Chen Rational Mechanics XII: Calculating Material Constants for Complicated Stress-Strain Experimental Curves

• 1、Henan Polytechnic University

Abstract：In many experimental cases, the stress is directly measured by the stress-sensor mounted on force action face and the strain is directly measured by the strain-sensor mounted on the material free boundary. The strain measured by the sensor is different from the strain calculated by the length variation in that, at the local braking-down zone, the strain sensor gives out zero strain while the calculated length-variation strain is non-zero. Such a kind of measurement way gives out the intrinsic stress-strain relationship. This topic is studied by Chen Zhida in rational mechanics frame. Chen rational mechanics theory is based on the additive decomposition of deformation gradient. The new theoretic formulation introduces the local relative rotation concept which can be expressed by the local rotation angular parameter. On intrinsic sense, this angular represents the non-linear feature of stress-strain relation. By the new theory, the plastic parameter is expressed by the local rotation angular and the breaking-down stress is expressed by the critical rotation angular. For the experimental stress-strain data from elastic deformation to breaking-down, the calculating method of material constants is studied. By this method, the complicated deformation curve can be well expressed by the initial elastic constants and the local rotation angular. For initial isotropic material, the non-linear feature of stress-strain relation is expressed by two elastic constants and one path-dependent local rotation angular parameter.

keywords： local rotation,non-linear,stress-strain,rational mechanics

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