scholarly journals The relationship between viscoelasticity and elasticity

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200419
Author(s):  
J. H. Snoeijer ◽  
A. Pandey ◽  
M. A. Herrada ◽  
J. Eggers
Keyword(s):  
Soft Matter ◽  
Solid Mechanics ◽  
Large Deformations ◽  
Broad Class ◽  
Elastic Solid ◽  
Soft Materials ◽  
Elastic Response ◽  
Lagrangian Description ◽  
Elastic Stresses ◽  
The Relationship

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ , over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ  → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.

scholarly journals Effect of surface bending and stress on the transmission of line force to an elastic substrate

2018 ◽  
Vol 474 (2215) ◽  
pp. 20170775 ◽  
Author(s):  
Chung Yuen Hui ◽  
Zezhou Liu ◽  
Anand Jagota
Keyword(s):  
Elastic Modulus ◽  
Surface Stress ◽  
Broad Class ◽  
Local Stress ◽  
Soft Materials ◽  
Elastic Substrate ◽  
Capillary Length ◽  
Singular Stress ◽  
Line Load ◽  
Line Force

For a broad class of soft materials their surface stress can strongly influence mechanical behaviour. For example, a line force applied to the surface of an elastic substrate is locally supported by surface stress over an elasto-capillary length l c (surface stress/elastic modulus). Surface stress regularizes the otherwise highly singular stress and strain fields. However, surface such as lipid bilayer interfaces can also resist deformation by bending. This has not been studied either by experiments or theories. We analyse a theoretical model of the response of a half-space to a line force when the surface carries both a stress and resistance to bending. We find that surface bending further regularizes the singular fields. The local stress field near the line load can be separated into three regions. Region 1 occupies distances from the line load smaller than an elasto-capillary bending length l b (bending stiffness/elastic modulus to the 1/3 power) where surface bending dominates and the elastic stress and strains are continuous. Region 2 occupies intermediate distances between l b and l c   ( > l b ) where surface stress dominates. At distances larger than l c we retrieve the classical elasticity solution. The size of region 2 depends on κ = l c / l b and vanishes for small l c .

scholarly journals A fast and efficient MATLAB-based MPM solver: fMPMM-solver v1.1

2020 ◽  
Vol 13 (12) ◽  
pp. 6265-6284
Author(s):  
Emmanuel Wyser ◽  
Yury Alkhimenkov ◽  
Michel Jaboyedoff ◽  
Yury Y. Podladchikov
Keyword(s):  
Cantilever Beam ◽  
Large Scale ◽  
Solid Mechanics ◽  
Large Deformations ◽  
Material Point ◽  
Snow Avalanches ◽  
High Level Language ◽  
Numerical Accuracy ◽  
Computational Performance ◽  
High Level

Abstract. We present an efficient MATLAB-based implementation of the material point method (MPM) and its most recent variants. MPM has gained popularity over the last decade, especially for problems in solid mechanics in which large deformations are involved, such as cantilever beam problems, granular collapses and even large-scale snow avalanches. Although its numerical accuracy is lower than that of the widely accepted finite element method (FEM), MPM has proven useful for overcoming some of the limitations of FEM, such as excessive mesh distortions. We demonstrate that MATLAB is an efficient high-level language for MPM implementations that solve elasto-dynamic and elasto-plastic problems. We accelerate the MATLAB-based implementation of the MPM method by using the numerical techniques recently developed for FEM optimization in MATLAB. These techniques include vectorization, the use of native MATLAB functions and the maintenance of optimal RAM-to-cache communication, among others. We validate our in-house code with classical MPM benchmarks including (i) the elastic collapse of a column under its own weight; (ii) the elastic cantilever beam problem; and (iii) existing experimental and numerical results, i.e. granular collapses and slumping mechanics respectively. We report an improvement in performance by a factor of 28 for a vectorized code compared with a classical iterative version. The computational performance of the solver is at least 2.8 times greater than those of previously reported MPM implementations in Julia under a similar computational architecture.

Method for Obtaining Light Curing Printing Condition Based on New Theoretical Description

2020 ◽  
Author(s):  
Yang Li ◽  
Jun Yin
Keyword(s):  
Tissue Engineering ◽  
High Speed ◽  
Soft Materials ◽  
Theoretical Description ◽  
Gel Point ◽  
Digital Light Processing ◽  
Light Curing ◽  
The Relationship ◽  
Physical Quantities ◽  
Printing Method

Abstract Digital light processing (DLP) is widely used in tissue engineering in recent years. High resolution and high speed are the advantages of this printing method. The method of determining DLP process printing conditions by forming experiments is restricted by the formability of the material and it is difficult to apply to soft materials and materials that are not easily formed. In this study, through theoretical analysis that the concept of absorbances and gel point is introduced into the relationship between exposure time and forming thickness. This allows the forming conditions to be obtained by measurement of only physical quantities related to the nature of the material itself rather than through forming experiments. Which facilitates high-precision DLP printing of biomaterials.

1. The science of softness

2020 ◽  
pp. 1-18
Author(s):  
Tom McLeish
Keyword(s):  
Scientific Community ◽  
Soft Matter ◽  
Soft Materials ◽  
Visionary Leadership ◽  
Slow Dynamics ◽  
Length Scales ◽  
New Science ◽  
Motion Structure

‘The science of softness’ provides a brief history and overview of soft matter science. The development of soft matter science was propelled by a combination of communication within the scientific community; intrinsic conceptual overlap and commonality; and visionary leadership from a small number of pioneering scientists. Chemistry proved as essential an ingredient to the new science of soft matter as ideas and techniques from physics. The characteristics of soft matter include motion; structure on intermediate length scales; slow dynamics; and universality. Microscopy is the most obvious and direct example of experimental tools applied across the gamut of soft materials.

Study on the Relationship Between Interaction Factors and Stress Intensity Factor for Elliptical Flaws

2017 ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Elastic Solid ◽  
Element Analysis ◽  
Linear Elastic ◽  
Close Proximity ◽  
Interaction Factors ◽  
The Relationship

The interaction of multiple flaws in close proximity to one another may increase the stress intensity factor of the flaw in structures and components. This interaction effect is not distributed uniformly along the crack front. For instance, the strongest interaction is generally observed at the point closest to a neighboring flaw. For this reason, the closest point could show a higher value of the stress intensity factor than all other points in some cases, even if the original value at the point of the single flaw is relatively low. To clarify the condition when the closest point shows the maximum stress intensity factor, we investigated the interaction of two similar elliptical flaws in an infinite model subjected to remote tension loading. The stress intensity factor of the elliptical flaws was obtained by performing finite element analysis of a linear elastic solid. The results indicated that the interaction factors along the crack front can be expressed by a simple empirical formula. Finally, we show the relationship between geometrical features of the flaw and the stress intensity factor at the closest point to a neighboring flaw.

Cascading failures of interdependent modular small-world networks

2016 ◽  
Vol 30 (18) ◽  
pp. 1650174 ◽  
Author(s):  
Guowei Zhu ◽  
Xianpei Wang ◽  
Meng Tian ◽  
Dangdang Dai ◽  
Jiachuan Long ◽  
...  
Keyword(s):  
Broad Class ◽  
Small World ◽  
Cascading Failure ◽  
Cascading Failures ◽  
Small World Networks ◽  
Connected Component ◽  
Random Coupling ◽  
Global And Local ◽  
The Relationship ◽  
Local Perspectives

Much empirical evidence shows that many real-world networks fall into the broad class of small-world networks and have a modular structure. The modularity has been revealed to have an important effect on cascading failure in isolated networks. However, the corresponding results for interdependent modular small-world networks remain missing. In this paper, we investigate the relationship between cascading failures and the intra-modular rewiring probabilities and inter-modular connections under different coupling preferences, i.e. random coupling with modules (RCWM), assortative coupling in modules (ACIM) and assortative coupling with modules (ACWM). The size of the largest connected component is used to evaluate the robustness from global and local perspectives. Numerical results indicate that increasing intra-modular rewiring probabilities and inter-modular connections can improve the robustness of interdependent modular small-world networks under intra-attacks and inter-attacks. Meanwhile, experiments on three coupling strategies demonstrate that ACIM has a better effect on preventing the cascading failures compared with RCWM and ACWM. These results can be helpful to allocate and optimize the topological structure of interdependent modular small-world networks to improve the robustness of such networks.

Ageing and yield behaviour in model soft colloidal glasses

2009 ◽  
Vol 367 (1909) ◽  
pp. 5051-5071 ◽  
Author(s):  
C. Christopoulou ◽  
G. Petekidis ◽  
B. Erwin ◽  
M. Cloitre ◽  
D. Vlassopoulos
Keyword(s):  
Glassy State ◽  
High Stress ◽  
Elastic Solid ◽  
Elastic Response ◽  
Slow Step ◽  
Recoverable Strain ◽  
Highly Nonlinear ◽  
Yield Behaviour ◽  
Colloidal Glasses ◽  
Stress Dependent

We use multi-arm star polymers as model soft colloids with tuneable interactions and explore their behaviour in the glassy state. In particular, we perform a systematic rheological study with a well-defined protocol and address aspects of ageing and shear melting of star glasses. Ageing proceeds in two distinct steps: a fast step of O (10 3  s) and a slow step of O (10 4  s). We focus on creep and recovery tests, which reveal a rich, albeit complex response. Although the waiting time, the time between pre-shear (rejuvenation) of the glassy sample and measurement, affects the material’s response, it does not play the same role as in other soft glasses. For stresses below the yield value, the creep curve is divided into three regimes with increasing time: viscoplastic, intermediate steady flow (associated with the first ageing step) and long-time evolving elastic solid. This behaviour reflects the interplay between ageing and shear rejuvenation. The yield behaviour, as investigated with the stress-dependent recoverable strain, indicates a highly nonlinear elastic response intermediate between a low-stress Hookean solid and a high-stress viscoelastic liquid, and exemplifies the distinct characteristics of this class of hairy colloids. It appears that a phenomenological classification of different colloidal glasses based on yielding performance may be possible.

Emerging themes in soft matter: responsive and active soft materials

Soft Matter ◽  
2010 ◽  
Vol 6 (4) ◽  
pp. 703 ◽  
Author(s):  
Anna C. Balazs ◽  
Julia M. Yeomans
Keyword(s):  
Soft Matter ◽  
Soft Materials ◽  
Emerging Themes

Microstructural insights into the compressive failure of snow based on a peridynamic framework

2020 ◽  
Author(s):  
Jonas Ritter ◽  
Henning Löwe ◽  
Michael Zaiser
Keyword(s):  
Computed Tomography ◽  
Failure Modes ◽  
Large Deformations ◽  
Failure Mechanisms ◽  
Elastic Response ◽  
Problem Solution ◽  
Compaction Bands ◽  
Modes Of Failure ◽  
Computed Tomography Images ◽  
Non Local

<p>Highly-porous cohesive granular materials such as snow possess complex modes of failure. Apart from classical failure modes, they show microstructural failure and fragmentation associated with densification within a local, narrow zone. Therefore cracks may form and propagate even under compressive load (‘anticracks’,’compaction bands’). Such failure modes are of importance in a range of geophysical contexts. For instance, they may control the release of snow slab avalanches and influence fracturing of porous rock formations. In the snow context, specific failure mechanisms of the ice matrix and their interplay with the microstructure geometry of snow are still poorly understood. Recently, X-ray computed tomography images have provided insights into snow microstructure and capability of directly simulating its elastic response by the finite element method (FEM). However, apart from thermodynamically driven healing processes the inelastic post-peak behaviour of the microstructure is controlled by localized damage, large deformations and internal contacts. As a result of the well-known limitations of FEM to capture these processes we use Peridynamics (PD) as a non-local continuum method to approach the problem. Due to its formulation, (micro)cracks and damage are emergent features of the problem solution that do not need to be known or located in advance. Furthermore, the Lagrangian character of the governing equations makes the method suitable for simulating large deformations. In this contribution we perform confined uniaxial compression simulations of snow microstructures within a peridynamic framework. Computed tomography images of snow specimen serve as a simulation data base. The obtained results show a novel insight into local failure of snow and allow a better comprehension of the underlying failure mechanisms. This study contributes to improve non-local macroscopic constitutive models for snow for future applications.</p>

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