  Active solids are a large class of materials, including both living soft
tissues and artificial matter, that share the ability to undergo strain even in
absence of external loads. While in engineered materials the actuation is
typically designed a priori, in natural materials it is an unknown of the
problem. In such a framework, the identification of inactive regions in active
materials is of particular interest. An example of paramount relevance is
cardiac mechanics and the assessment of regions of the cardiac muscle with
impaired contractility. The impossibility to measure the local active forces
directly suggests us to develop a novel methodology exploiting kinematic data
from clinical images by a variational approach to reconstruct the local
contractility of the cardiac muscle. By finding the stationary points of a
suitable cost functional we recover the contractility map of the muscle.
Numerical experiments, including severe conditions with added noise to model
uncertainties, and data knowledge limited to the boundary, demonstrate the
effectiveness of our approach. Unlike other methods, we provide a spatially
continuous recovery of the contractility map without compromising the
computational efficiency.
