Modeling of deformation of the bimaterial with thin Non-linear interface inclusion

An incremental approach to solving the antiplane problem for bimaterial media with a thin, physically nonlinear inclusion placed on the materials interface is discussed. Using the jump functions method and the coupling problem of boundary values of the analytical functions method we reduce the problem to the system of singular integral equations (SSIE) on jump functions with variable coefficients allowing us to describe any quasi-static loads (monotonous or not) and their influence on the stress-strain state in the bulk. To solve the SSIE problem, an iterative analytical-numerical method is offered for various non-linear deformation models. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analyzed for a deformed body under a load of a balanced concentrated force system.

Towards simulating sequences of seismic and aseismic slip across scales: Initial benchmarks and future directions

<p>Numerical simulations of the earthquake cycle have made great progress over the past decades to address important questions in earthquake physics and fault mechanics. However, significant challenges in bridging multiscale interactions between long-term tectonic deformation, aseismic fault slip, earthquake nucleation, and dynamic rupture still remain. In this study, we present results from GARNET, a newly-developed numerical library to simulate sequences of seismic and aseismic slip across scales. This finite difference code utilizes a fully staggered spatially adaptive rectilinear grid. Furthermore, it incorporates an automatic discretization algorithm and combines different physical ingredients, including a visco-elasto-plastic rheology and quasi- and fully dynamic formulation of inertial effects into one algorithm. While PETSc and Kokkos libraries are included for parallel computing, an adaptive time stepping is integrated into the algorithm to resolve both long- and short-time scales, ranging from years to milliseconds during the dynamic propagation of earthquake rupture.</p><p> </p><p>Here we present results from two benchmarks (BP1 and BP3) based on the community code-verification effort for Sequences of Earthquakes and Aseismic Slip (SEAS) by the Southern California Earthquake Center (SCEC). BP1 benchmark is a 2D antiplane problem, with a 1D planar vertical strike-slip fault obeying rate-and-state friction, embedded in a 2D homogeneous, linear elastic half-space. The fault has a shallow seismogenic region with velocity-weakening friction and a deeper velocity-strengthening region, below which a relative plate motion rate is imposed. A periodic sequence of spontaneous, quasi-dynamic earthquakes and slow slip are simulated in the model. In the BP3 benchmark we consider full inertial effects during the dynamic rupture and we investigate its influence on earthquake behaviour and patterns. Results from these two benchmarks represent the first step towards more advanced seismic cycle models, which will help to enhance our understanding in earthquake physics.</p>

The Community Code Verification Exercise for Simulating Sequences of Earthquakes and Aseismic Slip (SEAS)

Numerical simulations of sequences of earthquakes and aseismic slip (SEAS) have made great progress over past decades to address important questions in earthquake physics. However, significant challenges in SEAS modeling remain in resolving multiscale interactions between earthquake nucleation, dynamic rupture, and aseismic slip, and understanding physical factors controlling observables such as seismicity and ground deformation. The increasing complexity of SEAS modeling calls for extensive efforts to verify codes and advance these simulations with rigor, reproducibility, and broadened impact. In 2018, we initiated a community code-verification exercise for SEAS simulations, supported by the Southern California Earthquake Center. Here, we report the findings from our first two benchmark problems (BP1 and BP2), designed to verify different computational methods in solving a mathematically well-defined, basic faulting problem. We consider a 2D antiplane problem, with a 1D planar vertical strike-slip fault obeying rate-and-state friction, embedded in a 2D homogeneous, linear elastic half-space. Sequences of quasi-dynamic earthquakes with periodic occurrences (BP1) or bimodal sizes (BP2) and their interactions with aseismic slip are simulated. The comparison of results from 11 groups using different numerical methods show excellent agreements in long-term and coseismic fault behavior. In BP1, we found that truncated domain boundaries influence interseismic stressing, earthquake recurrence, and coseismic rupture, and that model agreement is only achieved with sufficiently large domain sizes. In BP2, we found that complexity of fault behavior depends on how well physical length scales related to spontaneous nucleation and rupture propagation are resolved. Poor numerical resolution can result in artificial complexity, impacting simulation results that are of potential interest for characterizing seismic hazard such as earthquake size distributions, moment release, and recurrence times. These results inform the development of more advanced SEAS models, contributing to our further understanding of earthquake system dynamics.

Physically nonlinear deformation of a thin interphase inclusion under antiplane problem conditions

The longitudinal shear problem of the bimaterial with thin physically nonlinear inclusion at the interface matrix materials is considered. The solution of the formulated problem is constructed by the method of the conjugation of limit values of analytical functions with the use of the jump function method. A model of thin inclusion with arbitrary nonlinear strain characteristics is constructed. The solution of the problem is reduced to a system of singular integral equations with variable coefficients. A convergent iteration method for solving such a system for different types of physically nonlinear deformation is proposed. An incremental calculation method for calculating stress-strain state under multistep (including cyclic) quasi-static loading is developed. Numerical calculations of the body stress-strain state for various values of the parameters of the nonlinearity of the inclusion material are carried out. Their influence on the mode of deformation of the matrix under loading by a balanced system of concentrated forces is investigated.

Antiplane Deformation Of A Bimaterial Containing An Interfacial Crack With The Account Of Friction 2. Repeating And Cyclic Loading

The paper presents the exact solution of the antiplane problem for an inhomogeneous bimaterial with the interface crack exposed to the normal load and cyclic loading by a concentrated force in the longitudinal direction. Using discontinuity function method the problem is reduced to the solution of singular integral equations for the displacement and stress discontinuities at the domains with sliding friction. The paper provides the analysis of the effect of friction and loading parameters on the size of these zones. Hysteretic behaviour of the stress and displacement discontinuities in these domains is observed.