Tectonic modelling state of the art and future challenges&#160;
Authors: Le Pourhiet Laetitia 
Published: March 2021

&lt;p&gt;Tectonic modelling is a very wide area of application over a large range of time scale and length scale. What mainly characterize this modelling field is the coexistence of brittle fractures which relates to the field of fracture mechanics and plastic to viscous shear zones which belongs to the two main branch of continuum mechanics (solid and fluid respectively).&lt;/p&gt;&lt;p&gt;This type of problems arises sometimes in engineering but material do not change their behavior with loading rate or with time or with temperature, and rarely are engineers interested in modelling large displacement in post failure stage. &amp;#160;As a result, tectonicists cannot use commercial packages to simulate their problems and need to develop methodologies specific to their field.&lt;/p&gt;&lt;p&gt;Historically, the first tectonics models made use of simple analogue materials and corresponded more to modelism than actual analogue models. While the imaging of the models, and the characterization of the analogue materials have made a lot of progress in the last 15 years, up to recently, most analogue models still relied on sand and silicone putty to represent the brittle and viscous counter part of tectonic plates.&lt;/p&gt;&lt;p&gt;Since the late 80&amp;#8217;s, but mostly during the years 2000, numerical modelling has exploded on the market, as contrarily to analogue modelling, it was easier to capture the thermal dependence of frictional-viscous transition, I use frictional here because most models in tectonics use continuum mechanics approach and in fine do not include brittle material s.s. but rather frictional shear bands. Some groups run these types of simulation routinely in 3D today but this performance has been made at the cost of a major simplification in the rheology: the disappearance of elasticity and compressibility which was present in late 90&amp;#8217;s early 2000 simulations and is still very costly because the treatment of &amp;#8220;brittle&amp;#8221; rheology seriously amped code performances.&lt;/p&gt;&lt;p&gt;Until recently, in both analogue and numerical modelling, I have some kind of feeling that we have been running the same routine experiments over and over again with better performance, or better acquisition. &amp;#160;&lt;/p&gt;&lt;p&gt;We are now entering a new exciting era in tectonic modelling both from experimental and numerical side: a ) emergence of complex analogue material or rheological laws that efforts in upscaling from micro-mechanical process observed on the field to plate boundary scale, or from earthquake cycle to plate tectonics, b) emergence of new interesting set up&amp;#8217;s in terms of boundary conditions in 3D, c) development of robust numerical technics for brittle behavior d) development of new applications to make our field more predictive that will enlarge the community of end-users of the modelling results&lt;/p&gt;&lt;p&gt;I will review these novelties with some of the work develop with colleagues and students but also with examples from the literature and try to quickly draw a picture of where we are at and where we go.&lt;/p&gt;