A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.Comment: 31 pages, 17 figure

A computational framework for rheologically complex thermo-visco-elastic materials

Fractional calculus has been proved to be very effective in representing the visco-elastic relaxation response of materials with memory such as polymers. Moreover, in modelling the temperature dependency of the material functions in thermo-visco-elasticity, the standard time-temperature superposition principle is known to be ineffective in most of the cases (thermo-rehological complexity). In this work, a novel finite element formulation and numerical implementation is proposed for the simulation of transient thermal analysis in thermo-rehologically complex materials. The parameters of the visco-elastic fractional constitutive law are assumed to be temperature dependent functions and an internal history variable is introduced to track the changes in temperature which are responsible for the phase transition of the material. The numerical approximation of the fractional derivative is employed via the so called Gr\"unwald-Letnikov approximation. The proposed model is used to numerically solve some test cases related to relaxation and creep tests conducted on a real polymer (Etylene Vynil Acetate), which is used as the major encapsulant of solar cells in photovoltaics

Computational modeling of viscoelastic backsheet materials for photovoltaics

The viscoelastic response of backsheet materials significantly affects the durability of the photovoltaic (PV) module. In this study, the viscoelastic response of commercially available backsheet materials is experimentally characterized and computationally modeled. An extensive viscoelastic experimental study on backsheet materials is carried out, considering the temperature-dependent properties for characterizing the mechanical properties. Based on an experimental campaign, small-strain viscoelastic models based on the Prony-series (PS) and Fractional Calculus (FC) Models are proposed here. The form of the constitutive equations for both models is summarized, and the finite element implementation is described in detail. Following identifications of relevant material parameters, we validate the model with the experimental data that shows good predictability. A comparative study of model responses under different loading conditions is also reported to assess the advantages and disadvantages of both models. Such an extensive experimental study and constitutive modeling will help design and simulate a more comprehensive modeling of PV modules, as illustrated by the benchmark problems

Phase field modelling and simulation of damage occurring in human vertebra after screws fixation procedure

The present endeavor numerically exploits the use of a phase-field model to simulate and investigate fracture patterns, deformation mechanisms, damage, and mechanical responses in a human vertebra after the incision of pedicle screws under compressive regimes. Moreover, the proposed phase field framework can elucidate scenarios where different damage patterns, such as crack nucleation sites and crack trajectories, play a role after the spine fusion procedure, considering several simulated physiological movements of the vertebral body. A convergence analysis has been conducted for the vertebra-screws model, considering several mesh refinements, which has demonstrated good agreement with the existing literature on this topic. Consequently, by assuming different angles for the insertion of the pedicle screws and taking into account a few vertebral motion loading regimes, a plethora of numerical results characterizing the damage occurring within the vertebral model has been derived. Overall, the phase field results may shed more light on the medical community, which will be useful in enhancing clinical interventions and reducing post-surgery bone failure and screw loosening.Comment: 23 pages, 9 figures. arXiv admin note: text overlap with arXiv:2207.0936

Crack trajectories in materials containing voids via phase-field modelling

Fracture growth in a material is strongly influenced by the presence of inhomogeneities, which deviate crack trajectories from rectilinearity and deeply affect failure. Increasing crack tortuosity is connected to enhancement of fracture toughness, while often a crack may even be stopped when it impinges a void, which releases the stress concentration. Therefore, the determination of crack trajectories is important in the design against failure of materials and mechanical pieces. The recently developed phase-field approach (AT1 and AT2 models), based on a variational approach to damage localization, is believed to be particularly suited to describe complex crack trajectories. This belief is examined through a comparison between simulations and photoelastic experiments on PMMA plates, which have been designed in a new way, to highlight the effects of notches and circular holes on fracture propagation. The latter is shown to initiate from a notch and to be strongly attracted by voids. When a void is hit, fracture is arrested, unless the void contains a notch on its internal surface, from which a new crack nucleates and propagates. Different mechanical models are tested where fracture initiates and grows (i.) under Mode I compact tension, (ii.) four-point bending and (iii.) a tensile stress indirectly generated during compression of samples containing a circular hole. The experiments show that the fracture propagation may be designed to develop in different tortuous paths, involving multiple arrests and secondary nucleation. Simulations performed with an ad hoc implemented version of the AT1 and AT2 phase-field methods (equipped with spectral decomposition, in which a crack is simulated as a highly localized zone of damage accumulation) are shown to be in close agreement with experiments and therefore confirm the validity of the approach and its potentialities for mechanical design.Comment: In press on the International Journal of Solids and Structure

A microfluidic platform with permeable walls for the analysis of vascular and extravascular mass transport

Considerable advances have been made in microfluidic devices and their applications since the development of soft lithographic techniques [1]. We developed a PDMS based double channel chip consisting of two microfluidic channels that mimic the vascular and extravascular compartments. The two channels are designed to be confined by sidewalls and connected by a membrane composed by arrays of pillars constituting a permeable vascular wall [2]. The inner surface of the vascular channel is uniformly coated with Human Umbilical Vein Endothelial Cells (HUVEC) resulting in well-controlled 3D model of blood vessel with endothelial barrier functions. In Figure.1A and B, the photolithographic, etching, and replica molding steps needed for realizing double-channel chips are presented together with an image (right) of the vascular channel after cell seeding and self-organization in a tubular shape. The extravascular compartment can be integrated with tumor cells of different type, potentially organized in a 3D fashion inside an extracellular matrix or with extracellular matrix components. The integration of the two compartments allow us to study the transport and permeation of therapeutic molecules, nanomedicines and cells through the endothelial barrier and the efficacy of the administered treatment. Other applications such as modeling of metastatic cell and leucocytes adhesion and migration across the endothelial barrier allow us to characterize cell extravasation from the vascular bed. The vascular transport and subsequent adhesion dynamics of nano-constructs and cells to the vascular channel are also predicted using a 3D computational framework based on coupling Lattice Boltzmann (LB) and Immersed Boundary (IB) methods. The fluid solver for the incompressible Navier-Stokes equations is based on the three dimensional D3Q19 Lattice-Boltzmann Method. The dynamics of deformable nano-constructs and cells is simulated through a neo-Hookean membrane constitutive model coupled iteratively with the fluid (Figure.1C). The combination of microfluidic chips and computational modeling provides a formidable tool for boosting our understanding on disease development and drug delivery. Please click Additional Files below to see the full abstract