By Jacques Besson, Georges Cailletaud, Jean-Louis Chaboche, Samuel Forest, Marc Blétry
There at present exists an important hole among fabrics versions utilized by engineers and those to be had in learn laboratories. wisdom move has to be facilitated through software program improvement and databases, but in addition via details and instructing. From that point of view, Nonlinear Mechanics of Materials deals an replace of the information essential to comprehend and use the latest types of fabrics habit and harm in structures.
After offering numerical instruments, and classical plasticity and viscoplasticity, this paintings offers an outline of wear and tear mechanics, heterogeneous fabrics mechanics, finite pressure, nonlinear structural research and pressure localization phenomena, through looking equilibrium among a theoretical process and genuine fabrics models.
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Additional resources for Non-Linear Mechanics of Materials
Most of the hardening rules developed later in this chapter will introduce an energy dissipation (see Sect. 2). General expression for one-dimensional elastoplasticity In the general case, the “loading–unloading” conditions are the following; – elastic behavior if: f (σ, Ai ) < 0 – elastic unloading if: f (σ, Ai ) = 0 – plastic flow if: f (σ, Ai ) = 0 and f˙(σ, Ai ) < 0 and f˙(σ, Ai ) = 0 (˙ε = σ˙ /E) (˙ε = σ˙ /E) (˙ε = σ˙ /E + ε˙ p ) General concepts 21 The plastic modulus H generally depends on plastic strain and on the hardening variables.
New models can be developed easily by considering the combination of several elements. This introduction offers the opportunity to present in a simple framework most of the concepts used for tridimensional loading cases. The mechanical response of the systems will be considered in three different planes, allowing us to illustrate the behavior for various loading types: – hardening, or monotonic increase of the stress or the strain (strain–stress plane, ε–σ ); – creep, a test performed under constant stress (time–strain plane, t–ε); – relaxation, a test performed under constant strain (time–stress plane, t–σ ).
There are only three types, elasticity, time independent plasticity, and viscosity. The corresponding elements are: 1. The spring, characterizing linear elasticity, for which strain is totally reversible after unloading, and providing a one-to-one relation between stress and strain components (Fig. 2a). 2. The dash-pot, representing linear (Fig. 2b) or nonlinear (Fig. 2c) viscosity. The viscosity is said to be “pure” if a one-to-one relation between load and strain rate is introduced. If the relation is linear, the corresponding model is Newton’s law.