scholarly journals Spatially random modulus and tensile strength: Contribution to variability of strain, damage, and fracture in concrete

2021 ◽  
pp. 105678952110130
Author(s):  
Daniel Castillo ◽  
Tuan HA Nguyen ◽  
Jarkko Niiranen
Keyword(s):  
Tensile Strength ◽  
Damage Model ◽  
Local Strain ◽  
Modeling Methodology ◽  
Damage And Fracture ◽  
Non Local ◽  
Overall Performance ◽  
Spatially Varying ◽  
Force Displacement ◽  
Lower Contribution

This paper explores the computational modeling of nonlocal strain, damage, and fracture in concrete, considering the isolated contribution of two random, spatially variable properties related to the fracture process: Young’s modulus (E) and tensile strength (ft). Applying a continuum damage model, heterogeneous specimens of concrete with random and spatially varying E or ft were found to produce substantial differences when contrasted with traditional homogeneous (non-random) specimens. These differences include variable and uncertain strain and damage, wandering of the failure paths, and differing (sometimes lower) peak forces, i.e. increased probabilities of failure in the heterogeneous specimens. It is found that ft variability contributes more (from 1.7 to up to 4 times more, depending on the parameter) to the overall performance variability of the concrete than E variability, which has a comparatively lower contribution. Performance is evaluated using (1) force-displacement response, (2) individual, average, and standard deviation maps of non-local strain and damage, (3) fracture paths and strain and damage values along the fractures. The modeling methodology is illustrated for two specimen geometries: a square plate with a circular hole, and an L-shaped plate. The computational results correlate well with reported experimental data of fracture in concrete specimens.

scholarly journals A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

Metals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 47
Author(s):  
Jelena Živković ◽  
Vladimir Dunić ◽  
Vladimir Milovanović ◽  
Ana Pavlović ◽  
Miroslav Živković
Keyword(s):  
Phase Field ◽  
Damage Evolution ◽  
Deformation Gradient ◽  
Damage Model ◽  
Steel Structures ◽  
Plasticity Model ◽  
Metal Plasticity ◽  
Damage And Fracture ◽  
Von Mises ◽  
Von Mises Plasticity

Steel structures are designed to operate in an elastic domain, but sometimes plastic strains induce damage and fracture. Besides experimental investigation, a phase-field damage model (PFDM) emerged as a cutting-edge simulation technique for predicting damage evolution. In this paper, a von Mises metal plasticity model is modified and a coupling with PFDM is improved to simulate ductile behavior of metallic materials with or without constant stress plateau after yielding occurs. The proposed improvements are: (1) new coupling variable activated after the critical equivalent plastic strain is reached; (2) two-stage yield function consisting of perfect plasticity and extended Simo-type hardening functions. The uniaxial tension tests are conducted for verification purposes and identifying the material parameters. The staggered iterative scheme, multiplicative decomposition of the deformation gradient, and logarithmic natural strain measure are employed for the implementation into finite element method (FEM) software. The coupling is verified by the ‘one element’ example. The excellent qualitative and quantitative overlapping of the force-displacement response of experimental and simulation results is recorded. The practical significances of the proposed PFDM are a better insight into the simulation of damage evolution in steel structures, and an easy extension of existing the von Mises plasticity model coupled to damage phase-field.

Local and non-local damage model with extended stress decomposition for concrete

2021 ◽  
pp. 105678952199872
Author(s):  
Bilal Ahmed ◽  
George Z Voyiadjis ◽  
Taehyo Park
Keyword(s):  
Shear Stress ◽  
Degrees Of Freedom ◽  
Biaxial Loading ◽  
Damage Model ◽  
Local Model ◽  
Uniaxial Tensile ◽  
Gradient Theory ◽  
Principal Stresses ◽  
Stress Decomposition ◽  
Non Local

In this work, a new damage model for concrete is proposed with an extension of the stress decomposition (limited to biaxial cases), to capture shear damage due to the opposite signed principal stresses. To extract the pure shear stress, the assumption is made that one component of the shear stress is a minimum absolute of the two principal stresses. The opposite signed principal stresses are decomposed into shear stress and uniaxial tensile/compressive stress. A local model is implemented in Abaqus UMAT and it is further extended to a non-local model by utilization of the gradient theory. The concept of three length scales (tension, compression, and shear) is kept the same as the recently proposed nonlocal damage model by the authors. The nonlocal model is implemented in the Abaqus UEL-UMAT subroutine with an eight-node quadrilateral user-defined element, having five degrees of freedom at corner nodes (displacement in X/Y direction and tensile/compressive and shear nonlocal equivalent strain) and two degrees of freedom at internal nodes. Some examples of a local model including uniaxial and biaxial loading are addressed. Also, five examples of mixed crack mode and mode-I cracking are presented to comprehensively show the performance of this model.

scholarly journals Non-local spatially varying finite mixture models for image segmentation

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Javier Juan-Albarracín ◽  
Elies Fuster-Garcia ◽  
Alfons Juan ◽  
Juan M. García-Gómez
Keyword(s):  
Image Segmentation ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Non Local ◽  
Spatially Varying

On velocity gradient dynamics and turbulent structure

2015 ◽  
Vol 780 ◽  
pp. 60-98 ◽  
Author(s):  
J. M. Lawson ◽  
J. R. Dawson
Keyword(s):  
Velocity Gradient ◽  
Local Strain ◽  
Turbulent Structure ◽  
Stochastic Estimation ◽  
Spatially Resolved ◽  
Gradient Dynamics ◽  
Layer Structures ◽  
Non Local ◽  
Conditional Averaging

The statistics of the velocity gradient tensor $\unicode[STIX]{x1D63C}=\boldsymbol{{\rm\nabla}}\boldsymbol{u}$, which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by $\unicode[STIX]{x1D63C}$. Structures are studied through the footprints they leave in conditional averages of the $Q=-\text{Tr}(\unicode[STIX]{x1D63C}^{2})/2$ field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the $Q$ field conditioned upon $\unicode[STIX]{x1D63C}$ and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the $Q$ field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.

Bifurcation and chaos of axially moving nanobeams considering two scale effects based on non-local strain gradient theory

2021 ◽  
pp. 2140010
Author(s):  
Jing Wang ◽  
Huoming Shen ◽  
Bo Zhang ◽  
Jianqiang Sun ◽  
Yuanyuan Zhang
Keyword(s):  
Strain Gradient ◽  
Scale Effects ◽  
Period Doubling ◽  
Local Strain ◽  
Strain Gradient Theory ◽  
Discrete Equation ◽  
Gradient Theory ◽  
Scale Parameters ◽  
Non Local ◽  
Axially Moving

The nonlinear vibration of axially moving nanobeams at the microscale exhibits remarkable scale effects. A model of an axially moving nanobeam is established based on non-local strain gradient theory and considering two scale effects. The discrete equation of a non-autonomous planar system is obtained using the Galerkin method. The response characteristics of the system are determined using phase diagrams and Poincaré sections, and the effects of the scale parameters on the form of the motion are analyzed. The results show that as the non-local parameter and the material characteristic length parameter vary, the system undergoes multiple forms of motion, including periodic, period-doubling and chaotic motions. Two routes to chaos — period-doubling bifurcation and intermittent chaos — are identified in the variation ranges of the two scale parameters.

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