Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics

Tubon, John D. Toaquiza; Moreno-Flores, Omar; Sree, Vivek D.; Tepole, Adrián Buganza

doi:10.1007/s10237-022-01624-y

“…This also facilitates implementation of the multi-FEM model in commercial solvers like Abaqus [34]. In the absence of a closed-form of the strain energy density function, one needs to solve the multiscale mechanics equations (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) for each element in the mesh. This will increase the computational complexity of the problem significantly.…”

Section: Mechanics Of a Single Fiber And Comparison With Literaturementioning

confidence: 99%

“…Some of the continuum mechanics models, such as, the Gasser-Ogden-Holzapfel (GOH) [11] model, include even microstructural information on the tissue histology such as collagen fiber orientation in the strain energy density function. More recently, Toaquiza Tubon et al [12] developed a histology informed strain energy based formulation for collagenous tissues that models the mechanics and damage of collagenous tissues.…”

Section: Introductionmentioning

confidence: 99%

Modelling the Mechanical Behavior of Collagenous Materials by Considering Multiscale Effects

Dingari,

Sharma,

Rizvi

et al. 2024

Preprint

0

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Collagen is an important component of many biological tissues and plays a key role in the physiological functions of the tissue. The mechanical properties of biological tissues are important for many medical and pharmaceutical applications. For instance, to probe the interaction between a medical device and a tissue it becomes important to study the stress and deformation within the tissue under external load. Modelling the mechanics of collagenous tissues is non-trivial because of the anisotropic and hyperelastic nature of the tissue. The arrangement of the collagen within the tissue governs the directional dependence of its mechanical properties. Further, collagen mechanics is itself a strong function of the arrangement of various collagenous components (tropocollagen molecules, fibrils, fibers) at various length scales. Therefore to accurately model the mechanics of a collagenous tissue at macroscopic length scale it is necessary to consider the multiscale mechanics of collagen. In this work, we develop a multiscale-informed finite element method (multi-FEM) framework to model the mechanics of a collagenous tissue. We propose a novel exponential strain energy density function for the mechanics of collagen fibers, which shows excellent agreement with the strain energy density of a collagen fiber obtained by considering multiscale effects (molecule to fiber). Further, this exponential strain energy density is used to simulate the macroscopic mechanics of the tissue using finite element method. Using this multi-FEM framework, we systematically investigate the influence of various lower-length scale collagen properties on the macroscopic stress response of the collagenous tissue. This framework can be very useful in the development of high-fidelity computational models of collagenous tissues that can include the huge variability in the tissue properties.

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“…Most soft tissues have inherent directionality due to their collagen fiber-based and/or aligned cellular microstructures [68,69], toward which tools of analysis from Finsler geometry might be anticipated to aptly apply. The mechanics of skin deformation [68,70,71], degradation [72,73], and tearing [73,74] are investigated herein. Like most biological materials, the microstructure of skin is complex.…”

Section: Soft Tissue and Skin Mechanicsmentioning

confidence: 99%

Generalized Finsler Geometry and the Anisotropic Tearing of Skin

Clayton

2023

Symmetry

0

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A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on the position and the state vector, where the latter dependence allows for both the direction (i.e., as in Finsler geometry) and magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer’s lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models.

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“…Some of the continuum mechanics models, such as, the Gasser-Ogden-Holzapfel (GOH) (Gasser, Ogden and Holzapfel 2006) model, include even microstructural information on the tissue histology such as collagen fiber orientation in the strain energy density function. More recently, Toaquiza Tubon et al (Toaquiza Tubon, et al 2022) developed a histology informed strain energy based formulation for collagenous tissues that models the mechanics and damage of collagenous tissues. Though continuum mechanics models ignore the microstructure of the tissue, they have been extremely successful in predicting the macroscopic response.…”

Section: Introductionmentioning

confidence: 99%

Modelling the Mechanical Behavior of Collagenous Materials by Considering Multiscale Effects

Dingari,

Sharma,

Rizvi

et al. 2024

Preprint

0

View full text Add to dashboard Cite

Collagen is an important component of many biological tissues and plays a key role in the physiological functions of the tissue. The mechanical properties of biological tissues are important for many medical and pharmaceutical applications. For instance, to probe the interaction between a medical device and a tissue it becomes important to study the stress and deformation within the tissue under external load. Modelling the mechanics of collagenous tissues is non-trivial because of the anisotropic and hyperelastic nature of the tissue. The arrangement of the collagen within the tissue governs the directional dependence of its mechanical properties. Further, collagen mechanics is itself a strong function of the arrangement of various collagenous components (tropocollagen molecules, fibrils, fibers) at various length scales. Therefore to accurately model the mechanics of a collagenous tissue at macroscopic length scale it is necessary to consider the multiscale mechanics of collagen. In this work, we develop a multiscale-informed finite element method (multi-FEM) framework to model the mechanics of a collagenous tissue. We propose a novel exponential strain energy density function for the mechanics of collagen fibers, which shows excellent agreement with the strain energy density of a collagen fiber obtained by considering multiscale effects (molecule to fiber). Further, this exponential strain energy density is used to simulate the macroscopic mechanics of the tissue using finite element method. Using this multi-FEM framework, we systematically investigate the influence of various lower-length scale collagen properties on the macroscopic stress response of the collagenous tissue. This framework can be very useful in the development of high-fidelity computational models of collagenous tissues that can include the huge variability in the tissue properties.

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Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics

Cited by 16 publications

References 54 publications

Modelling the Mechanical Behavior of Collagenous Materials by Considering Multiscale Effects

Modelling the Mechanical Behavior of Collagenous Materials by Considering Multiscale Effects

Generalized Finsler Geometry and the Anisotropic Tearing of Skin

Modelling the Mechanical Behavior of Collagenous Materials by Considering Multiscale Effects

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