混凝土相关外文翻译

混凝土相关外文翻译内容摘要：

（ 3） where ()c and ()t are the weighting functions of pressive and tensile internal variables, respectively. The principles for determining ()c and ()t are as follows: for the loading process with dominant tensile stress states, ()t=1 and ()c=0。 similarly, for the loading process with dominant pressive stress states, ()t=0 and ()c=1。 for other loading conditions, 0 ()t1, 0 ()c1 , and ()t+ ()c =1. Finally, the yield criterion can be expressed as ( , , ) ( , , , , ) 0c t c tf k k f k k k k； (4) According to the theory of the consistent ratedependent model, a consistency condition should be satisfied: f ： 0ctct ctctf f f fd d d d dkk kk             (5) Two thermodynamicsbased plastic constitutive models of concrete that have simple forms and can satisfy the energy laws naturally have been developed by Leng et al. (2020). Results from both models, obtained under static loading, agree with experimental results. The two models have been established, respectively, in HaighWestergaard stress space and principle stress space, the difference being that the Lode angle is neglected in the HaighWestergaard stress space model and considered in the principle stress space model. The two yield criteria can be expressed as 温州大学本科毕业设计 建筑与土木工程学院 3 22221 2 1 2() 1[ ( ) ] [ ( ) ]t c t cpqa p a p p b p b p p     (6) and 222 3122 2 21 2 3()( ) ( ) 1A A A       (7) where p is the volumetric stress。 q is the shear stress。  and  are the shift stresses on the hydrostatic axis and principle stress axis, respectively。 1A , 2A , and 3A are the stress dimensions, where 1 2 1 2 3( ) ( )i i i i t cA a a a p p       i=(1,2,3,)。 cp and tp are the intersection points of the yield surface and hydrostatic axis。 and 1a , 2a , 3a ， 1b and 2b are dimensionless parameters to be determined The plastic flow rules of the two models are, respectively, 220 .5 ( )1tcpvpsp p pd AqdB        (8) and 2 2 2 2 2 21 2 3 2 3 1 1 3 2 1 2 1: : [ ( ) ] : [ ( ) ] : [ ( ) ]pppd d d A A A A A A            (9) where 220 . 5 ( )[ ] ( )2 tcp p p qB   ； 2()ctpp  , the relative level of shift stress。 pvd and psd are the volumetric plastic strain increment and deviatoric plastic strain increment, respectively。 12()tcA a p a p p  。 12()tcB b p b p p  。 and 1pd , 2pd and 3pd are three principle plastic strain increments. According to the results of experiments (Suaris and Shah 1985。 Reinhardt 1984), the relationships between the pressive and tensile strengths of concrete and the internal variable and rate of the internal variable are ( ) ( )c d c c c c cf f H S （ 10） and ( ) ( )td t t t t tf f H S （ 11） where cdf and tdf are dynamic strengths of concrete under uniaxial pression and tension, respectively, and ()ccH ,。