Round 3: Tossup 10

A class of methods in solid mechanics named for this quantity include Castiligano’s method, in which partial derivatives of this quantity give partial displacements. Alan Griffith took the derivative of this quantity with respect to crack length to derive his theory of fracture mechanics, in which the square of stress intensity factor is proportional to the areal release rate of this quantity. The maximum volumetric density of this quantity that can be reached before a material ruptures defines its toughness. The volumetric (10[1])density of this quantity associated with elastic strain is one-half Young’s modulus (-5[1])times strain squared. For a Hookean spring, this quantity is equal to one-half spring constant times displacement (-5[1])squared. (10[3])For 10 points, work is a transfer of what quantity measured in joules? ■END■ (10[1])

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