Mechanical and Civil Engineering Seminar
Mechanics of fracture and failure of solids continues to elicit challenges in terms of modeling and simulation, and investigation of the physical mechanisms in a range of engineering, biological and geological materials like metals, polymers, and rocks. Here, I will give an overview of two major efforts in my group focusing on addressing the multiscale nature of fracture in two seemingly different but societally relevant applications: (1)Physics-based modeling of earthquake propagation on frictional interfaces , and (2) modeling of fracture in soft materials.
In the first half of my talk, I will focus on a new computational algorithm for modeling earthquake ruptures with high resolution fault zone physics. I will present a hybrid method that combines Finite element method (FEM) and Spectral boundary integral (SBI) equation through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small-scale heterogeneities and from the superior performance and accuracy of SBI. I will present a verification of the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises and show that the method enables exact near field truncation of the elastodynamic solution. I will further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off-fault complexities using a unique model of a fault zone with explicit representation of small scale secondary faults and branches enabling new insights into earthquake rupture dynamics that may not be realizable in homogenized isotropic plasticity or damage models. Next, I will briefly discuss our recent efforts in extending this method to consistently simulate sequences of seismic and aseismic slip in a fault zone by combining adaptive explicit and implicit integration schemes enabling us to vary the time step over more than seven orders of magnitude and to potentially explore the interplay between geometric, rheological, and frictional complexities over short and long time scales.
In the second half of my talk, I will introduce a new paradigm for modeling failure and damage evolution in networked materials such as rubber, gels, soft tissues, and lattice materials. Understanding the multiscale nature of deformation in these networked structures holds key for uncovering origins of fragility in many complex systems including biological tissues and enables designing novel materials. However, these processes are intrinsically multiscale and for large scale structures it is computationally prohibitive to adopt a full discrete approach. Modern approaches have largely focused on applying advanced homogenization methods to approximately upscale the complex microstructure. However, fracture is known to be highly sensitive to local heterogeneities and topology. Here, I will introduce an adaptive numerical algorithm for solving polymer networks using an extended version of the Quasi-Continuum (QC) method. In regions of high interest, for example near defects or cracks, each polymer chain is idealized using the worm like chain model. Away from these imperfections, the network structure is computationally homogenized to yield an anisotropic material tensor consistent with the underlying network structure. Overall, only a fraction of the network nodes is solved at each time step enabling accurate modeling of the complex crack evolution without apriori constraint on the fracture energy or near crack tip deformation mechanism while maintaining the influence of large scale elastic loading in the bulk. I demonstrate the accuracy and efficiency of the method by applying it to study the fracture of large scale polymer network problems as a first step towards modeling multi-physics problems in failure of fluid infiltrated soft materials. I will close by discussing some possible future applications of this modeling framework in both engineering and geophysical problems.