Optimization-based comparison of different approaches for the automatized calculation of residual stresses and fiber orientations in arteries

Residual stresses and fiber orientations in arterial walls can be approximated by means of the simulation of growth and remodeling processes. In order to enable a comparison of different approaches of combined growth and remodeling in one framework, a method based on the optimization of model parameters is developed. The minimization of a mechano-biologically motivated objective function permits to evaluate the approaches with respect to their ability of effectively reducing stress peaks and stress inhomogeneities in the arterial wall. This examination is performed for a simplified, one-layered, rotationally symmetric arterial segment in order to enable the analysis of the fundamental mechanisms included in the individual model variants. Once the most probable growth mechanism is identified, multi-layered segments can be analyzed in more detail

Modeling and experimental investigations of the stress-softening behavior of soft collagenous tissues

This paper deals with the formulation of a micro-mechanically based dam-age model for soft collagenous tissues. The model is motivated by (i) a sliding filament model proposed in the literature [1] and (ii) by experimental observations from electron microscopy (EM) images of human abdominal aorta specimens, see [2]. Specifically, we derive a continuum damage model that takes into account statistically distributed pro- teoglycan (PG) bridges. The damage model is embedded into the constitutive framework proposed by Balzani et al. [3] and adjusted to cyclic uniaxial tension tests of a hu- man carotid artery. Furthermore, the resulting damage distribution of the model after a circumferential overstretch of a simplified arterial section is analyzed in a finite element calculation

An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential equation. In this contribution, we present how Hamilton’s principle provides a physically sound strategy for the derivation of transient field equations for all state variables. Therefore, we begin with a demonstration how Hamilton’s principle generalizes the principle of stationary action for rigid bodies. Furthermore, we show that the basic idea behind Hamilton’s principle is not restricted to isothermal mechanical processes. In contrast, we propose an extended Hamilton principle which is applicable to coupled problems and dissipative microstructure evolution. As example, we demonstrate how the field equations for all state variables for thermo-mechanically coupled problems, i.e., displacements, temperature, and internal variables, result from the stationarity of the extended Hamilton functional. The relation to other principles, as the principle of virtual work and Onsager’s principle, is given. Finally, exemplary material models demonstrate how to use the extended Hamilton principle for thermo-mechanically coupled elastic, gradient-enhanced, rate-dependent, and rate-independent materials. © 2021, The Author(s)

An extended Hamilton functional for the thermodynamic topology optimization of hyperelastic structures

We present our work on a new variational approach for thermodynamic topology optimization of hyperelastic structures: building upon our previous works, we follow a thermodynamic approach for deriving a field equation that describes the evolution of the density. The problem of topology optimization is consequently solved without the need of expensive optimization routines. Furthermore, our new formulation can also be applied to hyperelastic structures which show a remarkable difference to structures optimized for small deformations. Important aspects like tension/compression asymmetry and buckling are inherently included in the topology optimization approach due to the large deformation formulation

MODELING OF ANISOTROPIC GROWTH AND RESIDUAL STRESSES IN ARTERIAL WALLS

Based on the multiplicative decomposition of the deformation gradient, a local formulation for anisotropic growth in soft biological tissues is formulated by connecting the growth tensor to the main anisotropy directions. In combination with an anisotropic driving force, the model enables an effective stress reduction due to growth-induced residual stresses. A method for the imitation of opening angle experiments in numerically simulated arterial segments, visualizing the deformations related to residual stresses, is presented and illustrated in a numerical example

Residual stresses resulting from growth and remodeling in arterial walls

A model for multiplicative anisotropic growth in soft biological tissues, which relates the growth tensor to the fibrous tissue structure, is combined with a fiber remode- ling framework. Both adaptation mechanisms are supposed to be governed by the intensity and the directions of the tensile principal stresses. Numerical examples on idealized arterial segments, illustrating stress and fiber angle distributions as well as resulting residual stresses in cases with and without fiber remodeling, are presented. It turns out that all processes including growth and remodeling are necessary to obtain qualitatively realistic distributions of fiber orientations, residual stresses, and stresses under loading

Continuum multiscale modeling of absorption processes in micro- and nanocatalysts

In this paper, we propose a novel, semi-analytic approach for the two-scale, computational modeling of concentration transport in packed bed reactors. Within the reactor, catalytic pellets are stacked, which alter the concentration evolution. Firstly, the considered experimental setup is discussed and a naive one-scale approach is presented. This one-scale model motivates, due to unphysical fitted values, to enrich the computational procedure by another scale. The computations on the second scale, here referred to as microscale, are based on a proper investigation of the diffusion process in the catalytic pellets from which, after continuum-consistent considerations, a sink term for the macroscopic advection–diffusion–reaction process can be identified. For the special case of a spherical catalyst pellet, the parabolic partial differential equation at the microscale can be reduced to a single ordinary differential equation in time through a semi-analytic approach. After the presentation of our model, we show results for its calibration against the macroscopic response of a simple standard mass transport experiment. Based thereon, the effective diffusion parameters of the catalyst pellets can be identified. © 2022, The Author(s)

Efficient and robust numerical treatment of a gradient-enhanced damage model at large deformations

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed by Junker et al. in 2019, to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples including snapback and springback phenomena. © 2021 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd

Modeling of damage in soft biological tissues and application to arterial walls

A new material model is proposed for the description of stress-softening observed in cyclic tension tests performed on soft biological tissues. The modeling framework is based on the concept of internal variables introducing a scalar-valued variable for the representation of fiber damage. Remanent strains in fiber direction can be represented as a result of microscopic damage of the fiber crosslinks. Particular internal variables are defined able to capture the nature of soft biological tissues that no damage occurs in the physiological loading domain. A specific model is adjusted to experimental data taking into account the supra-physiological loading regime. For the description of the physiological domain polyconvex functions are used which also take into account fiber dispersion in a phenomenological approach. The applicability of the model in numerical simulations is shown by a representative example where the damage distribution in an arterial cross-section is analyzed

Modeling of damage in soft biological tissues and application to arterial walls

A new material model is proposed for the description of stress-softening observed in cyclic tension tests performed on soft biological tissues. The modeling framework is based on the concept of internal variables introducing a scalar-valued variable for the representation of fiber damage. Remanent strains in fiber direction can be represented as a result of microscopic damage of the fiber crosslinks. Particular internal variables are defined able to capture the nature of soft biological tissues that no damage occurs in the physiological loading domain. A specific model is adjusted to experimental data taking into account the supra-physiological loading regime. For the description of the physiological domain polyconvex functions are used which also take into account fiber dispersion in a phenomenological approach. The applicability of the model in numerical simulations is shown by a representative example where the damage distribution in an arterial cross-section is analyzed