Goal-oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

Coal body is a type of fractured rock mass in which lots of cleat fractures developed. Its mechanical properties vary with the parametric variation of coal rock block, face cleat and butt cleat. Based on the linear elastic theory and displacement equivalent principle and simplifying the face cleat and butt cleat as multi-bank penetrating and intermittent cracks, the model was established to calculate the elastic modulus and Poisson's ratio of coal body combined with cleat. By analyzing the model, it also obtained the influence of the parameter variation of coal rock block, face cleat and butt cleat on the elastic modulus and Poisson's ratio of the coal body. Study results showed that the connectivity rate of butt cleat and the distance between face cleats had a weak influence on elastic modulus of coal body. When the inclination of face cleat was 90°, the elastic modulus of coal body reached the maximal value and it equaled to the elastic modulus of coal rock block. When the inclination of face cleat was 0°, the elastic modulus of coal body was exclusively dependent on the elastic modulus of coal rock block, the normal stiffness of face cleat and the distance between them. When the distance between butt cleats or the connectivity rate of butt cleat was fixed, the Poisson's ratio of the coal body initially increased and then decreased with increasing of the face cleat inclination.

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Stochastic homogenization and macroscopic modelling of composites and flow through porous media

Theoretical and Applied Mechanics ◽

10.2298/tam0229337t ◽

2002 ◽

pp. 337-378 ◽

Cited By ~ 5

Author(s):

Jozef Telega ◽

Wlodzimierz Bielski

Keyword(s):

Porous Medium ◽

Random Distribution ◽

Flow Through Porous Media ◽

Macroscopic Models ◽

Linear Elastic ◽

Multi Scale ◽

Convergence Method ◽

Flow Through ◽

The Mean ◽

Random Porous Medium

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .

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Fatigue Failure Analysis Using the Theory of Critical Distance

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.462-463.663 ◽

2011 ◽

Vol 462-463 ◽

pp. 663-667 ◽

Cited By ~ 3

Author(s):

Ruslizam Daud ◽

Ahmad Kamal Ariffin ◽

Shahrum Abdullah ◽

Al Emran Ismail

Keyword(s):

Stress Concentration ◽

Fatigue Failure ◽

Notch Root ◽

High Stress ◽

Critical Distance ◽

Future Research ◽

Element Analysis ◽

Linear Elastic ◽

The Finite Element Analysis ◽

Elastic Fracture

This paper explores the initial potential of theory of critical distance (TCD) which offers essential fatigue failure prediction in engineering components. The intention is to find the most appropriate TCD approach for a case of multiple stress concentration features in future research. The TCD is based on critical distance from notch root and represents the extension of linear elastic fracture mechanics (LEFM) principles. The approach is allowing possibilities for fatigue limit prediction based on localized stress concentration, which are characterized by high stress gradients. Using the finite element analysis (FEA) results and some data from literature, TCD applications is illustrated by a case study on engineering components in different geometrical notch radius. Further applications of TCD to various kinds of engineering problems are discussed.

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Fatigue Crack Growth Analysis with Extended Finite Element for 3D Linear Elastic Material

Metals ◽

10.3390/met11030397 ◽

2021 ◽

Vol 11 (3) ◽

pp. 397

Author(s):

Yahya Ali Fageehi

Keyword(s):

Finite Element ◽

Fatigue Crack ◽

Fatigue Life ◽

Crack Propagation ◽

Crack Growth ◽

Mixed Mode ◽

Propagation Path ◽

Loading Conditions ◽

Extended Finite Element ◽

Linear Elastic

This paper presents computational modeling of a crack growth path under mixed-mode loadings in linear elastic materials and investigates the influence of a hole on both fatigue crack propagation and fatigue life when subjected to constant amplitude loading conditions. Though the crack propagation is inevitable, the simulation specified the crack propagation path such that the critical structure domain was not exceeded. ANSYS Mechanical APDL 19.2 was introduced with the aid of a new feature in ANSYS: Smart Crack growth technology. It predicts the propagation direction and subsequent fatigue life for structural components using the extended finite element method (XFEM). The Paris law model was used to evaluate the mixed-mode fatigue life for both a modified four-point bending beam and a cracked plate with three holes under the linear elastic fracture mechanics (LEFM) assumption. Precise estimates of the stress intensity factors (SIFs), the trajectory of crack growth, and the fatigue life by an incremental crack propagation analysis were recorded. The findings of this analysis are confirmed in published works in terms of crack propagation trajectories under mixed-mode loading conditions.

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Constitutive Modeling of the Densification Behavior in Open-Porous Cellular Solids

Materials ◽

10.3390/ma14112731 ◽

2021 ◽

Vol 14 (11) ◽

pp. 2731

Author(s):

Ameya Rege

Keyword(s):

Constitutive Model ◽

Cell Walls ◽

Compressive Strain ◽

Pore Collapse ◽

Compressive Response ◽

Linear Elastic ◽

Nonlinear Springs ◽

Different Types ◽

Point Of Intersection ◽

Good Agreement

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement.

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