Elastica-based strain energy functions for soft biological tissue

Continuum strain energy functions are developed for soft biological tissues that possess long fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to obtain a continuum strain energy function. Notably, we avoid solving the full fourth-order, nonlinear, partial differential equation for the elastica by resorting to other assumptions, kinematic and energetic, on the response of the individual, elastica-like fibrils.Comment: To appear in J. Mech. Phys. Solid

Comparison of Two Bulk Energy Approaches for the Phasefield Modeling of Two-variant Martensitic Laminate Microstructure

The unusual thermomechanical properties of shape memory alloys are closely connected to the formation and evolution of their microstructure. At lower temperatures, shape memory alloys typically consists of martensitic laminates with coherent twin boundaries. We propose a large strain phasefield model for the formation and dissipative evolution of such two-variant martensitic twinned laminate microstructures. Our model accounts for the coherence-dependence of the interface energy density and contains a Ginzburg-Landau type evolution equation. We introduce two conceptually different modeling approaches for the regularized bulk energy, i.e. external and internal mixing. We construct a suitable gradient-extended incremental variational framework for the proposed formulation and discretize it by use of finte elements. Finally, we demonstrate the modeling capabilities of our formulation by means of two-dimensional finite element simulations of laminate formation in two-phasic martensitic CuAlNi and compare the energetic modeling properties of the two proposed bulk energy approaches

Quasi-rigidity: some uniqueness issues

Quasi-rigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasi-rigidity a complete theory for these granular assemblies? Does it provide unique predictions of the assembly's behavior, or must some other process be invoked to decide between several possibilities? We provide evidence that quasi-rigidity is a complete theory by showing that two possible sources of indeterminacy do not exist for the case of disk shaped grains. One possible source of indeterminacy arises from zero-frequency modes present in the packing. This problem can be solved by considering the conditions required to obtain force equilibrium. A second possible source of indeterminacy is the necessity to choose the status (sliding or non-sliding) at each contact. We show that only one choice is permitted, if contacts slide only when required by Coulomb friction.Comment: 14 pages, 3 figures, submitted to Phys Rev E (introduction and conclusion revised

CR-EST: a resource for crop ESTs

The crop expressed sequence tag database, CR-EST (http://pgrc.ipk-gatersleben.de/cr-est/), is a publicly available online resource providing access to sequence, classification, clustering and annotation data of crop EST projects. CR-EST currently holds more than 200 000 sequences derived from 41 cDNA libraries of four species: barley, wheat, pea and potato. The barley section comprises approximately one-third of all publicly available ESTs. CR-EST deploys an automatic EST preparation pipeline that includes the identification of chimeric clones in order to transparently display the data quality. Sequences are clustered in species-specific projects to currently generate a non-redundant set of ∼22 600 consensus sequences and ∼17 200 singletons, which form the basis of the provided set of unigenes. A web application allows the user to compute BLAST alignments of query sequences against the CR-EST database, query data from Gene Ontology and metabolic pathway annotations and query sequence similarities from stored BLAST results. CR-EST also features interactive JAVA-based tools, allowing the visualization of open reading frames and the explorative analysis of Gene Ontology mappings applied to ESTs

Phase-field models for brittle and cohesive fracture

In this paper we first recapitulate some basic notions of brittle and cohesive fracture models, as well as the phase-field approximation to fracture. Next, a critical assessment is made of the sensitivity of the phase-field approach to brittle fracture, in particular the degradation function, and the use of monolithic versus partitioned solution schemes. The last part of the paper makes extensions to a recently developed phase-field model for cohesive fracture, in particular for propagating cracks. Using some simple examples the current state of the cohesive phase-field model is shown

A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials - Application to Uniaxial Cyclic Response of Concrete

In complex materials, numerous intertwined phenomena underlie the overall response at macroscale. These phenomena can pertain to different engineering fields (mechanical , chemical, electrical), occur at different scales, can appear as uncertain, and are nonlinear. Interacting with complex materials thus calls for developing nonlinear computational approaches where multi-scale techniques that grasp key phenomena at the relevant scale need to be mingled with stochastic methods accounting for uncertainties. In this chapter, we develop such a computational approach for modeling the mechanical response of a representative volume of concrete in uniaxial cyclic loading. A mesoscale is defined such that it represents an equivalent heterogeneous medium: nonlinear local response is modeled in the framework of Thermodynamics with Internal Variables; spatial variability of the local response is represented by correlated random vector fields generated with the Spectral Representation Method. Macroscale response is recovered through standard ho-mogenization procedure from Micromechanics and shows salient features of the uniaxial cyclic response of concrete that are not explicitly modeled at mesoscale.Comment: Computational Methods for Solids and Fluids, 41, Springer International Publishing, pp.123-160, 2016, Computational Methods in Applied Sciences, 978-3-319-27994-

A framework for polyconvex large strain phase-field methods to fracture

Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy-Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn-Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu-Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials

Long-term fire resilience of the Ericaceous Belt, Bale Mountains, Ethiopia

Fire is the most frequent disturbance in the Ericaceous Belt (ca 3000- 4300 m.a.s.l.), one of the most important plant communities of tropical African mountains. Through resprouting after fire, Erica establishes a positive fire feedback under certain burning regimes. However, present-day human activity in the Bale Mountains of Ethiopia includes fire and grazing systems that may have a negative impact on the resilience of the ericaceous ecosystem. Current knowledge of Erica-fire relationships is based on studies of modern vegetation, lacking a longer time perspective that can shed light on baseline conditions for the fire feedback. We hypothesize that fire has influenced Erica communities in the Bale Mountains at millennial timescales. To test this, we (1) identify the fire history of the Bale Mountains through a pollen and charcoal record from Garba Guracha, a lake at 3950 m.a.s.l., and (2) describe the long-term bidirectional feedback between wildfire and Erica, which may control the ecosystem's resilience. Our results support fire occurrence in the area since ca 14 000 years ago, with particularly intense burning during the early Holocene, 10.8-6.0 cal ka BP. We show that a positive feedback between Erica abundance and fire occurrence was in operation throughout the Lateglacial and Holocene, and interpret the Ericaceous Belt of the Ethiopian mountains as a long-term fire resilient ecosystem. We propose that controlled burning should be an integral part of landscape management in the Bale Mountains National Park