Alexander Edmund Ehret

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Ehret

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Alexander Edmund

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0000-0002-8740-8900

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Publications 1 - 10 of 19

Moment-based, univariate n-point quadrature rules in application to the full network model of rubber elasticity
Britt, Ben R.; Ehret, Alexander Edmund (2024)
Computer Methods in Applied Mechanics and Engineering
In this contribution we provide numerical methods to implement full network models with particular application to affine isotropic networks as they are frequently applied in theories of rubber elasticity. Unlike the common approaches, the average of the single chains’ responses is not obtained by spherical integration but by solving a univariate integral expressed in terms of the squared stretch of a fibre's or chain's end-to-end vector. In addition to the free energy function of these individual elements the methods are informed by the statistical moments of the distribution of stretch in the network, which throughout the work is assumed to be determined by affine kinematics. We exemplify the proposed procedure for two quadrature methods, which distinguish in terms of the positions of the n integration points and the corresponding weights. While the first method uses constant equal weights of 1/n and hence only requires the computation of n integration points, the second, Gauss-type method also requires the determination of the corresponding weights and builds on a recent development, previously implemented for up to 3 points (Britt & Ehret, Comput. Methods Appl. Mech. Engrg. 415, 2023). However, the structure of the solution strategy applies to a wider range of univariate quadrature rules. Both methods exemplified here can be made exact for polynomial chain free energy functions of arbitrary order, and are illustrated in application to the affine full network model of rubber elasticity with non-Gaussian chains. The results indicate high accuracy of the new methods and therefore identify them as useful and efficient alternatives to the existing approaches for computing the full network response.
Stretch-induced damage in endothelial monolayers
Choi, Young; Jakob, Raphael; Ehret, Alexander Edmund; et al. (2024)
Biomaterials Advances
Endothelial cells are constantly exposed to mechanical stimuli, of which mechanical stretch has shown various beneficial or deleterious effects depending on whether loads are within physiological or pathological levels, respectively. Vascular properties change with age, and on a cell-scale, senescence elicits changes in endothelial cell mechanical properties that together can impair its response to stretch. Here, high-rate uniaxial stretch experiments were performed to quantify and compare the stretch-induced damage of monolayers consisting of young, senescent, and aged endothelial populations. The aged and senescent phenotypes were more fragile to stretch-induced damage. Prominent damage was detected by immunofluorescence and scanning electron microscopy as intercellular and intracellular void formation. Damage increased proportionally to the applied level of deformation and, for the aged and senescent phenotype, induced significant detachment of cells at lower levels of stretch compared to the young counterpart. Based on the phenotypic difference in cell-substrate adhesion of senescent cells indicating more mature focal adhesions, a discrete network model of endothelial cells being stretched was developed. The model showed that the more affine deformation of senescent cells increased their intracellular energy, thus enhancing the tendency for cellular damage and impending detachment. Next to quantifying for the first-time critical levels of endothelial stretch, the present results indicate that young cells are more resilient to deformation and that the fragility of senescent cells may be associated with their stronger adhesion to the substrate.
Multiscale mechanical analysis of the elastic modulus of skin
Wahlsten, Adam; Stracuzzi, Alberto; Lüchtefeld, Ines; et al. (2023)
Acta Biomaterialia
The mechanical properties of the skin determine tissue function and regulate dermal cell behavior. Yet measuring these properties remains challenging, as evidenced by the large range of elastic moduli reported in the literature—from below one kPa to hundreds of MPa. Here, we reconcile these disparate results by dedicated experiments at both tissue and cellular length scales and by computational models considering the multiscale and multiphasic tissue structure. At the macroscopic tissue length scale, the collective behavior of the collagen fiber network under tension provides functional tissue stiffness, and its properties determine the corresponding elastic modulus (100–200 kPa). The compliant microscale environment (0.1–10 kPa), probed by atomic force microscopy, arises from the ground matrix without engaging the collagen fiber network. Our analysis indicates that indentation-based elasticity measurements, although probing tissue properties at the cell-relevant length scale, do not assess the deformation mechanisms activated by dermal cells when exerting traction forces on the extracellular matrix. Using dermal-equivalent collagen hydrogels, we demonstrate that indentation measurements of tissue stiffness do not correlate with the behavior of embedded dermal fibroblasts. These results provide a deeper understanding of tissue mechanics across length scales with important implications for skin mechanobiology and tissue engineering. Statement of Significance: Measuring the mechanical properties of the skin is essential for understanding dermal cell mechanobiology and designing tissue-engineered skin substitutes. However, previous results reported for the elastic modulus of skin vary by six orders of magnitude. We show that two distinct deformation mechanisms, related to the tension–compression nonlinearity of the collagen fiber network, can explain the large variations in elastic moduli. Furthermore, we show that microscale indentation, which is frequently used to assess the stiffness perceived by cells, fails to engage the fiber network, and therefore cannot predict the behavior of dermal fibroblasts in stiffness-tunable fibrous hydrogels. This has important implications for how to measure and interpret the mechanical properties of soft tissues across length scales.
A quadriphasic mechanical model of the human dermis
Sachs, David; Jakob, Raphael; Restivo, Gaetana; et al. (2024)
Biomechanics and Modeling in Mechanobiology
The present study investigates the multiphasic nature of the mechanical behavior of human dermis. Motivated by experimental observations and by consideration of its composition, a quadriphasic model of the dermis is proposed, distinguishing solid matrix components, interstitial fluid and charged constituents moving within the fluid, i.e., anions and cations. Compression and tensile experiments with and without change of osmolarity of the bath are performed to characterize the chemo-mechanical coupling in the dermis. Model parameters are determined through inverse analysis. The computations predict a dominant role of the permeability in the determination of the temporal evolution of the mechanical response of the tissue. In line with the previous studies on other tissues, the analysis shows that an ideal model based on Donnan's equilibrium overestimates the osmotic pressure in skin for the case of very dilute solutions. The quadriphasic model is applied to predict changes in dermal cell environment and therefore alterations in what is called the "mechanome," associated with skin stretch. The simulations indicate that skin deformation causes a variation in several local variables, including in particular the electric field associated with a deformation-induced non-homogeneous distribution of fixed charges.
Univariate Gauss quadrature for structural modelling of tissues and materials with distributed fibres
Britt, Ben R.; Ehret, Alexander Edmund (2023)
Computer Methods in Applied Mechanics and Engineering
This work presents a method for computing the averaged free energy and constitutive relations in hyperelastic material models with distributed fibres, as they apply to soft fibre-reinforced materials and biological tissues. While these models are currently implemented through either spherical cubature of the fibre free energy or its Taylor series, we here propose a new method based on a univariate Gauss quadrature rule with integration points and weights informed by the statistical moments of the distribution of fibre stretch. As an intrinsic property, the new approach separates the integration of the fibre constitutive law from the integration of the orientation distribution, the latter leading to structural tensors of even order. Provided the latter 2n−1 tensors are computed accurately up to tensorial order 2(2n−1), the method integrates exactly any polynomial of order 2n−1 that agrees with the fibre law at the n integration points. After formally introducing the quadrature method for generally non-affine fibre deformations and arbitrary order, we focus on the important special case of affine fibre kinematics and discuss the rules with n≤3 integration points, for which the corresponding positions and weights are determined analytically. At a computational cost comparable to the existing approaches, the new method does not require the fibre law to be analytic and can thus robustly deal with piece-wise definitions of the fibre energy, in contrast to Taylor-series approaches, and it does not induce additional anisotropy as it can occur with spherical cubature rules. The 3-point rule is further investigated and illustrated in numerical examples relating to soft collagenous tissues based on a Fortran implementation of the method suitable for use in finite element analyses.
Discrete Network Models inspire a new class of Continuum Constitutive Models for Fibre Network Materials
Britt, Ben R.; Stracuzzi, Alberto; Mazza, Edoardo; et al. (2022)
WCCM-APCOM 2022 Book of Abstract
The influence of aspect ratio on the determination of tearing energy in mode I fracture tests
Kahle, Eleni; Ehret, Alexander Edmund; Mazza, Edoardo (2023)
Engineering Fracture Mechanics
The energy for tearing is a classical measure of fracture toughness for elastic materials at finite strains. The prominent approach to quantify the tearing energy utilizes a tensile test on edge-cut thin rectangular specimens with low height-to-width ratio to determine the critical stretch at which a crack propagates from the tip of the cut. The analysis of the experiment, proposed by Rivlin and Thomas (1953), relies on the assumption that a large portion of the test piece is in a state of plane strain, and that the change of the total elastic energy is equal to the energy release due to the formation of new crack surfaces. While these assumptions are well justified for test pieces with sufficiently low height-to-width ratio, limitations in the availability and homogeneity of various sample materials have enforced the use of specimens with higher height-to-width ratios. In order to analyse the applicability of the classical theory and the corresponding errors, we investigate in the present work the influence of the sample's height-to-width ratio on the estimation of the tearing energy in mode I fracture tests. Exemplified with experiments and simulations for the elastomer Ecoflex 1:1, we show that reliable measurements can be obtained even for a quadratic sample geometry. For tough materials, however, significant overestimation of the tearing energy is expected already for a height-to-width ratio larger than 1/2. Surprisingly, in very brittle materials the tearing energy is vice-versa prone to be underestimated by up to 10% for ratios up to 1. The error also depends on the non-linear stress–strain characteristics, as illustrated by the use of different constitutive models. While a generally valid geometrical criterion cannot be defined based on the present results, our results suggest that the error hardly exceeds 10% for height-to-width ratios of up to 1/2.
The affine network revisited: insights through a new class of constitutive models
Britt, Ben R.; Mazza, Edoardo; Ehret, Alexander Edmund (2022)
Variations on Ogden's model: close and distant relatives
Ehret, Alexander Edmund; Stracuzzi, Alberto (2022)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
The power law in terms of stretch, the truncated series representation and the Valanis-Landel hypothesis are distinguished features of Ogden's strain-energy density function. While they represent a set of special constitutive choices, they have also been shown recently to allow a particular molecular statistical interpretation of the model, where each of these ingredients can be associated with a step in the development of the strain-energy density of the polymer network from the statistical mechanics of long-chain molecules. The schematic of this perspective brings us into a position to vary these steps individually. By this means, Ogden's theory can be embedded in a certain family of models within the large class of isotropic hyperelastic materials, whose members can be identified as close and distant 'relatives'.This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
The anisotropic and region-dependent mechanical response of wrap-around tendons under tensile, compressive and combined multiaxial loads
Böl, Markus; Leichsenring, Kay; Kohn, Stephan; et al. (2024)
Acta Biomaterialia
The present work reports on the multiaxial region and orientation-dependent mechanical properties of two porcine wrap-around tendons under tensile, compressive and combined loads based on an extensive study with n=175 samples. The results provide a detailed dataset of the anisotropic tensile and compressive longitudinal properties and document a pronounced tension-compression asymmetry. Motivated by the physiological loading conditions of these tendons, which include transversal compression at bony abutments in addition to longitudinal tension, we systematically investigated the change in axial tension when the tendon is compressed transversally along one or both perpendicular directions. The results reveal that the transversal compression can increase axial tension (proximal-distal direction) in both cases to orders of 30%, yet by a larger amount in the first case (transversal compression in anterior-posterior direction), which seems to be more relevant for wrap-around tendons in-vivo. These quantitative measurements are in line with earlier findings on auxetic properties of tendon tissue, but show for the first time the influence of this property on the stress response of the tendon, and may thus reveal an important functional principle within these essential elements of force transmission in the body. Statement of significance: The work reports for the first time on multiaxial region and orientation-dependent mechanical properties of wrap-around tendons under various loads. The results indicate that differences in the mechanical properties exist between zones that are predominantly in a uniaxial tensile state and those that experience complex load states. The observed counterintuitive increase of the axial tension upon lateral compression points at auxetic properties of the tendon tissue which may be pivotal for the function of the tendon as an element of the musculoskeletal system. It suggests that the tendon's performance in transmitting forces is not diminished but enhanced when the action line is deflected by a bony pulley around which the tendon wraps, representing an important functional principle of tendon tissue.

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Alexander Edmund Ehret

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