| Continuum models of material mechanical behavior |  |
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| Rheology is the study of flow, the response of material to applied stresses. The relationships between stress and strain, and stress and strain rate characterise the macroscopic behavior of rocks. They lead to the constitutive equations linking stress and strain rate. "Constitutive" as they depend on the constitution of the material. The graph on the right shows the flow curves for three elementary stress-strain relationships: | ||||
| • Linear elastic flow (blue): For small stresses, most material are elastic. The characteristics of elastic flow are: 1/ Elastic flow occurs as soon as stress is applied. 2/ Strain increases as long as stress keeps increasing. The elastic flow curve is linear its slope is 1/E with E the Young modulus a physical properties characteristics of elastic flow. 3/ Strain does not accumulate if the stress is maintained constant. 4/The material rebounds to its original shape when stress is released. The mechanical analogue for elastic deformation is a spring. • Ideal Plastic behavior (green): In most material elastic behavior is limited to a certain level of stress above which the flow switch from elastic to plastic. This limit is called the yield stress. The characteristics of plastic flow are: 1/ Plastic flow occurs as soon as yield stress is reached. 2/ Plastic strain is accumulated at constant level of stress. The amount of strain depends on the duration over which stress is applied. Therefore the flow curve depends on t. 3/ The plastic part of deformation is permanent. When stress is released the material recovers only the elastic deformation. 4/ For and ideal plastic material there is no elastic component and plastic deformation occurs at constant level of stress, ie the yield stress. • Linear viscous behavior (purple): Linear viscous material (newtonian viscosity) have no yield stress. The flow curve is characterized by a linear relationship between stress and strain. Strain accumulates at varying and also constant stress (dashed purple line from D) and when the stress is removed the flow stops but the material does not return to its undeformed state. The mechanical analogue of viscous deformation is a dashpot. In a graph strain versus time, in experiments where the stress is maintained constant, elastic, ideal plastic and viscous behaviors reveal again three different relationships. |
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