Ductile deformation without localization: insights from numerical modeling

Strain is easily localized in a polyphase rock, especially if the rock undergoes syntectonic weakening processes. However, there is ample field evidence for distributed, rather than localized, deformation at the outcrop to hundreds of square kilometer scale. In these areas, distributed strain is evidenced by the presence of continuous foliations and a lack of distinct high-strain zones. Here, we use numerical modeling of viscous deformation to investigate the conditions that allow distributed rather than localized deformation. We identify three strain localization regimes for a system with rheologically strong and weak phases with or without stress-induced weakening. Regime I is characterized by distributed strain. It forms where either deformation-induced interconnection of the weak phase is not possible or the initial weak phase area is intermediate to high (i.e., > ~40–60% of total depending on weak phase geometry). Their resultant bulk strength is either strong or weak, respectively. Regime II is characterized by variably distributed areas of strain localization and develops if the initial proportion of weak phases is intermediate (i.e., 40–60% weak phase depending on geometry) and syntectonic weakening causes an increase (up to ~12%) of weak phase proportion. Regime III exhibits significant strain localization and only develops if the initial proportion of weak phases is relatively low (<20%) and syntectonic weakening increases the proportion of weak phases by over ~12%. Here, high-strain zones readily form irrespective of the initial distribution of rheologically weak and hard phases, and bulk strength is intermediate.