Systems and methods to determine elastic properties of materials

A system for determining one or more elastic properties of an in situ material, the system comprising:

• a first input means for receiving a first input signal representative of a driving force exerted on the material by an dynamic actuator at a driving-point;
• a second input means for receiving a second input signal representative of a driving-point velocity corresponding to the driving force;
• a third input means for receiving a third input signal representative of a driving-point displacement corresponding to the driving force;
• a signal generator means for generating a basis function signal for each one of a set of basis functions, the set of basis functions corresponding to the terms of a force balance differential equation model of the motion of the driving-point, the differential equation model comprising a nonlinear spring-damper system represented by polynomial function of the driving-point displacement and a polynomial function of the driving-point velocity, and each other basis function comprising a function of any one or more of the input signals;
• and
• a processor means for analyzing the set of basis function signals in relation to the first input signal to determine coefficients of a linear combination of the function signals which best fits the first input signal, wherein each coefficient corresponding to a displacement term is then representative of a stiffness property of the material, and each coefficient corresponding to a velocity term is then representative of a viscosity property of the material.