelasticity is presented. It is shown that the two theories are consistent within the linear regime under the condition of a small perturbation from an isotropically swollen state of the gel. The relationships between the material properties in the linear theory and those in the nonlinear theory are established by a linearization procedure. Both linear and nonlinear solutions are presented for swelling kinetics of substrate-constrained and freestanding hydrogel layers. A new procedure is suggested to fit the experimental data with the nonlinear theory. A nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on nonlinear continuum theories for hydrogels with compressible and incompressible constituents. The incompressible instantaneous response of the aggregate imposes a constraint to the finite element discretization in order to satisfy the LBB condition for numerical stability of the mixed method. Three problems of practical interests are considered: constrained swelling, flat-punch indentation, and fracture of hydrogels. Constrained swelling may lead to instantaneous surface instability. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, and is compared with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson’s ratio and loading rate are discussed. On the study of hydrogel fracture, a method for calculating the transient energy release rate for crack growth in hydrogels, based on a modified path-independent J-integral, is presented. The transient energy release rate takes into account the energy dissipation due to diffusion. Numerical simulations are performed for a stationary center crack loaded in mode I, with both immersed and non-immersed chemical boundary conditions. Both sharp crack and blunted notch crack models are analyzed over a wide range of applied remote tensile strains. Comparisons to linear elastic fracture mechanics are presented. A critical condition is proposed for crack growth in hydrogels based on the transient energy release rate. The applicability of this growth condition for simulating concomitant crack propagation and solvent diffusion in hydrogels is discussed.Engineering Mechanic

Surface and bulk stresses drive morphological changes in fibrous microtissues

Engineered fibrous tissues consisting of cells encapsulated within collagen gels are widely used three-dimensional in vitro models of morphogenesis and wound healing. Although cell-mediated matrix remodeling that occurs within these scaffolds has been extensively studied, less is known about the mesoscale physical principles governing the dynamics of tissue shape. Here, we show both experimentally and by using computer simulations how surface contraction through the development of surface stresses (analogous to surface tension in fluids) coordinates with bulk contraction to drive shape evolution in constrained three-dimensional microtissues. We used microelectromechanical systems technology to generate arrays of fibrous microtissues and robot-assisted microsurgery to perform local incisions and implantation. We introduce a technique based on phototoxic activation of a small molecule to selectively kill cells in a spatially controlled manner. The model simulations, which reproduced the experimentally observed shape changes after surgical and photochemical operations, indicate that fitting of only bulk and surface contractile moduli is sufficient for the prediction of the equilibrium shape of the microtissues. The computational and experimental methods we have developed provide a general framework to study and predict the morphogenic states of contractile fibrous tissues under external loading at multiple length scales.Published versio

Modeling the mechanosensitive collective migration of cells on the surface and the interior of morphing soft tissues

Cellular contractility, migration, and extracellular matrix (ECM) mechanics are critical for a wide range of biological processes including embryonic development, wound healing, tissue morphogenesis, and regeneration. Even though the distinct response of cells near the tissue periphery has been previously observed in cell-laden microtissues, including faster kinetics and more prominent cell-ECM interactions, there are currently no models that can fully combine coupled surface and bulk mechanics and kinetics to recapitulate the morphogenic response of these constructs. Mailand \textit{et al.} (2019) had shown the importance of active elastocapillarity in cell-laden microtissues, but modeling the distinct mechanosensitive migration of cells on the periphery and the interior of highly deforming tissues has not been possible thus fur, especially in the presence of active elastocapillary effects. This paper presents a framework for understanding the interplay between cellular contractility, migration, and ECM mechanics in dynamically morphing soft tissues accounting for distinct cellular responses in the bulk and the surface of tissues. The major novelty of this approach is that it enables modeling the distinct migratory and contractile response of cells residing on the tissue surface and the bulk, where concurrently the morphing soft tissues undergoes large deformations driven by cell contractility. Additionally, the proposed model is validated through simulation results that capture the changes in shape and cell concentration for wounded and intact microtissues, enabling the interpretation of experimental data.Comment: 20 pages, 13 figure

NN-EVP: A physics informed neural network-based elasto-viscoplastic framework for predictions of grain size-aware flow response under large deformations

We propose a physics informed, neural network-based elasto-viscoplasticity (NN-EVP) constitutive modeling framework for predicting the flow response in metals as a function of underlying grain size. The developed NN-EVP algorithm is based on input convex neural networks as a means to strictly enforce thermodynamic consistency, while allowing high expressivity towards model discovery from limited data. It utilizes state-of-the-art machine learning tools within PyTorch's high-performance library providing a flexible tool for data-driven, automated constitutive modeling. To test the performance of the framework, we generate synthetic stress-strain curves using a power law-based model with phenomenological hardening at small strains and test the trained model for strain amplitudes beyond the training data. Next, experimentally measured flow responses obtained from uniaxial deformations are used to train the framework under large plastic deformations. Ultimately, the Hall-Petch relationship corresponding to grain size strengthening is discovered by training flow response as a function of grain size, also leading to efficient extrapolation. The present work demonstrates a successful integration of neural networks into elasto-viscoplastic constitutive laws, providing a robust automated framework for constitutive model discovery that can efficiently generalize, while also providing insights into predictions of flow response and grain size-property relationships in metals and metallic alloys under large plastic deformations

Learning hyperelastic anisotropy from data via a tensor basis neural network

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 neural network layers, and L1 regularization. The proposed tensor-basis neural network can discover both the type and orientation of the anisotropy and provide an accurate model of the stress response. The method is demonstrated with data from hyperelastic materials with off-axis transverse isotropy and orthotropy, as well as materials with less well-defined symmetries induced by fibers or spherical inclusions. Both plain feed-forward neural networks and input-convex neural network formulations are developed and tested. Using the latter, a polyconvex potential can be established, which, by satisfying the growth condition can guarantee the existence of boundary value problem solutions.Comment: 36 pages, 20 figure

Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen

Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent generalization performance. In these models, the stress prediction follows from a linear combination of invariant-dependent coefficient functions and known tensor basis generators. However, thus far the formulations have been limited to stress representations based on the classical Rivlin and Ericksen form, while the performance of alternative representations has yet to be investigated. In this work, we survey a variety of tensor basis neural network models for modeling hyperelastic materials in a finite deformation context, including a number of so far unexplored formulations which use theoretically equivalent invariants and generators to Finger-Rivlin-Ericksen. Furthermore, we compare potential-based and coefficient-based approaches, as well as different calibration techniques. Nine variants are tested against both noisy and noiseless datasets for three different materials. Theoretical and practical insights into the performance of each formulation are given.Comment: 32 pages, 20 figures, 4 appendice