Browsing by Author "Bleiler, Christian"

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Open Access
Continuum-mechanical modelling across scales : homogenisation methods and their application to microstructurally-based skeletal muscle modelling
(Stuttgart : Institute for Modelling and Simulation of Biomechanical Systems, Chair of Continuum Biomechanics and Mechanobiology, University of Stuttgart, 2021) Bleiler, Christian; Röhrle, Oliver (Prof., PhD)
A variety of materials, such as biological soft tissues, exhibit large inter- and intra-subject microstructural variations that cannot be captured with individual material tests on the macroscopic observation scale. In such scenarios, multiscale modelling approaches are used instead, which explicitly incorporate the microstructure and provide macroscopic quantities through suitable homogenisation methods. This enables the description of biological soft tissue behaviour arising from microstructural changes, for example, those caused by disease. This thesis, therefore, deals with the multiscale continuum-mechanical modelling of materials and the particular application of such methods to the description of skeletal muscle tissue. Besides a general introduction to the subject, novel analytical estimates for the effective macroscopic potential of two-phase, hyperelastic, incompressible solids are presented. These are based on the so-called tangent second-order homogenisation method and are applicable for highly nonlinear, anisotropic material behaviour at large strains. Subsequently, a novel multiscale model for skeletal muscle is presented, which describes the macroscopic behaviour of soft tissue as a direct consequence of properties at smaller scales, such as the stiffness and arrangement of individual collagen fibres. The methods and models presented in this thesis are discussed by means of representative examples, thus demonstrating their merits in comparison to alternative approaches.
Open Access
A microstructurally-based, multi-scale, continuum-mechanical model of skeletal muscle tissue
(2019) Bleiler, Christian; Ponte Castañeda, Pedro; Röhrle, Oliver
Open Access
A physiology-guided classification of active-stress and active-strain approaches for continuum-mechanical modeling of skeletal muscle tissue
(2021) Klotz, Thomas; Bleiler, Christian; Röhrle, Oliver
The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.
Open Access
Strain measures and energies for crimped fibres and novel analytical expressions for fibre populations : ingredients for structural fibre network models
(2022) Bleiler, Christian; Röhrle, Oliver
This paper deals with the structural modelling of fibre networks with a focus on the description of populations of initially crimped fibres. It presents a systematic approach of introducing appropriate strain measures for single fibres based on a deformation decomposition and by transferring knowledge from the field of elastoplasticity. On this basis, for example, the often used Biot-type fibre strain measures λ-λwand λ/λw-1, with stretch λand waviness λw, are consistently assigned to different classes of material strain (“additive”) or intermediate strain (“multiplicative”) descriptions, respectively. We review in this work different fibre strain energies based on the different stain measures and present extensive comparisons on the physical implications and the results on the fibre population and network scale. These investigations also include formulations with a Hencky-type energy based on a logarithmic strain. Furthermore, we present novel analytical expressions for fibre populations that make the evaluation of integral expression superfluous and thus lead to a significant reduction in computational time.