Toughness is proportional to the amount of energy stored/put in to a material (o

Question

Toughness is proportional to the amount of energy stored/put in to a material (or structure) when a stress is applied. Compact bone from the tibia has a tensile failure stress of 150 MPa and a tensile strain at failure of 1.5%. The anterior collateral ligament has a tensile failure stress of 35 MPa and a strain at failure of 30%. Which is probably mechanically tougher, the bone or the ligament? We calculated Young's Modulus for each but aren't sure of how to relate Youngs Modulus to Toughness- Thanks!

Explanation / Answer

energy = 1/2*stress*strain*volume, energy of tibia = 1/2*150*0.015*volume = 1.125*volume energy of ligament = 1/2* 35*0.3*volume = 5.25*volume since toughness of material is energy required to break per unit volume. so ligament is stronger.

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