Introduction

How a material responds to load is an everyday concern for civil engineers. As an example we can consider a beam that forms some part of a structure. When loads are applied to the structure the beam experiences deflections. If the loads are continuously increased the beam will experience progressively increasing deflections and ultimately the beam will fail. If the applied loads are small in comparison with the load at failure then the response of the beam may be proportional, i.e. a small change in load will result in a correspondingly small change in deflection. This proportional behaviour will not continue if the load approaches the failure value. At that point a small increase in load will result in a very large increase in deflection. We say the beam has failed. The mode of failure will depend on the material from which the beam is made. A steel beam will bend continuously and the steel itself will appear to flow much like a highly viscous material. A concrete beam will experience cracking at critical locations as the brittle cement paste fractures. Flow and fracture are the two failure modes we find in all materials of interest in civil engineering. Generally speaking, the job of the civil engineer is threefold: first to calculate the expected deflection of the beam when the loads are small; second to estimate the critical load at which failure is incipient; and third to predict how the beam may respond under failure conditions.