By Lili Wang
The first target of this paintings is to offer the reader an realizing of pressure wave behaviour whereas making an allowance for the dynamic constitutive equations of elastic-plastic solids. the writer has mixed a 'materials features' strategy with a 'singularity floor' method during this paintings, which readers will locate to be a unique and distinctive path to fixing their difficulties. * is helping engineers comprehend the consequences and behaviour of rigidity waves in quite a few fabrics* Aids within the means of engineering layout, checking out, and review
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Extra info for Foundations of Stress Waves
60) Note that in the deductions of the kinematic and the dynamic compatibility equations, the material properties are not involved. Therefore, these equations are true for the plane waves in any continuum. Nevertheless, the determination of the wave speed D is related to the constitutive relationship of the materials. In general, the relation between [σ ] and [ε] and the relations between [∂σ /∂X] and [∂ε/∂X] are different, therefore the velocities of a shock wave and an acceleration wave are different.
This study will help us understand the limitations of the primary theory, and make clear under what conditions such approximate theory is applicable. Under a uni-axial stress σX (X, t), the axial strain of the bar is: εX = ∂uX σX (X, t) = ∂X E Besides this component, the bar also has transversal strain due to Poisson effect: ∂uY = −νεX (X, t) ∂Y ∂uZ εZ = = −νεX (X, t) ∂Z εY = In the above equations, uX , uY , and uZ are the displacement components in X, Y , and Z axes, respectively, ν is the Poisson ratio.
37) the compatibility equations on the characteristic lines, either Eq. 24) or Eq. 38 ) Obviously, if the relationship σ = σ (ε) is known, the function C = C(ε) and ϕ = ϕ(ε) are also known functions (Fig. 5). 31), the procedures previously applied for solving the elastic wave problem are still available, namely, the problem is reduced to solve a Cauchy problem in AOX region and a Picard problem in AOt region (Fig. 5). The elastic wave parts in the constant value region AOX and in the simple wave region AOt are exactly identical with that discussed previously (Fig.