We simulate the stresses induced by temperature changes in a putative hard layer near the surface of comet 67P/Churyumov--Gerasimenko with a thermo-viscoelastic model. Such a layer could be formed by the recondensation or sintering of water ice (and dust grains), as suggested by laboratory experiments and computer simulations, and would explain the high compressive strength encountered by experiments on board the Philae lander. Changes in temperature from seasonal insolation variation penetrate into the comets surface to depths controlled by the thermal inertia, causing the material to expand and contract. Modelling this with a Maxwellian viscoelastic response on a spherical nucleus, we show that a hard, icy layer with similar properties to Martian permafrost will experience high stresses: up to tens of MPa, which exceed its material strength (a few MPa), down to depths of centimetres to a metre. The stress distribution with latitude is confirmed qualitatively when taking into account the comets complex shape but neglecting thermal inertia. Stress is found to be comparable to the material strength everywhere for sufficient thermal inertia ($gtrsim50$ J m$^{-2}$ K$^{-1}$ s$^{-1/2}$) and ice content ($gtrsim 45%$ at the equator). In this case, stresses penetrate to a typical depth of $sim0.25$ m, consistent with the detection of metre-scale thermal contraction crack polygons all over the comet. Thermal fracturing may be an important erosion process on cometary surfaces which breaks down material and weakens cliffs.
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