A new total‐Lagrangian smooth particle hydrodynamics approximation for the simulation of damage and fracture of ductile materials

Abstract

Summary Smooth particle hydrodynamics (SPH) is gaining popularity for the simulation of solids subjected to machining, wear, and impacts. Its attractiveness is due to its abilities to simulate problems, involving large deformations resulting from the absence of mesh as well as the development of the total‐Lagrangian version of SPH (TLSPH) to solve tensile instabilities and an hourglass control algorithm to reduce rank‐deficiency problems. However, when TLSPH is used with continuum damage mechanics, nonphysical residual forces can emerge and lead to instabilities. To solve this issue, the “pseudospring” method that scales the kernel function with damage was proposed by Chakraborty and Shaw. This method preserves local linear momentum and is stable for elastic solids but can generate instabilities when solids damage after experiencing high plastic strains. In this contribution, we present a new TLSPH approximation that conserves both linear and angular momenta, which is suitable for the simulation of damage and fracture of ductile materials. Using single‐edge notched samples and tensile tests, we show that this approximation is stable whatever the stress/strain state and is in good agreement with finite element simulations and experimental results.

Contact framework for total Lagrangian smoothed particle hydrodynamics using an adaptive hybrid kernel scheme

“…Therefore, it leads to a problem called tensile instability 34 . It also creates numerical fracture problems 45 . However, the neighbour number increases when the body is subjected to compression.…”

“…34 It also creates numerical fracture problems. 45 However, the neighbour number increases when the body is subjected to compression. On the other hand, neighbour particles using the Lagrangian kernel are always the same, as shown in Figure 2B.…”

“…Other applications in fatigue and fracture mechanics can be found in literature, [42][43][44] and damage mechanics applications. 45 Despite the fact that the TLSPH contributes to significant improvement, the TLSPH is not naturally applicable for contact algorithms, 46 and a problem with geometry change. In dynamic problems with contact between two different bodies, particle interaction at the contact surface must be updated at every time step.…”

“…An improved TLSPH using an upwind scheme was reported 40,41 and applied for large strain solid dynamics problems. Other applications in fatigue and fracture mechanics can be found in literature, 42–44 and damage mechanics applications 45 . Despite the fact that the TLSPH contributes to significant improvement, the TLSPH is not naturally applicable for contact algorithms, 46 and a problem with geometry change.…”

An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity

“…• existence of numerical instabilities of various types, such as the so-called tensile instability (when using a non-Lagrangian description of the problem) [6,11,21,22], the appearance of zero-energy modes due to the rank-deficiency introduced as a result of using particle (reduced nodal) integration [10,23], pressure spurious oscillations in the vicinity of near incompressibility [1,24,25] and the possible development of long term instabilities [12], and…”