Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework

In this article, we developed a thermodynamically consistent non-local microcracking model for quasi-brittle materials with application to concrete. The model is implemented using a novel graph-based finite element analysis (GraFEA) approach that allows for (i) the probabilistic modeling of the growth and coalescence of microcracks, (ii) the modeling of crack closure using a kinematics-based approach, and (iii) the modeling of rate effects on microcracking. The developed theoretical model and its computational framework is also implemented into the dynamics-based Abaqus/Explicit finite element program through a vectorized user-material subroutine interface. We further demonstrate the procedure for obtaining the parameters (including the non-local intrinsic material length scale, which governs the fracture process) and consequently validate the simulations with independent experimental results.

Rate and Temperature Effect in Nanoindentation Testing on Hardness in SLM IN718

The microstructure and mechanical hardness of Inconel 718 (INC718) hexagonal honeycomb cellular structure manufactured by Selective Laser Melting (SLM) was studied in this work. Non-heat-treated SLM-produced samples with cell wall thicknesses of 0.4, 0.6 and 0.8 mm were studied. The hardness was measured using MTS Nanoindenter. For room temperature, continuous hardness measurements over penetration depths up to 2 µm under three different strain rates of 0.02, 0.05 and 0.08 s−1 was performed. For the 100 and 200°C, single hardness measurements at eight different depths were performed. The grain size was found to change considerably as the cell wall thickness changed from 0.6 mm to 0.4 mm compared to the change from 0.8 mm to 0.6 mm. similar trend in mechanical hardness reduction and strain rate sensitivity changes were observed between the three samples. The microstructure and hardness showed anisotropy between the planes parallel and perpendicular to the build planes as well. Temperature and strain rate indentation size effect model developed by the second author was modified and used to evaluate the intrinsic material length scale used in gradient plasticity theory.

An assessment of phase field fracture: crack initiation and growth

The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Strain Gradient Plasticity Modeling to Evaluate Material Plastic Deformation Behavior During Cold Gas Dynamic Spray Process

Severe plastic deformation (SPD) is the main feature of the Cold Spray (CS) process; which might result in producing metal grain refinement under extensive hydrostatic pressure and high strain rate loading conditions. In this study; an anisotropic strain gradient plasticity model (SGP) is presented to predict materials behavior in CS process. The enhanced dislocation densities produced throughout particle deformation affect coating material properties and modify their thermodynamic characteristics and kinetic of resistance to plastic deformations. This study also demonstrates that the SGP model can describe the experimentally observed trends and account for homogenization of the accumulated strains under dynamic recrystallization conditions. The evolution of statistically stored dislocation density through the characteristic material length scale parameter is in good agreement with experimental results and data reported by other research groups. The proposed SGP modeling is suggested as an express method to evaluate the advanced coating and additively manufactured materials; and powder feedstock used in thermal spray and 3D manufacturing applications.

Designing of Dynamic Spectrum Shifting in Terms of Non-Local Space-Fractional Mechanics

In this paper, the applicability of the space-fractional non-local formulation (sFCM) to design 1D material bodies with a specific dynamic eigenvalue spectrum is discussed. Such a formulated problem is based on the proper spatial distribution of material length scale, which maps the information about the underlying microstructure (it is important that the material length scale is one of two additional material parameters of sFCM compared to the classical local continuum mechanics—the second one, the order of fractional continua—is treated herein as a scaling parameter only). Technically, the design process for finding adequate length scale distribution is not trivial and requires the use of an inverse optimization procedure. In the analysis, the objective function considers a subset of eigenvalues reduced to a single value based on Kreisselmeier–Steinhauser formula. It is crucial that the total number of eigenvalues considered must be smaller than the limit which comes from the ratio of the sFCM length scale to the length of the material body.

On size-dependent bending behaviors of shape memory alloy microbeams via nonlocal strain gradient theory

This paper focuses on the size-dependent behaviors of functionally graded shape memory alloy (FG-SMA) microbeams based on the Bernoulli-Euler beam theory. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus and critical transformation stresses vary continuously along the longitudinal direction. According to the simplified linear shape memory alloy (SMA) constitutive equations and nonlocal strain gradient theory, the mechanical model was established via the principle of virtual work. Employing the Galerkin method, the governing differential equations were numerically solved. The functionally graded effect, nonlocal effect and size effect of the mechanical behaviors of the FG-SMA microbeam were numerically simulated and discussed. Results indicate that the mechanical behaviors of FG-SMA microbeams are distinctly size-dependent only when the ratio of material length scale parameter to the microbeam height is small enough. Both the increments of material nonlocal parameter and ratio of material length-scale parameter to the microbeam height all make the FG-SMA microbeam become softer. However, the stiffness increases with the increment of FG parameter. The FG parameter plays an important role in controlling the transverse deformation of the FG-SMA microbeam. This work can provide a theoretical basis for the design and application of FG-SMA microstructures.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

A simple size-dependent isogeometric approach for bending analysis of functionally graded microplates using the modified strain gradient elasticity theory

In this study, a simple size-dependent isogeometric approach for bending analysis of functionally graded (FG) microplates using the modified strain gradient theory (MSGT), simple first-order shear deformation theory (sFSDT) and isogeometric analysis is presented for the first time. The present approach reduces one variable when comparing with the original first-order shear deformation theory (FSDT) within five variables and only considers three material length scale parameters (MLSPs) to capture size effects. Effective material properties as Young’s modulus, Poisson’s ratio and density mass are computed by a rule of mixture. Thanks to the principle of virtual work, the essential equations which are solved by the isogeometric analysis method, are derived. Rectangular and circular FG microplates with different boundary conditions, volume fraction and material length scale parameter are exampled to evaluate the deflections of FG microplates.

Free torsional vibration of triangle microwire based on modified couple stress theory

In this article, the free torsional vibration of the noncircular microwire is obtained via modified couple stress theory. The noncircular cross section is considered to be equilateral triangle. The governing equations are derived using Hamilton’s principle, and the natural frequencies of the clamped-clamped and clamped-free microwires are obtained based on a Galerkin method. The natural frequency for analyzing of the results is considered to be dimensionless. The effects of the different parameters including the dimensionless material length scale parameter, the dimensionless edge length of the triangle, and mode number on the dimensionless natural frequency of the microwire are evaluated. Ultimately, the influence of the Poisson’s ratio on the natural frequency of the microwire under various boundary conditions is investigated.