One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical ...behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.
•Novel machine learning architecture for data-driven constitutive modeling.•Reducing required training data by incorporation of continuum mechanical knowledge.•Predictive constitutive modeling as ...required for designing new materials.
In this paper we introduce constitutive artificial neural networks (CANNs), a novel machine learning architecture for data-driven modeling of the mechanical constitutive behavior of materials. CANNs are able to incorporate by their very design information from three different sources, namely stress-strain data, theoretical knowledge from materials theory, and diverse additional information (e.g., about microstructure or materials processing). CANNs can easily and efficiently be implemented in standard computational software. They require only a low-to-moderate amount of training data and training time to learn without human guidance the constitutive behavior also of complex nonlinear and anisotropic materials. Moreover, in a simple academic example we demonstrate how the input of microstructural data can endow CANNs with the ability to describe not only the behavior of known materials but to predict also the properties of new materials where no stress-strain data are available yet. This ability may be particularly useful for the future in-silico design of new materials. The developed source code of the CANN architecture and accompanying example data sets are available at https://github.com/ConstitutiveANN/CANN.
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•The applied stress and microstructure model address the caveats of atomistic creep.•Physically affine atomistic models reduce creep rates by three orders of magnitude.•Dislocation ...gliding (strain bursts) and colony boundary sliding dominate the creep.•Interlamellar interfaces inhibit both the dislocation nucleation and its mobility.
Molecular dynamics (MD) simulations of creep generally face the problem that the creep most often evolves on time scales hard to capture with MD due to their typically short time step size. Consequently, MD studies of creep often use unrealistically high temperatures and stresses and simplified atomistic models to make creep-like processes happen on computationally accessible time scales. Apparently, this compromises the physical reliability of such studies. To alleviate this problem, we designed an MD model of titanium aluminide (TiAl) with a microstructure matching at least many of the key parameters of experimentally observed microstructures. We applied this MD model with stresses much lower than the ones used in most previous creep studies (well below yield stress) and in the temperature range 0.55TM-0.7TM, with melting temperature TM. Compared to typical previous MD studies, this much more realistic setup produces creep rates more than three orders of magnitude smaller and thus much closer to reality. We identified the driving mechanisms of primary creep on the nanosecond scale that agree very well with recent experimental observations, thus contributing towards the overarching goal of bridging the gap between atomistic creep simulations and continuum-scale creep simulations for engineering applications.
Efficient and accurate calculation of spatial integrals is of major interest in the numerical implementation of peridynamics (PD). The standard way to perform this calculation is a particle-based ...approach that discretizes the strong form of the PD governing equation. This approach has rapidly been adopted by the PD community since it offers some advantages. It is computationally cheaper than other available schemes, can conveniently handle material separation, and effectively deals with nonlinear PD models. Nevertheless, PD models are still computationally very expensive compared with those based on the classical continuum mechanics theory, particularly for large-scale problems in three dimensions. This results from the nonlocal nature of the PD theory which leads to interactions of each node of a discretized body with multiple surrounding nodes. Here, we propose a new approach to significantly boost the numerical efficiency of PD models. We propose a discretization scheme that employs a simple collocation procedure and is truly meshfree; i.e., it does not depend on any background integration cells. In contrast to the standard scheme, the proposed scheme requires a much smaller set of neighboring nodes (keeping the same physical length scale) to achieve a specific accuracy and is thus computationally more efficient. Our new scheme is applicable to the case of linear PD models and within neighborhoods where the solution can be approximated by smooth basis functions. Therefore, to fully exploit the advantages of both the standard and the proposed schemes, a hybrid discretization is presented that combines both approaches within an adaptive framework. The high performance of the developed framework is illustrated by several numerical examples, including brittle fracture and corrosion problems in two and three dimensions.
The constitutive modelling of soft biological tissues has rapidly gained attention over the last 20 years. Current constitutive models can describe the mechanical properties of arterial tissue. ...Predicting these properties from microstructural information, however, remains an elusive goal. To address this challenge, we are introducing a novel hybrid modelling framework that combines advanced theoretical concepts with deep learning. It uses data from mechanical tests, histological analysis and images from second-harmonic generation. In this first proof of concept study, our hybrid modelling framework is trained with data from 27 tissue samples only. Even such a small amount of data is sufficient to be able to predict the stress–stretch curves of tissue samples with a median coefficient of determination of
R
2
= 0.97 from microstructural information, as long as one limits the scope to tissue samples whose mechanical properties remain in the range commonly encountered. This finding suggests that deep learning could have a transformative impact on the way we model the constitutive properties of soft biological tissues.
Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate ...absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.
A novel numerical formulation for solving fluid–structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the ...structural field using the finite element method (FEM). As compared to fully mesh- or grid-based FSI frameworks, due to the Lagrangian nature of SPH this framework can be easily extended to account for more complex fluids consisting of multiple phases and dynamic phase transitions. Moreover, this approach facilitates the handling of large deformations of the fluid domain respectively the fluid–structure interface without additional methodological and computational efforts. In particular, to achieve an accurate representation of interaction forces between fluid particles and structural elements also for strongly curved interface geometries, the novel sliding boundary particle approach is proposed to ensure full support of SPH particles close to the interface. The coupling of the fluid and the structural field is based on a Dirichlet–Neumann partitioned approach, where the fluid field is the Dirichlet partition with prescribed interface displacements and the structural field is the Neumann partition subject to interface forces. To overcome instabilities inherent to weakly coupled schemes an iterative fixed-point coupling scheme is employed. Several numerical examples in form of well-known benchmark tests are considered to validate the accuracy, stability, and robustness of the proposed formulation. Finally, the filling process of a highly flexible thin-walled balloon-like container is studied, representing a model problem close to potential application scenarios of the proposed scheme in the field of biomechanics.
•Smoothed particle hydrodynamics and finite element coupling scheme.•Sliding boundary particle approach for accurate representation of interface forces.•Capable of strongly curved and deformable interface geometries.•Iterative fixed-point coupling following a Dirichlet–Neumann partitioned approach.
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Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by ...factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy (R2=0.92) the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein.
Peridynamic (PD) models are commonly implemented by exploiting a particle-based method referred to as
standard
scheme. Compared to numerical methods based on classical theories (e.g., the finite ...element method), PD models using the meshfree standard scheme are typically computationally more expensive mainly for two reasons. First, the nonlocal nature of PD requires advanced quadrature schemes. Second, non-uniform discretizations of the standard scheme are inaccurate and thus typically avoided. Hence, very fine uniform discretizations are applied in the whole domain even in cases where a fine resolution is per se required only in a small part of it (e.g., close to discontinuities and interfaces). In the present study, a new framework is devised to enhance the computational performance of PD models substantially. It applies the standard scheme only to localized regions where discontinuities and interfaces emerge, and a less demanding quadrature scheme to the rest of the domain. Moreover, it uses a multi-grid approach with a fine grid spacing only in critical regions. Because these regions are identified dynamically over time, our framework is referred to as
multi-adaptive
. The performance of the proposed approach is examined by means of two
real-world
problems, the Kalthoff–Winkler experiment and the bio-degradation of a magnesium-based bone implant screw. It is demonstrated that our novel framework can vastly reduce the computational cost (for given accuracy requirements) compared to a simple application of the standard scheme.
Intermetallic γ(TiAl)-based alloys find their application as high-temperature materials for aero engine and automotive components. Microstructure optimization and microalloying play key roles in ...optimizing these alloys. Several pioneering experimental works showed improved mechanical properties of γ(TiAl)-based alloys containing Niobium (Nb). Despite Nb being a key alloying element, its contribution remains debated, if not least understood, due to the TiAl microstructure's complexity with hierarchical interfaces. This work examines the effects of Nb on the high-temperature deformation behavior of TiAl alloys using atomistic simulations. These revealed that Nb alloying retarded the stress-induced phase transformation of γ → α2, favoring a refined microstructure with the dislocation sources from microstructure boundaries and interfaces at high temperature and improving thus the ductility. Our microstructure-informed atomistic models reveal a comprehensive picture of the underlying nanomechanical events.
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