Ben R. Britt

Last Name

Britt

First Name

Ben R.

ORCID

0000-0001-5867-3038

Show all metadata

Search Results

Publications 1 - 9 of 9

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.
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
Constitutive modelling of fibre networks with stretch distributions
Britt, Ben R. (2023)
Fibre networks are ubiquitous and present in many materials, including tissues and rubber-like materials. This dissertation is dedicated to the modelling of their mechanical behaviour. In the first part of this dissertation a new framework for constitutive modelling of fibre networks has been developed. In this framework, the network internal length scale associated with the individual fibres and the length scale of application as a network is distinguished. The new approach is based on the formulation of the deformation dependent network (strain) energy, expressed as an average of the individual fibre (strain) energies. The key modelling aspect lies in the determination of this average from the distribution of energetically relevant quantities, such as the fibre element stretch. The rest of the thesis focuses on determining the network energy from the fibre element stretch distribution. This is possible if the stretch fully determines the energy of a fibre element. It is shown how the stretch distribution can be described in terms of its cumulative distribution function (CDF), probability density function (PDF) and statistical moments. Moreover, it is elaborated how such descriptions can be inferred from preliminary discrete network simulations or a constrained energy minimisation problem and used to determine the network energy. In the second part of this dissertation, the new framework has been applied to affinely deforming networks, and a thorough investigation of the corresponding fibre element stretch distribution, has been conducted. Hence, the second part reconciles the new stretch-based approach with the common orientation based approach, where the dependence of the affine stretch on initial fibre orientation is exploited to determine the network energy as an integral over the space of all orientations. The CDF and PDF as well as moments of the affine stretch are derived, and corresponding methods to approximate the network energy are elaborated. In the third part, special quadrature rules have been derived to numerically evaluate the integral over the stretch distribution, i.e. the integral representing the average fibre element energy. These quadrature rules are constructed from the moments of the stretch distribution and use stretch valued integration points. Choosing the moments of the affine stretch distribution derived in the second part, these quadrature rules offer an alternative to spherical cubature rules typically used in the common orientation based approach. In addition to the quadrature rules for determining the network energy also their differentiation, essential to deduce stress and tangent tensors, is elaborated.
The affine network revisited: insights through a new class of constitutive models
Britt, Ben R.; Mazza, Edoardo; Ehret, Alexander Edmund (2022)
Discrete network models of endothelial cells and their interactions with the substrate
Jakob, Raphael; Britt, Ben R.; Giampietro, Costanza; et al. (2024)
Biomechanics and Modeling in Mechanobiology
Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers.
Constitutive modelling of fibre networks with stretch distributions. Part I: Theory and illustration
Britt, Ben R.; Ehret, Alexander Edmund (2022)
Journal of the Mechanics and Physics of Solids
In this contribution, we propose a novel continuum mechanical concept to determine the homogenised mechanical response of random fibre networks. Their free energy is calculated as an average of the fibre free energy over the distribution of stretch, which forms the core of the new theory. The fibre-scale kinematic information contained in this distribution is intrinsic to the model and available for any state of macroscopic deformation in addition to the homogenised macroscopic response. In contrast to the various approaches that use directional averaging over the unit sphere, the presented model does not rely on a relation between fibre deformation and orientation, and therefore applies to highly non-affine networks as well as affine ones. In the present Part I of the work, the new concept is formally introduced, put into perspective with current approaches, and elaborated for the case of networks of elastic fibres with uniform orientation distribution, which generate a macroscopically isotropic hyperelastic response. The essential constitutive assumption of the theory establishes a relation between the macroscopic deformation of the network and the microscopic stretch distribution within. A phenomenological approach is used to illustrate the new concept, expressing statistical moments of the stretch distribution in terms of the macroscopic principal strain invariants. Application of the concept to 2D and 3D Voronoi networks with fibres of different properties finally exemplifies the accurate agreement of the model with discrete network simulations in terms of both the macroscopic and microscopic response. While the here presented phenomenological variant of the approach therefore represents an advance in the analytical multiscale modelling of network materials itself, the work also provides the basis for further developments, where the relation between the stretch distribution and macroscopic strain is derived from alternative principles.
Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology
Stracuzzi, Alberto; Britt, Ben R.; Mazza, Edoardo; et al. (2022)
Biomechanics and Modeling in Mechanobiology
Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.
Constitutive modelling of fibre networks with stretch distributions, Part II: Alternative representation, affine distribution and anisotropy
Britt, Ben R.; Ehret, Alexander Edmund (2023)
Journal of the Mechanics and Physics of Solids
In this paper, the concept for modelling materials with fibre network microstructures introduced in Part I of this series is reconsidered. At first, an alternative representation of the theory is provided that entails advantages in terms of numerical implementation. Next, the new constitutive approach is applied to affine networks, whose fibre stretches are distributed according to the affine distribution. Despite the tremendously widespread use of this model, it seems that the general form of the corresponding distribution has remained largely unexplored to date. The thus obtained reformulation of the affine full network model provides deep insight into this concept, and may help overcoming well-known numerical problems with the associated spherical integration, e.g. when highly non-linear or piece-wise defined fibre laws are used. The latter case is typical for applications in biomechanics, where fibres are frequently assumed to have negligible compressive resistance. While the developments of our theory thus far had focused on isotropic networks, we here showcase for the affine case how the anisotropy caused by non-uniform directional distributions of the fibres can be incorporated in the novel approach. Finally, it is shown that several earlier approaches to model networks of affinely deforming fibres or polymer chains result as special cases of our theory.

Publications 1 - 9 of 9

Ben R. Britt

Last Name

First Name

ORCID

Organisational unit

Filters

Search Results