GAMM Mitteilungen最新文献

{"title":"Recent topics in biomechanics and mechanobiology","authors":"Alexander E. Ehret, Markus Böl","doi":"10.1002/gamm.201900017","DOIUrl":"10.1002/gamm.201900017","url":null,"abstract":"Biomechanics may be seen as an independent discipline of research with its own methods, approaches, and a very long history—questions related to the functioning of living matter have preoccupied philosophers and scientists for millennia, in fact. Notwithstanding, it was continuously advanced by the theories and techniques established for classical engineering materials. Both the specific developments and those adopted and adapted from other mechanical disciplines render biomechanics a continuously evolving field until today. The progress in biomechanical research also profits from the advances in other fields, including instrumentation and techniques for experimental analyses and, in the recent decades, particularly computational science. The new insights gained from experiments serve to continuously refine models and to reconsider problems. The available computational power allows the inclusion of the increasing amount and detail of information in models of ever-growing complexity. In about the last two decades mechanobiology has emerged as an independent discipline, yet complementary to biomechanics in many aspects. Unravelling the relations between mechanical loads and the cells' biological response requires a deep understanding of cell and tissue biology, and thus represents a multidisciplinary task. Accordingly, the corresponding model formulations need to couple the mechanical field quantities with those of other physical disciplines and with the kinetics of biochemical reactions to integrate mechanics in the complex pathways of biological systems. Evidently, such deep understanding of the mechanobiological processes may help shedding light on dysfunctions and pathological situations, and also biomechanical research has incessantly been driven by medical questions from its infancy until today. Both biomechanics and mechanobiology, but in particular the joint disciplines can therefore be considered as life sciences able to face more and more detailed research problems. Concomitant with the emerging complex questions are changes in the research strategies from general to specific aspects, from singleto multiscale approaches, from monoto multiphysics problems, and from isolated problem considerations to systems approaches. With the issues 3 and 4 of this volume of the GAMM-Mitteilungen, we are very glad to present seven contributions that reflect these recent trends and their advances in biomechanics and mechanobiology. Issue 3 contains three overview-oriented articles: the article by S. Brandstaeter, S. L. Fuchs, R. C. Aydin, and C. J. Cyron presents stomach biomechanics as an emerging topic and highlights challenges. The work by M. K. Rausch, M. Mathur, and W. D. Meador gives deep insight into the biomechanics of the tricuspid annulus under healthy, diseased and repaired conditions. S. Schmitt, M. Günther, and D. F. B. Häufle in their article provide a new view on muscle models as biophysical systems. Issue 4 is dedicated to specific modelin","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"42 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.201900017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77037365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three-field mixed finite element formulations for gradient elasticity at finite strains","authors":"Johannes Riesselmann,&nbsp;Jonas Wilhelm Ketteler,&nbsp;Mira Schedensack,&nbsp;Daniel Balzani","doi":"10.1002/gamm.202000002","DOIUrl":"10.1002/gamm.202000002","url":null,"abstract":"<p>Gradient elasticity formulations have the advantage of avoiding geometry-induced singularities and corresponding mesh dependent finite element solution as apparent in classical elasticity formulations. Moreover, through the gradient enrichment the modeling of a scale-dependent constitutive behavior becomes possible. In order to remain <i>C</i>⁰ continuity, three-field mixed formulations can be used. Since so far in the literature these only appear in the small strain framework, in this contribution formulations within the general finite strain hyperelastic setting are investigated. In addition to that, an investigation of the inf sup condition is conducted and unveils a lack of existence of a stable solution with respect to the <i>L</i>²-<i>H</i>¹-setting of the continuous formulation independent of the constitutive model. To investigate this further, various discretizations are analyzed and tested in numerical experiments. For several approximation spaces, which at first glance seem to be natural choices, further stability issues are uncovered. For some discretizations however, numerical experiments in the finite strain setting show convergence to the correct solution despite the stability issues of the continuous formulation. This gives motivation for further investigation of this circumstance in future research. Supplementary numerical results unveil the ability to avoid singularities, which would appear with classical elasticity formulations.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82711635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A diffuse modeling approach for embedded interfaces in linear elasticity","authors":"Paul Hennig,&nbsp;Roland Maier,&nbsp;Daniel Peterseim,&nbsp;Dominik Schillinger,&nbsp;Barbara Verfürth,&nbsp;Markus Kästner","doi":"10.1002/gamm.202000001","DOIUrl":"10.1002/gamm.202000001","url":null,"abstract":"<p>In this contribution, we present a diffuse modeling approach to embed material interfaces into nonconforming meshes with a focus on linear elasticity. For this purpose, a regularized indicator function is employed that describes the distribution of the different materials by a scalar value. The material in the resulting diffuse interface region is redefined in terms of this indicator function and recomputed by a homogenization of the adjacent material parameters. The applied homogenization method fulfills the kinematic compatibility across the interface and the static equilibrium at the interface. In addition, an <i>hℓ</i>-adaptive refinement strategy based on truncated hierarchical B-spline is applied to provide an appropriate and efficient approximation of the diffuse interface region. We justify mathematically and demonstrate numerically that the applied approach leads to optimal convergence rates in the far field for one-dimensional problems. A two-dimensional example illustrates that the application of the <i>hℓ</i>-adaptive refinement strategy allows for a clear reduction of the error in the near and far field and a good resolution of the local stress and strain fields at the interface. The use of a higher continuous B-spline basis leads to efficient computations due to the higher continuity of the diffuse interface model.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86833375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spline- and hp-basis functions of higher differentiability in the finite cell method","authors":"Stefan Kollmannsberger,&nbsp;Davide D'Angella,&nbsp;Ernst Rank,&nbsp;Wadhah Garhuom,&nbsp;Simeon Hubrich,&nbsp;Alexander Düster,&nbsp;Paolo Di Stolfo,&nbsp;Andreas Schröder","doi":"10.1002/gamm.202000004","DOIUrl":"10.1002/gamm.202000004","url":null,"abstract":"<p>In this paper, the use of <i>hp</i>-basis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, <i>C</i>^<i>k</i> <i>hp</i>-basis functions based on classical B-splines and a new approach for the construction of <i>C</i>¹ <i>hp</i>-basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new <i>C</i>¹ approach also includes varying polynomial degrees. The properties of the <i>hp</i>-basis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the <i>C</i>^<i>k</i> <i>hp</i>-basis functions based on B-splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85125455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A detailed investigation of the model influencing parameters of the phase-field fracture approach","authors":"Carola Bilgen,&nbsp;Alena Kopaničáková,&nbsp;Rolf Krause,&nbsp;Kerstin Weinberg","doi":"10.1002/gamm.202000005","DOIUrl":"10.1002/gamm.202000005","url":null,"abstract":"<p>Phase-field approaches to fracture are gaining popularity to compute a priori unknown crack paths. In this work the sensitivity of such phase-field approaches with respect to its model specific parameters, that is, the critical length of regularization, the degradation function and the mobility, is investigated. The susceptibility of the computed cracks to the setting of these parameters is studied for problems of linear and finite elasticity. Furthermore, the convergence properties of different solution strategies are analyzed. Monolithic and staggered solution schemes for the solution of the arising nonlinear discrete systems are studied in detail. To conclude, we demonstrate the versatility of the phase-field fracture approach in a real-world problem by comparing different simulations of conchoidal fracture using structured and unstructured meshes.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73690733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator","authors":"K. Mang,&nbsp;M. Walloth,&nbsp;T. Wick,&nbsp;W. Wollner","doi":"10.1002/gamm.202000003","DOIUrl":"10.1002/gamm.202000003","url":null,"abstract":"<p>In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing the fracture irreversibility constraint. The key goal is the development of a reliable and efficient residual-type error estimator for the phase-field fracture model in each time-step. Based on this error estimator, error indicators for local mesh adaptivity are extracted. The proposed estimator is based on a technique known for singularly perturbed equations in combination with estimators for variational inequalities. These theoretical developments are used to formulate an adaptive mesh refinement algorithm. For the numerical solution, the fracture irreversibility is imposed using a Lagrange multiplier. The resulting saddle-point system has three unknowns: displacements, phase-field, and a Lagrange multiplier for the crack irreversibility. Several numerical experiments demonstrate our theoretical findings with the newly developed estimators and the corresponding refinement strategy.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81652308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On computational approaches of liver lobule function and perfusion simulation","authors":"Tim Ricken,&nbsp;Lena Lambers","doi":"10.1002/gamm.201900016","DOIUrl":"10.1002/gamm.201900016","url":null,"abstract":"<p>In recent years computational models have become more important for simulating hepatic processes and investigating liver diseases in silico and so various liver models have been published. The complex behavior of biological tissue with its hierarchical structure as well as the blood perfusion through the organ have been described using different approaches and numerical techniques. This paper shows and compares numerical approaches for function and perfusion simulation recently published and compares them with a multiscale function-perfusion model using the extended theory of porous media. We focus on the description of blood perfusion and liver tissue, but also on the simulation of liver diseases or the zonation of processes in the liver. Furthermore, the selected geometry is taken into account.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"42 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.201900016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74666097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A study of growth and remodeling in isotropic tissues, based on the Anand-Aslan-Chester theory of strain-gradient plasticity","authors":"Alfio Grillo,&nbsp;Salvatore Di Stefano,&nbsp;Ariel Ramírez-Torres,&nbsp;Michele Loverre","doi":"10.1002/gamm.201900015","DOIUrl":"10.1002/gamm.201900015","url":null,"abstract":"<p>Motivated by the increasing interest of the biomechanical community towards the employment of strain-gradient theories for solving biological problems, we study the growth and remodeling of a biological tissue on the basis of a strain-gradient formulation of remodeling. Our scope is to evaluate the impact of such an approach on the principal physical quantities that determine the growth of the tissue. For our purposes, we assume that remodeling is characterized by a coarse and a fine length scale and, taking inspiration from a work by Anand, Aslan, and Chester, we introduce a kinematic variable that resolves the fine scale inhomogeneities induced by remodeling. With respect to this variable, a strain-gradient framework of remodeling is developed. We adopt this formulation in order to investigate how a tumor tissue grows <i>and</i> how it remodels <i>in response</i> to growth. In particular, we focus on a type of remodeling that manifests itself in two different, but complementary, ways: on the one hand, it finds its expression in a stress-induced reorganization of the adhesion bonds among the tumor cells, and, on the other hand, it leads to a change of shape of the cells and of the tissue, which is generally not recovered when external loads are removed. To address this situation, we resort to a generalized Bilby-Kröner-Lee decomposition of the deformation gradient tensor. We test our model on a benchmark problem taken from the literature, which we rephrase in two ways: microscale remodeling is disregarded in the first case, and accounted for in the second one. Finally, we compare and discuss the obtained numerical results.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"42 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.201900015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84907268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The dynamics of the skeletal muscle: A systems biophysics perspective on muscle modeling with the focus on Hill-type muscle models","authors":"Syn Schmitt,&nbsp;Michael Günther,&nbsp;Daniel F. B. Häufle","doi":"10.1002/gamm.201900013","DOIUrl":"10.1002/gamm.201900013","url":null,"abstract":"<p>Skeletal muscle is one of the most fascinating and crucial ingredients of motion generation in nature. Since the beginning of science, people dedicate their life as researchers to enhance knowledge about this biological motor. Thus, the scientific knowledge about the skeletal muscle is overwhelmingly broad and detailed. This contribution collects knowledge about the active and passive dynamics of skeletal muscle. Furthermore, it highlights a special perspective in which not only the muscle itself, but also the role muscles play in the interaction with other structures is studied. The first section introduces this systems biophysics perspective, which clusters the investigation of the relations, interactions and dependencies between muscles and the other structures in the movement apparatus. In the second section, the muscles are considered in more detail by describing three approaches to muscle modeling. The third section deals with recent advances based on Hill-type models, such as, for example, the integration of mass.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"42 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.201900013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77993408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalized inelastic modeling concept for soft fibrous tissues","authors":"Markus Hillgärtner,&nbsp;Kevin Linka,&nbsp;Mikhail Itskov","doi":"10.1002/gamm.201900014","DOIUrl":"10.1002/gamm.201900014","url":null,"abstract":"<p>This contribution proposes a multiscale modeling approach, ranging from the macromolecular behavior of tropocollagen over collagen fibrils and the interfibrillar matrix up to bundles of collagen fibers. Two damage mechanisms are described: intramolecular damage inside the tropocollagen molecules based on a permanent opening of the triple helical conformation and damage in the interfibrillar matrix restricting the recovery of interfibrillar sliding. Both intramolecular and interfibrillar damage is considered as a probabilistic process based on detachment of adhesive bonds, where the probability of failure depends on the full load history of the bond. The presented modeling concept is based on generalized assumptions valid for most soft fibrous tissues, and can therefore be applied for a variety of tissues and load-cases. The final constitutive equations are validated against recent experimental data from uniaxial tension tests of rat tail tendon. All utilized material constants have a clear physical interpretation.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"42 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.201900014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83983642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}