Is a second marriage contract valid if the husband did not disclose that he was still married to his first wife?

Firstly: 

The fuqaha’
(may Allaah have mercy on them) have listed some things which give either
spouse the right to annul the marriage contract. Among these they mention
annulment based on physical defects, in the sense that it is permissible for
either the husband or the wife to request annulment of the marriage contract
if one of them finds physical defects in the other. 

It says in
al-Mawsoo’ah al-Fiqhiyyah (29/68): 

The fuqaha’
of the four madhhabs are agreed that it is permissible to separate the
spouses on the grounds of physical defects. End quote. 

Not every
physical defect that either spouse finds in the other means that it is
permissible to annul the marriage, rather the guideline with regard to these
faults is that it is that which prevents fulfilment of the purpose of
marriage, such as physical pleasure, love, tranquillity, offspring and so
on. 

Ibn Taymiyah
said in al-Ikhtiyaaraat (p. 222): A woman may be rejected because of
any physical defect that prevents full physical pleasure. End quote. 

Ibn
al-Qayyim said: By analogy, every physical defect that puts one spouse off
the other, and prevents fulfilment of the purpose of marriage such as
compassion and love, results in giving the option of annulling the marriage.
End quote. 

Shaykh Ibn
‘Uthaymeen said:  

The correct
view is that there is a guideline on this issue, which is whatever people
regard as a physical defect that prevents full physical pleasure,  this is a
physical defect. Defects with regard to marriage are the same as defects
with regard to financial transactions, because both are shortcomings that
affect the contract. End quote. 

Secondly: 

The fact
that a man is married to another woman is not a defect for which the
marriage contract may be annulled, because the man has the right to marry a
second, third and fourth wife, and she does not have the right to demand
that the marriage be annulled if he is treating them all fairly. 

Shaykh Ibn
Jibreen was asked: Is it essential for a marriage to be valid that the man
should tell the woman whom he wants to marry that he has another wife, if
she does not ask him about that? Are there any consequences if he denies it
when asked? 

He replied: 

The man is
not obliged to tell his wife or her family that he is already married if
they do not ask him, but that is not usually concealed. Marriage cannot be
done except after a period of researching and asking on the part of both
spouses, to ensure that they are suited to one another. But it is not
permissible to conceal anything. If one party lies and on the basis of that
the other party decides to go ahead with the marriage, then the latter is
given the choice. If he says that he is not married and he is lying, then
she is allowed to have the marriage annulled. If they say that she is a
virgin and that is not the case, then he has the choice of going ahead with
the marriage or of leaving her. End quote. 

Fawaa’id
wa Fataawa Tuhimm al-Mar’ah al-Muslimah, 114.