Dynamic fracture mechanics

A variational free-discontinuity formulation of brittle fracture was given by Francfortand Marigo [1], where the total energy is minimized with respect to the crackgeometry and the displacement field simultaneously. The entire evolution of cracksincluding their initiation and branching is determined by this minimization principlerequiring no further criterion. However, a direct numerical discretization of themodel faces considerable difficulties as the displacement field is discontinuous inthe presence of cracks.

A Continuum Phase Field Model for Fracture

Thank you very much for downloading mathematical foundations of elasticity. As you may know, people have search numerous times for their favorite books like this mathematical foundations of elasticity, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their laptop. mathematical foundations of elasticity is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the mathematical foundations of elasticity is universally compatible with any devices to read.

Mathematical Foundations Of Elasticity

Crack initiation in brittle materials is not covered by classical fracture mechanics that deals only with the growth of pre-existing cracks. In order to overcome this deficiency, the Finite Fracture Mechanics concept assumes the instantaneous formation of cracks of finite size at initiation. Within this framework, a coupled criterion was proposed at the beginning of the 2000’s requiring two necessary conditions to be fulfilled simultaneously. The first one compares the tensile stress to the tensile strength, while the other uses an energy balance and the material toughness. The present analysis is restricted to the 2D case, and, through a wide list of references, it is shown that this criterion gives predictions in agreement with experiments in various cases of stress concentration, which can be classified in two categories: the singularities, i.e. indefinitely growing stresses at a point, and the non-singular stress raisers. It is applied to different materials and structures: notched specimens, laminates, adhesive joints or embedded inclusions. Of course, a lot of work remains to do in these domains but also in domains that are almost not explored such as fatigue loadings and dynamic loadings as well as a sound 3D extension. Some ideas in these directions are issued before concluding that FFM and the coupled criterion have filled a gap in fracture mechanics.

A review of Finite Fracture Mechanics: crack initiation at singular and non-singular stress raisers

Abstract The paper summarizes recent efforts in formulating an elastic-plastic-fracture model for the finite-element analysis of concrete structures. Based on the geometrical considerations, a four-parameter fracture (or yielding) criterion was proposed which embraces some of the simpler existing models. Isotropic elastic and anisotropic elastic behaviors were proposed for the initial loading and the post-failure behaviors. A plastic model displaying mixed hardening was proposed to describe material behaviors between the initial yielding and the fracture failure. Incremental stress-strain relationships were derived based on the associated flow rule and Ziegler's kinematic hardening rule. Three different types of failure modes were considered. A simple crushing coefficient was defined based on a dual criterion to identify the crushing type, the cracking type and the mixed type of failure. Material parameters required for each element of the plastic-fracture model were determined. An important feature of the paper is that matrix formulations for all the constitutive equations were derived and are available for finite-element implementations.

A Plastic-Fracture Model for Concrete

Asymmetric crack onset at open-holes under tensile and in-plane bending loading

In recent years, functionally graded adhesives (FGAs) have been developed and successfully applied with the objective to reduce the stress concentrations occurring in bonded joints and to exploit their full lightweight design potential. The present work provides a computational framework based on a general predictive analytical model for FGA joints with composite adherends under mechanical and thermal loading embedded in an optimization procedure. In this way, an optimal homogenization of the adhesive stresses using FGAs is achieved. The proposed analysis approach follows the idea of general sandwich-type analyses and is thus applicable to various adhesive joint configurations as e.g. single lap joints, L-joints, T-joints, reinforcement patches and even balanced double lap joints. For the case of homogeneous adhesives, closed-form analytical solutions are presented and compared to existing solutions in literature. The predicted adhesive stress distributions of several FGA joint configurations are studied and compared to numerical results of finite element analyses where a good agreement is obtained. Moreover, a comprehensive study regarding the optimized functional grading for two particular joint configurations is performed and discussed. The corresponding grading functions are obtained solving an underlying optimization problem that minimizes a predefined objective function characterized by an equivalent stress quantity.

Homogenization of mechanical and thermal stresses in functionally graded adhesive joints

Equivalent strain failure criterion for multiaxially loaded incompressible hyperelastic elastomers

Nonlinear elastic finite fracture mechanics: Modeling mixed-mode crack nucleation in structural glazing silicone sealants

. Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak-layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this two-part work we propose a novel closed-form analytical model for a snowpack under skier loading and a mixed-mode failure criterion for the nucleation of weak-layer failure. In the first part of this two-part series we introduce a closed-form analytical model of a snowpack accounting for the deformable layer. Despite the importance of persistent weak layers for slab avalanche release, no simple analytical model considering weak-layer deformations is available. The proposed model provides deformations of the snow slab, weak-layer stresses and energy release rates of cracks within the weak layer. It generally applies to skier-loaded slopes as well as stability tests such as the propagation saw test. A validation with a numerical reference model shows very good agreement of the stress and energy release rate results in several parametric studies including analyses of the bridging effect and slope angle dependence. The proposed model is used to analyze 93 propagation saw tests. Computed weak-layer fracture toughness values are physically meaningful and in excellent agreement with finite element analyses. In the second part of the series ( Rosendahl and Weisgraeber ,  2020 ) we make use of the present mechanical model to establish a novel failure criterion crack nucleation in weak layers.
The code used for the analyses in both parts is publicly available under https://github.com/2phi/weac (last access: 6 January 2020) ( 2phi ,  2020 ) .

/pdf/modeling-snow-slab-avalanches-caused-by-weak-layer-failure-38e0542qct.pdf

Philipp Laurens Rosendahl

Papers

Asymmetric crack onset at open-holes under tensile and in-plane bending loading

Homogenization of mechanical and thermal stresses in functionally graded adhesive joints

Equivalent strain failure criterion for multiaxially loaded incompressible hyperelastic elastomers

Nonlinear elastic finite fracture mechanics: Modeling mixed-mode crack nucleation in structural glazing silicone sealants

Modeling snow slab avalanches caused by weak-layer failure – Part 1: Slabs on compliant and collapsible weak layers