AnisoMPM

Abstract

Dynamic fracture surrounds us in our day-to-day lives, but animating this phenomenon is notoriously difficult and only further complicated by anisotropic materials---those with underlying structures that dictate preferred fracture directions. Thus, we present AnisoMPM: a robust and general approach for animating the dynamic fracture of isotropic, transversely isotropic, and orthotropic materials. AnisoMPM has three core components: a technique for anisotropic damage evolution, methods for anisotropic elastic response, and a coupling approach. For anisotropic damage, we adopt a non-local continuum damage mechanics (CDM) geometric approach to crack modeling and augment this with structural tensors to encode material anisotropy. Furthermore, we discretize our damage evolution with explicit and implicit integration, giving a high degree of computational efficiency and flexibility. We also utilize a QR-decomposition based anisotropic constitutive model that is inversion safe, more efficient than SVD models, easy to implement, robust to extreme deformations, and that captures all aforementioned modes of anisotropy. Our elasto-damage coupling is enforced through an additive decomposition of our hyperelasticity into a tensile and compressive component in which damage is used to degrade the tensile contribution to allow for material separation. For extremely stiff fibered materials, we further introduce a novel Galerkin weak form discretization that enables embedded directional inextensibility. We present this as a hard-constrained grid velocity solve that poses an alternative to our anisotropic elasticity that is locking-free and can model very stiff materials.

MPM-driven Dynamic Desiccation Cracking and Curling in Unsaturated Soils

“…MPM was first introduced into computer graphics by 9 to simulate snow. Due to its excellent physical accuracy and natural support for topology changes, MPM has been extensively applied to simulate various phenomena including sand 21 , lava 22 , viscoelastic/viscoplastic foam 23,24 , cloth 25 , fracture 10,26,11 , magnetized material 27 , multi-species coupling 28,4,3 , even hydrophobicity and hydrophilicity 29 . In order to address the significant numerical dissipation in MPM, affine particle-in-cell (APIC) 30 incorporated a local velocity gradient to preserve the momentum of particles, and Fei et al 31 further improved it with several advection strategies.…”

A‐ULMPM: An Adaptively Updated Lagrangian Material Point Method for Efficient Physics Simulation without Numerical Fracture

“…The seminal work of Zhu and Bridson [ZB05] first introduced the FLIP method for sand simulation. Subsequent works further explored its strength in simulating a broader spectrum of material behaviors including snow [SSC * 13], granular materials [DBD16, KGP * 16, TGK * 17, GPH * 18], foam [RGJ * 15, YSB * 15], complex fluids [FLGJ19, GTJS17], cloth, hair and fiber collisions [JGT17, FMB * 17, FBGZ18], fracture [WFL * 19, WCL * 20] and phase change [SSJ * 14,GWW * 18,SH * 21]. We also note the related works of [MSW * 09] for hair simulation, [SMT08] for cloth simulation, [NGL10] for sand simulation and [PAKF13] for bubble simulation, which bear similarities to MPM due to their hybrid nature.…”

Remeshing‐free Graph‐based Finite Element Method for Fracture Simulation

“…This achieves a realistic dynamic fracture simulation for isotropic materials. Further study [WCL*20] devoted to formulating non‐local CDM to simulate anisotropic material fracture.…”

“…This poses challenges like the generation of thin (or sliver) elements, instability and heavy computational cost. To avoid these effects, authors have explored remeshing‐free techniques like eXtended finite element method (XFEM) [KBT17, CMSK20] and the material point method (MPM) [PKA*05, WDG*19, HFG*18, WFL*19, WCL*20]. The system matrix of XFEM scales linearly with the introduction of new cracks, which in turn requires more computation time.…”