Numerical modeling of thermo‐mechanical failure processes in granitic rock with polygonal finite elements

Abstract

This paper considers numerical modeling of intensive heating induced thermo‐mechanical failure processes in granitic rock. For this end, a numerical method based on polygonal finite elements and a damage‐plasticity model is developed. A staggered scheme is employed to solve the global thermo‐mechanical problem. The rock failure is described by a Rankine‐Mohr‐Coulomb plasticity model with separate scalar damage variables for tension and compression. Consistent tangent operator is derived for this model. Special attention is given to the temperature dependence of the thermo‐mechanical material properties of heterogeneous rock. In the numerical examples, the method is first verified with an analytical solution of thermal stresses in a hollow cylinder, and then qualitatively validated with the problems of thermal cracking of concentric cylinders and uniaxial compressive test on rock under elevated temperatures. Finally, the method is applied in novel simulations inspired by the degradation of sauna stones under slow heating‐rapid cooling and the comminution by rapid heating‐cooling cycles.

The sensitivity analysis of dynamic electric breakdown damage model and simulation of granite by high voltage electric pulse

“…The specific process is described in detail in Potyondy's related literature [46,47]. The particle model was converted to a granite geometry model using Voronoi tessellation [48][49][50]. Then, the mineral components corresponding to the coordinate points of the spatial grid are judged in the granite geometric model, and the corresponding initial material properties are assigned, as shown in table 3.…”

3D numerical prediction of thermal weakening effects on granite

“…The original derivation is by Saksala. 21 The resulting consistent damage-elastoplastic tangent stiffness operator, relating the strain increment to stress increment 𝛿𝛔 = 𝐄 epd ∶ 𝛿𝛆, is 𝐄 epd = 𝜙𝐄 + (1 − 𝜔 c ) 𝜔 t σ ⊗ 𝐑 UC ∶ 𝐄 + (A1) In (A5), II is the fourth order unit tensor. Moreover, 𝑔 t and 𝑔 c are the damage functions in Equation (5).…”

“…Quartz bearing rocks, such as granite and gneiss, are particularly prone to temperature weakening due to its α‐β transition at about 573°C 4 . An extensive body of both experimental 1,5–16 and numerical 11–14,16–22 studies naturally exist on the temperature effects in various rocks.…”

“…[1][2][3] As high temperature has a detrimental effect on rock strength, especially in case of Quartz bearing rocks, good understanding of the weakening effects and their prediction by numerical or analytical methods is an asset of substantial importance in rock engineering. Quartz bearing rocks, such as granite and gneiss, are particularly prone to temperature weakening due to its α-β transition at about 573 • C. 4 An extensive body of both experimental 1,[5][6][7][8][9][10][11][12][13][14][15][16] and numerical [11][12][13][14][16][17][18][19][20][21][22] studies naturally exist on the temperature effects in various rocks.…”

Homogenization of discrete diffusion models by asymptotic expansion

“…Transport of mass, heat, or electric charge through heterogeneous solid material is an important problem in a number of practical applications. A large number of experimental and numerical works concerning heterogeneous materials are devoted to study the transport of moisture or water, 1,2 heat, 3,4 or chlorides 5,6 . Particularly in civil engineering, the transport behavior of concrete is of paramount importance as temperature, relative humidity, and/or chemical substances largely influence its mechanical behavior as well as durability 7 …”