A micromorphic continuum formulation for finite strain inelasticity

This work proposes a generalized theory of deformation which can capture scale effects also in a homogenously deforming body. Scale effects are relevant for small structures but also when it comes to high strain concentrations as in the case of localised shear bands or at crack tips, etc. In this context, so-called generalized continuum formulations have been proven to provide remedy as they allow for the incorporation of internal length-scale parameters which reflect the micro-structural influence on the macroscopic material response. Here, we want to adopt a generalized continuum framework which is based on the mathematical description of a combined macro- and micro-space [8]. The approach introduces additional degrees of freedom which constitute a so-called micromorphic deformation. First the treatment presented is general in nature but will be specified for the sake of an example and the number of extra degrees of freedom will be reduced to four. Based on the generalized deformation description new strain and stress measures are defined which lead to the formulation of a corresponding generalized variational principle. Of great advantage is the fact that the constitutive law is defined in the generalized space but can be classical otherwise. This limits the number of the extra material parameters necessary to those needed for the specification of the micro-space, in the example presented to only one

Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other

Modeling intracranial aneurysm stability and growth: An integrative mechanobiological framework for clinical cases

We present a novel patient-specific fluid-solid-growth framework to model the mechanobiological state of clinically detected intracranial aneurysms (IAs) and their evolution. The artery and IA sac are modeled as thick-walled, non-linear elastic fiber-reinforced composites. We represent the undulation distribution of collagen fibers: the adventitia of the healthy artery is modeled as a protective sheath whereas the aneurysm sac is modeled to bear load within physiological range of pressures. Initially, we assume the detected IA is stable and then consider two flow-related mechanisms to drive enlargement: (1) low wall shear stress; (2) dysfunctional endothelium which is associated with regions of high oscillatory flow. Localized collagen degradation and remodelling gives rise to formation of secondary blebs on the aneurysm dome. Restabilization of blebs is achieved by remodelling of the homeostatic collagen fiber stretch distribution. This integrative mechanobiological modelling workflow provides a step towards a personalized risk-assessment and treatment of clinically detected IAs

A unified concept of elastic-viscoplastic Cosserat and micromorphic continua

The paper is concerned with a unified formulation and treatment of Cosserat, micromorphic, and more general continua. First the classical understanding of Cosserat and micromorphic continua is reviewed and critically examined. It is shown that the strain measures of the micromorphic continuum as suggested by Eringen and co-workers do exihibit shortcomings which become evident when discussing the Euler-Lagrange equations of a corresponding action. Assuming that invariance of the strain measures should be required with respect to the group SO(3) alone and not to that of GL+ (3), new strain measures of the micromorphic continuum and corresponding field equations are derived. A new unified understanding of Cosserat and micromorphic continua is propagated which views the rotation field in case of the Cosserat continuum as a first approximation of a generalized displacement field. The unified treatment allows for a straightforward formulation of finite strain viscoplasticity of such continua. The formulation is based on a multiplicative decomposition of the micro stretch tensor. Furthermore it allows for the application of constitutive laws of the unified type generally formulated for classical continua